Daily Papers

The majority of quantization methods have been proposed to reduce the model size of Vision Transformers, yet most of them have overlooked the quantization of non-linear operations. Only a few works have addressed quantization for non-linear operations, but they applied a single quantization method across all non-linear operations. We believe that this can be further improved by employing a different quantization method for each non-linear operation. Therefore, to assign the most error-minimizing quantization method from the known methods to each non-linear layer, we propose a mixed non-linear quantization that considers layer-wise quantization sensitivity measured by SQNR difference metric. The results show that our method outperforms I-BERT, FQ-ViT, and I-ViT in both 8-bit and 6-bit settings for ViT, DeiT, and Swin models by an average of 0.6%p and 19.6%p, respectively. Our method outperforms I-BERT and I-ViT by 0.6%p and 20.8%p, respectively, when training time is limited. We plan to release our code at https://gitlab.com/ones-ai/mixed-non-linear-quantization.

The Muon optimizer, based on matrix orthogonalization, has recently shown faster convergence and up to 2x computational efficiency over AdamW in LLM pretraining. Like AdamW, Muon is stateful, requiring storage of both model weights and accumulated gradients. While 8-bit AdamW variants mitigate this overhead using blockwise quantization, they are typically stable only under dynamic quantization - which improves stability on linear quantization for extreme values. In this paper, we introduce the 8-bit Muon optimizer using blockwise quantization, supporting both linear and dynamic schemes. We demonstrate that 8-bit Muon maintains stability under both, while delivering sim74\% reduction in memory footprint compared to full-precision Muon. In extensive experiments, 8-bit Muon closely matches the performance of Muon while outperforming AdamW and 8-bit AdamW in pre-training a 1.6B model on 4B FineWeb tokens. It also shows competitive results when fine-tuning the Llama 3.2 3B model on post-training data. We also provide a theoretical perspective to help explain this robustness under quantization.

Weight quantization effectively reduces memory consumption and enables the deployment of large language models on CPU-based edge devices, yet existing hardware-friendly methods often rely on uniform quantization, which suffers from poor weight-distribution fitting and high dequantization overhead under low-bit settings. In this paper, we propose ELUTQ, an efficient quantization framework featuring a novel quantization format termed Hierarchical Linear Quantization (HLQ). HLQ is designed to better capture the statistical characteristics of weights without increasing the computational cost of bit-serial LUT-based GEMM operations, thereby eliminating dequantization overhead. HLQ is orthogonal to existing quantization algorithms. For the LLaMA3.1-8B model, when combined with post-training quantization, HLQ improves uniform quantization by achieving approximately 8 percent perplexity reduction at 3-bit precision and 85 percent perplexity reduction at 2-bit precision. When combined with efficient finetuning techniques, HLQ further improves model accuracy. We also integrate a disk-offload technique into ELUTQ, enabling it to complete the quantization of LLaMA3.1-70B using only 64 GB of CPU memory and 48 GB of VRAM, significantly reducing the hardware requirements for large-scale model quantization. To enable efficient deployment on edge devices, ELUTQ provides high-performance CPU kernels to support end-to-end inference. Under a 4-thread configuration with batch size 1, our 2-bit quantized LLaMA2-7B model achieves a throughput of more than 25 tokens per second on an Apple M2 chip. All the code is available at https://github.com/Nkniexin/ELUTQ.

This study presents an ensemble technique, SPQ (SVD-Pruning-Quantization), for large language model (LLM) compression that combines variance-retained singular value decomposition (SVD), activation-based pruning, and post-training linear quantization. Each component targets a different source of inefficiency: i) pruning removes redundant neurons in MLP layers, ii) SVD reduces attention projections into compact low-rank factors, iii) and 8-bit quantization uniformly compresses all linear layers. At matched compression ratios, SPQ outperforms individual methods (SVD-only, pruning-only, or quantization-only) in perplexity, demonstrating the benefit of combining complementary techniques. Applied to LLaMA-2-7B, SPQ achieves up to 75% memory reduction while maintaining or improving perplexity (e.g., WikiText-2 5.47 to 4.91) and preserving accuracy on downstream benchmarks such as C4, TruthfulQA, and GSM8K. Compared to strong baselines like GPTQ and SparseGPT, SPQ offers competitive perplexity and accuracy while using less memory (6.86 GB vs. 7.16 GB for GPTQ). Moreover, SPQ improves inference throughput over GPTQ, achieving up to a 1.9x speedup, which further enhances its practicality for real-world deployment. The effectiveness of SPQ's robust compression through layer-aware and complementary compression techniques may provide practical deployment of LLMs in memory-constrained environments. Code is available at: https://github.com/JiaminYao/SPQ_LLM_Compression/

Since Large Language Models or LLMs have demonstrated high-quality performance on many complex language tasks, there is a great interest in bringing these LLMs to mobile devices for faster responses and better privacy protection. However, the size of LLMs (i.e., billions of parameters) requires highly effective compression to fit into storage-limited devices. Among many compression techniques, weight-clustering, a form of non-linear quantization, is one of the leading candidates for LLM compression, and supported by modern smartphones. Yet, its training overhead is prohibitively significant for LLM fine-tuning. Especially, Differentiable KMeans Clustering, or DKM, has shown the state-of-the-art trade-off between compression ratio and accuracy regression, but its large memory complexity makes it nearly impossible to apply to train-time LLM compression. In this paper, we propose a memory-efficient DKM implementation, eDKM powered by novel techniques to reduce the memory footprint of DKM by orders of magnitudes. For a given tensor to be saved on CPU for the backward pass of DKM, we compressed the tensor by applying uniquification and sharding after checking if there is no duplicated tensor previously copied to CPU. Our experimental results demonstrate that \prjname can fine-tune and compress a pretrained LLaMA 7B model from 12.6 GB to 2.5 GB (3bit/weight) with the Alpaca dataset by reducing the train-time memory footprint of a decoder layer by 130times, while delivering good accuracy on broader LLM benchmarks (i.e., 77.7% for PIQA, 66.1% for Winograde, and so on).

Second-order optimizers, maintaining a matrix termed a preconditioner, are superior to first-order optimizers in both theory and practice. The states forming the preconditioner and its inverse root restrict the maximum size of models trained by second-order optimizers. To address this, compressing 32-bit optimizer states to lower bitwidths has shown promise in reducing memory usage. However, current approaches only pertain to first-order optimizers. In this paper, we propose the first 4-bit second-order optimizers, exemplified by 4-bit Shampoo, maintaining performance similar to that of 32-bit ones. We show that quantizing the eigenvector matrix of the preconditioner in 4-bit Shampoo is remarkably better than quantizing the preconditioner itself both theoretically and experimentally. By rectifying the orthogonality of the quantized eigenvector matrix, we enhance the approximation of the preconditioner's eigenvector matrix, which also benefits the computation of its inverse 4-th root. Besides, we find that linear square quantization slightly outperforms dynamic tree quantization when quantizing second-order optimizer states. Evaluation on various networks for image classification demonstrates that our 4-bit Shampoo achieves comparable test accuracy to its 32-bit counterpart while being more memory-efficient. The source code will be made available.

Quantization-aware training (QAT) is essential for extremely low-bit large language models (LLMs). Current QAT methods are mainly based on scalar quantization (SQ), which enables efficient optimization but suffers from severe performance degradation at 2-bit precision. On the other hand, vector quantization (VQ) provides substantially higher representational capacity, but its discrete codebook lookup prevents end-to-end training. We propose LC-QAT, a 2-bit weight-only VQ-QAT framework that represents quantized weights via a learned affine mapping over discrete vectors, which yields a high-quality PTQ initialization and enables fully differentiable end-to-end optimization without explicit codebook lookup in the training forward pass. This strong post-training initialization makes LC-QAT highly data-efficient. Experiments across diverse LLMs demonstrate that LC-QAT consistently outperforms state-of-the-art QAT methods while using only 0.1%--10% of the training data. Our results establish LC-QAT as a practical and scalable solution for extreme low-bit model deployment. Codes are publicly available at https://github.com/AI9Stars/UniSVQ.

Post-Training Quantization (PTQ) is an effective technique for compressing Large Language Models (LLMs). While many studies focus on quantizing both weights and activations, it is still a challenge to maintain the accuracy of LLM after activating quantization. To investigate the primary cause, we extend the concept of kernel from linear algebra to quantization functions to define a new term, "quantization kernel", which refers to the set of elements in activations that are quantized to zero. Through quantitative analysis of the quantization kernel, we find that these elements are crucial for maintaining the accuracy of quantized LLMs. With the decrease of quantization kernel, the precision of quantized LLMs increases. If the quantization kernel proportion is kept below 19% for OPT models and below 1% for LLaMA models, the precision loss from quantizing activations to INT8 becomes negligible. Motivated by the goal of developing a quantization method with small quantization kernel, we propose CrossQuant: a simple yet effective method for quantizing activations. CrossQuant cross-quantizes elements using row and column-wise absolute maximum vectors, achieving a quantization kernel of approximately 16% for OPT models and less than 0.1% for LLaMA models. Experimental results on LLMs (LLaMA, OPT) ranging from 6.7B to 70B parameters demonstrate that CrossQuant improves or maintains perplexity and accuracy in language modeling, zero-shot, and few-shot tasks.

Deploying large language models (LLMs) is challenging due to their significant memory and computational requirements. While some methods address this by developing small or tiny language models from scratch, these approaches demand extensive GPU training. Compressing pre-trained LLMs for edge devices offers a compelling alternative. Beyond pruning and quantization, Neural Architecture Search (NAS) enables effective compression, yet prior NAS approaches often limit the search space and decouple architecture from quantization. We introduce a differentiable NAS framework that explores the entire space and jointly optimizes architectural configurations alongside mixed-precision quantization for linear layers of LLMs. Experiments demonstrate superior accuracy-latency trade-offs: our models achieve up to 1.4x faster inference than sequential NAS-then-quantization baselines at comparable accuracy, or up to 6% higher average accuracy across seven reasoning tasks at equivalent latency.

Although quantization for linear layers has been widely used, its application to accelerate the attention process remains limited. SageAttention utilizes 8-bit matrix multiplication, 16-bit matrix multiplication with 16-bit accumulator, and precision-enhancing methods, implementing an accurate and 2x speedup kernel compared to FlashAttention2. To further enhance the efficiency of attention computation while maintaining precision, we propose SageAttention2, which utilizes significantly faster 4-bit matrix multiplication (Matmul) alongside additional precision-enhancing techniques. First, we propose to quantize matrixes (Q, K) to INT4 in a warp-level granularity and quantize matrixes (widetilde P, V) to FP8. Second, we propose a method to smooth Q and V, enhancing the accuracy of attention with INT4 QK and FP8 PV. Third, we analyze the quantization accuracy across timesteps and layers, then propose an adaptive quantization method to ensure the end-to-end metrics over various models. The operations per second (OPS) of SageAttention2 surpass FlashAttention2 and xformers by about 3x and 5x on RTX4090, respectively. Comprehensive experiments confirm that our approach incurs negligible end-to-end metrics loss across diverse models, including those for large language processing, image generation, and video generation. The codes are available at https://github.com/thu-ml/SageAttention.

The computational cost of transformer models makes them inefficient in low-latency or low-power applications. While techniques such as quantization or linear attention can reduce the computational load, they may incur a reduction in accuracy. In addition, globally reducing the cost for all inputs may be sub-optimal. We observe that for each layer, the full width of the layer may be needed only for a small subset of tokens inside a batch and that the "effective" width needed to process a token can vary from layer to layer. Motivated by this observation, we introduce the Adaptive Computation Module (ACM), a generic module that dynamically adapts its computational load to match the estimated difficulty of the input on a per-token basis. An ACM consists of a sequence of learners that progressively refine the output of their preceding counterparts. An additional gating mechanism determines the optimal number of learners to execute for each token. We also describe a distillation technique to replace any pre-trained model with an "ACMized" variant. The distillation phase is designed to be highly parallelizable across layers while being simple to plug-and-play into existing networks. Our evaluation of transformer models in computer vision and speech recognition demonstrates that substituting layers with ACMs significantly reduces inference costs without degrading the downstream accuracy for a wide interval of user-defined budgets.

Large language models (LLMs) have shown remarkable capabilities in various tasks. However their huge model size and the consequent demand for computational and memory resources also pose challenges to model deployment. Currently, 4-bit post-training quantization (PTQ) has achieved some success in LLMs, reducing the memory footprint by approximately 75% compared to FP16 models, albeit with some accuracy loss. In this paper, we propose SmoothQuant+, an accurate and efficient 4-bit weight-only PTQ that requires no additional training, which enables lossless in accuracy for LLMs for the first time. Based on the fact that the loss of weight quantization is amplified by the activation outliers, SmoothQuant+ smoothes the activation outliers by channel before quantization, while adjusting the corresponding weights for mathematical equivalence, and then performs group-wise 4-bit weight quantization for linear layers. We have integrated SmoothQuant+ into the vLLM framework, an advanced high-throughput inference engine specially developed for LLMs, and equipped it with an efficient W4A16 CUDA kernels, so that vLLM can seamlessly support SmoothQuant+ 4-bit weight quantization. Our results show that, with SmoothQuant+, the Code Llama-34B model can be quantized and deployed on a A100 40GB GPU, achieving lossless accuracy and a throughput increase of 1.9 to 4.0 times compared to the FP16 model deployed on two A100 40GB GPUs. Moreover, the latency per token is only 68% of the FP16 model deployed on two A100 40GB GPUs. This is the state-of-the-art 4-bit weight quantization for LLMs as we know.

We introduce Transformer-VQ, a decoder-only transformer computing softmax-based dense self-attention in linear time. Transformer-VQ's efficient attention is enabled by vector-quantized keys and a novel caching mechanism. In large-scale experiments, Transformer-VQ is shown highly competitive in quality, with strong results on Enwik8 (0.99 bpb), PG-19 (26.6 ppl), and ImageNet64 (3.16 bpb). Code: https://github.com/transformer-vq/transformer_vq

Quantization emerges as one of the most promising compression technologies for deploying efficient large models for various real time application in recent years. Considering that the storage and IO of weights take up the vast majority of the overhead inside a large model, weight only quantization can lead to large gains. However, existing quantization schemes suffer from significant accuracy degradation at very low bits, or require some additional computational overhead when deployed, making it difficult to be applied to large-scale applications in industry. In this paper, we propose decoupleQ, achieving a substantial increase in model accuracy, especially at very low bits. decoupleQ abandons the traditional heuristic quantization paradigm and decouples the model parameters into integer and floating-point parts, thus transforming the quantization problem into a traditional mathematical optimization problem with constraints, which is then solved alternatively by off-the-shelf optimization methods. Quantization via decoupleQ is linear and uniform, making it hardware-friendlier than non-uniform counterpart, and enabling the idea to be migrated to high-bit quantization to enhance its robustness. Our method has achieved well on-line accuracy near fp16/bf16 on the 2-bit quantization of large speech models in ByteDance. The code is available at https://github.com/bytedance/decoupleQ

Low-bit quantization of network weights and activations can drastically reduce the memory footprint, complexity, energy consumption and latency of Deep Neural Networks (DNNs). However, low-bit quantization can also cause a considerable drop in accuracy, in particular when we apply it to complex learning tasks or lightweight DNN architectures. In this paper, we propose a training procedure that relaxes the low-bit quantization. We call this procedure DNN Quantization with Attention (DQA). The relaxation is achieved by using a learnable linear combination of high, medium and low-bit quantizations. Our learning procedure converges step by step to a low-bit quantization using an attention mechanism with temperature scheduling. In experiments, our approach outperforms other low-bit quantization techniques on various object recognition benchmarks such as CIFAR10, CIFAR100 and ImageNet ILSVRC 2012, achieves almost the same accuracy as a full precision DNN, and considerably reduces the accuracy drop when quantizing lightweight DNN architectures.

With the rising popularity of Large Language Models (LLMs), there has been an increasing interest in compression techniques that enable their efficient deployment. This study focuses on the Post-Training Quantization (PTQ) of LLMs. Drawing from recent advances, our work introduces QuantEase, a layer-wise quantization framework where individual layers undergo separate quantization. The problem is framed as a discrete-structured non-convex optimization, prompting the development of algorithms rooted in Coordinate Descent (CD) techniques. These CD-based methods provide high-quality solutions to the complex non-convex layer-wise quantization problems. Notably, our CD-based approach features straightforward updates, relying solely on matrix and vector operations, circumventing the need for matrix inversion or decomposition. We also explore an outlier-aware variant of our approach, allowing for retaining significant weights (outliers) with complete precision. Our proposal attains state-of-the-art performance in terms of perplexity and zero-shot accuracy in empirical evaluations across various LLMs and datasets, with relative improvements up to 15% over methods such as GPTQ. Leveraging careful linear algebra optimizations, QuantEase can quantize models like Falcon-180B on a single NVIDIA A100 GPU in sim3 hours. Particularly noteworthy is our outlier-aware algorithm's capability to achieve near or sub-3-bit quantization of LLMs with an acceptable drop in accuracy, obviating the need for non-uniform quantization or grouping techniques, improving upon methods such as SpQR by up to two times in terms of perplexity.

Vector Quantization (VQ) is a widely used method for converting continuous representations into discrete codes, which has become fundamental in unsupervised representation learning and latent generative models. However, VQ models are often hindered by the problem of representation collapse in the latent space, which leads to low codebook utilization and limits the scalability of the codebook for large-scale training. Existing methods designed to mitigate representation collapse typically reduce the dimensionality of latent space at the expense of model capacity, which do not fully resolve the core issue. In this study, we conduct a theoretical analysis of representation collapse in VQ models and identify its primary cause as the disjoint optimization of the codebook, where only a small subset of code vectors are updated through gradient descent. To address this issue, we propose SimVQ, a novel method which reparameterizes the code vectors through a linear transformation layer based on a learnable latent basis. This transformation optimizes the entire linear space spanned by the codebook, rather than merely updating the code vector selected by the nearest-neighbor search in vanilla VQ models. Although it is commonly understood that the multiplication of two linear matrices is equivalent to applying a single linear layer, our approach works surprisingly well in resolving the collapse issue in VQ models with just one linear layer. We validate the efficacy of SimVQ through extensive experiments across various modalities, including image and audio data with different model architectures. Our code is available at https://github.com/youngsheen/SimVQ.

As large language models become increasingly prevalent, memory bandwidth constraints significantly limit inference throughput, motivating post-training quantization (PTQ). In this paper, we propose FireQ, a co-designed PTQ framework and an INT4-FP8 matrix multiplication kernel that accelerates LLM inference across all linear layers. Specifically, FireQ quantizes linear layer weights and key-values to INT4, and activations and queries to FP8, significantly enhancing throughput. Additionally, we introduce a three-stage pipelining for the prefill phase, which modifies the FlashAttention-3 kernel, effectively reducing time-to-first-token in the prefill phase. To minimize accuracy loss from quantization, we develop novel outlier smoothing techniques tailored separately for linear and attention layers. In linear layers, we explicitly use per-tensor scaling to prevent underflow caused by the FP8 quantization scaling factor of INT4 quantization, and channel-wise scaling to compensate for coarse granularity of INT4. In attention layers, we address quantization challenges posed by rotary positional embeddings (RoPE) by combining pre-RoPE and post-RoPE scaling strategies. FireQ significantly outperforms state-of-the-art methods, achieving 1.68x faster inference in feed-forward network layers on Llama2-7B and 1.26x faster prefill phase performance on Llama3-8B compared to QServe, with negligible accuracy loss.

Quantization to low bitwidth is a standard approach for deploying large language models, however, a few extreme weights and activations stretch the dynamic range and reduce the effective resolution of the quantizer. A common mitigation approach is to apply some fixed orthogonal transforms, such as Hadamard matrices, before quantization, which typically reduces the dynamic range. Yet, these transforms ignore the statistics of the data, and their optimality is currently not understood. In this work, we derive, for the first time, closed-form optimal linear blockwise transforms for joint weight-activation quantization using standard data-free quantizers for common numerical formats. Specifically, we provide derivations of the optimal adaptive (data-aware) transforms for round-to-nearest (RTN), AbsMax-scaled block quantizers for both integer and floating-point formats. The resulting construction, which we call WUSH, combines a Hadamard backbone with a data-dependent component based on second-order moments, yielding a non-orthogonal transform that is provably optimal under mild assumptions and remains structured for efficient implementation. Preliminary experimental results show that our approach consistently improves upon the Hadamard transform for common formats.

Linear attention replaces growing KV caches with fixed-size recurrent states, yet these persistent states can become a substantial memory bottleneck under concurrent serving. Directly quantizing recurrent states to low precision often leads to severe accuracy degradation, as quantization errors propagate through successive state updates. We discover that the impact of these errors depends on two complementary dimensions: temporally, errors in long-lived memory can persist across many decoding steps; spatially, errors in different key rows affect model outputs differently, while state magnitudes vary substantially along both rows and columns. Motivated by these observations, we propose STEPQuant, a spatial-temporal post-training quantization framework for Delta-rule recurrent states. STEPQuant allocates precision according to error magnitude and memory lifetime, and jointly fits key-row and value-column scales based on state distributions and key-row impact on output error. Experiments on Qwen3.8-27B and Kimi-Linear-48B-A3B-Instruct across both long- and short-generation benchmarks show that STEPQuant closely matches FP32-state accuracy under a nominal 6-bit budget and outperforms uniform INT8 in its 4-bit configuration. Integrated into SGLang with optimized GPU kernels, 6-bit STEPQuant achieves over 5x recurrent-state compression and reduces total serving memory by up to 68.7%. Our code is available at https://github.com/Dreamer-Toby/STEPQuant.

Vision Transformers (ViTs) have become one of the most commonly used backbones for vision tasks. Despite their remarkable performance, they often suffer significant accuracy drops when quantized for practical deployment, particularly by post-training quantization (PTQ) under ultra-low bits. Recently, reconstruction-based PTQ methods have shown promising performance in quantizing Convolutional Neural Networks (CNNs). However, they fail when applied to ViTs, primarily due to the inaccurate estimation of output importance and the substantial accuracy degradation in quantizing post-GELU activations. To address these issues, we propose APHQ-ViT, a novel PTQ approach based on importance estimation with Average Perturbation Hessian (APH). Specifically, we first thoroughly analyze the current approximation approaches with Hessian loss, and propose an improved average perturbation Hessian loss. To deal with the quantization of the post-GELU activations, we design an MLP Reconstruction (MR) method by replacing the GELU function in MLP with ReLU and reconstructing it by the APH loss on a small unlabeled calibration set. Extensive experiments demonstrate that APHQ-ViT using linear quantizers outperforms existing PTQ methods by substantial margins in 3-bit and 4-bit across different vision tasks. The source code is available at https://github.com/GoatWu/APHQ-ViT.

Diffusion transformers have demonstrated remarkable capabilities in generating videos. However, their practical deployment is severely constrained by high memory usage and computational cost. Post-Training Quantization provides a practical way to reduce memory usage and boost computation speed. Existing quantization methods typically apply a static bit-width allocation, overlooking the quantization difficulty of activations across diffusion timesteps, leading to a suboptimal trade-off between efficiency and quality. In this paper, we propose a inference time NVFP4/INT8 Mixed-Precision Quantization framework. We find a strong linear correlation between a block's input-output difference and the quantization sensitivity of its internal linear layers. Based on this insight, we design a lightweight predictor that dynamically allocates NVFP4 to temporally stable layers to maximize memory compression, while selectively preserving INT8 for volatile layers to ensure robustness. This adaptive precision strategy enables aggressive quantization without compromising generation quality. Beside this, we observe that the residual between the input and output of a Transformer block exhibits high temporal consistency across timesteps. Leveraging this temporal redundancy, we introduce Temporal Delta Cache (TDC) to skip computations for these invariant blocks, further reducing the computational cost. Extensive experiments demonstrate that our method achieves 1.92times end-to-end acceleration and 3.32times memory reduction, setting a new baseline for efficient inference in Video DiTs.

In this paper, we present a simple optimization-based preprocessing technique called Weight Magnitude Reduction (MagR) to improve the performance of post-training quantization. For each linear layer, we adjust the pre-trained floating-point weights by solving an ell_infty-regularized optimization problem. This process greatly diminishes the maximum magnitude of the weights and smooths out outliers, while preserving the layer's output. The preprocessed weights are centered more towards zero, which facilitates the subsequent quantization process. To implement MagR, we address the ell_infty-regularization by employing an efficient proximal gradient descent algorithm. Unlike existing preprocessing methods that involve linear transformations and subsequent post-processing steps, which can introduce significant overhead at inference time, MagR functions as a non-linear transformation, eliminating the need for any additional post-processing. This ensures that MagR introduces no overhead whatsoever during inference. Our experiments demonstrate that MagR achieves state-of-the-art performance on the Llama family of models. For example, we achieve a Wikitext2 perplexity of 5.95 on the LLaMA2-70B model for per-channel INT2 weight quantization without incurring any inference overhead.

Post-training quantization is widely used to deploy large language models in resource-constrained settings, yet its evaluation relies almost exclusively on accuracy and perplexity. We show that these metrics fail to capture behavioral changes induced by quantization. We introduce correctness agreement, a decision-level metric that measures overlap in correct predictions between a base model and its quantized variants, independent of absolute accuracy. Across multiple models and quantization schemes from 8-bit to 2-bit, we find that behavioral divergence emerges under moderate quantization even when task performance appears preserved. To explain this effect, we analyze quantization as a structural operator on attention weights and quantify layer-wise distortions using statistical and distributional measures. Our results reveal non-linear breakpoints at low bit-widths and show that query and key projections are consistently more sensitive than value and output projections. These findings expose an illusion of equivalence between base and quantized models and motivate behavioral evaluation beyond conventional performance metrics.

Vision Transformers (ViTs) have achieved state-of-the-art performance on various computer vision applications. However, these models have considerable storage and computational overheads, making their deployment and efficient inference on edge devices challenging. Quantization is a promising approach to reducing model complexity, and the dyadic arithmetic pipeline can allow the quantized models to perform efficient integer-only inference. Unfortunately, dyadic arithmetic is based on the homogeneity condition in convolutional neural networks, which is not applicable to the non-linear components in ViTs, making integer-only inference of ViTs an open issue. In this paper, we propose I-ViT, an integer-only quantization scheme for ViTs, to enable ViTs to perform the entire computational graph of inference with integer arithmetic and bit-shifting, and without any floating-point arithmetic. In I-ViT, linear operations (e.g., MatMul and Dense) follow the integer-only pipeline with dyadic arithmetic, and non-linear operations (e.g., Softmax, GELU, and LayerNorm) are approximated by the proposed light-weight integer-only arithmetic methods. More specifically, I-ViT applies the proposed Shiftmax and ShiftGELU, which are designed to use integer bit-shifting to approximate the corresponding floating-point operations. We evaluate I-ViT on various benchmark models and the results show that integer-only INT8 quantization achieves comparable (or even slightly higher) accuracy to the full-precision (FP) baseline. Furthermore, we utilize TVM for practical hardware deployment on the GPU's integer arithmetic units, achieving 3.72sim4.11times inference speedup compared to the FP model. Code of both Pytorch and TVM is released at https://github.com/zkkli/I-ViT.

Recently, quantization has been widely used for the compression and acceleration of large language models~(LLMs). Due to the outliers in LLMs, it is crucial to flatten weights and activations to minimize quantization error with the equally spaced quantization points. Prior research explores various pre-quantization transformations to suppress outliers, such as per-channel scaling and Hadamard transformation. However, we observe that these transformed weights and activations can still remain steep and outspread. In this paper, we propose FlatQuant (Fast and Learnable Affine Transformation), a new post-training quantization approach to enhance flatness of weights and activations. Our approach identifies optimal affine transformations tailored to each linear layer, calibrated in hours via a lightweight objective. To reduce runtime overhead, we apply Kronecker decomposition to the transformation matrices, and fuse all operations in FlatQuant into a single kernel. Extensive experiments show that FlatQuant sets up a new state-of-the-art quantization benchmark. For instance, it achieves less than 1% accuracy drop for W4A4 quantization on the LLaMA-3-70B model, surpassing SpinQuant by 7.5%. For inference latency, FlatQuant reduces the slowdown induced by pre-quantization transformation from 0.26x of QuaRot to merely 0.07x, bringing up to 2.3x speedup for prefill and 1.7x speedup for decoding, respectively. Code is available at: https://github.com/ruikangliu/FlatQuant.

Diffusion Transformers (DiTs) have achieved impressive performance in text-to-image and text-to-video generation. However, their high computational cost and large parameter sizes pose significant challenges for usage in resource-constrained scenarios. Effective compression of models has become a crucial issue that urgently needs to be addressed. Post-training quantization (PTQ) is a promising solution to reduce memory usage and accelerate inference, but existing PTQ methods suffer from severe performance degradation under extreme low-bit settings. After experiments and analysis, we identify two key obstacles to low-bit PTQ for DiTs: (1) the weights of DiT models follow a Gaussian-like distribution with long tails, causing uniform quantization to poorly allocate intervals and leading to significant quantization errors. This issue has been observed in the linear layer weights of different DiT models, which deeply limits the performance. (2) two types of activation outliers in DiT models: (i) Mild Outliers with slightly elevated values, and (ii) Salient Outliers with large magnitudes concentrated in specific channels, which disrupt activation quantization. To address these issues, we propose LRQ-DiT, an efficient and accurate post-training quantization framework for image and video generation. First, we introduce Twin-Log Quantization (TLQ), a log-based method that allocates more quantization intervals to the intermediate dense regions, effectively achieving alignment with the weight distribution and reducing quantization errors. Second, we propose an Adaptive Rotation Scheme (ARS) that dynamically applies Hadamard or outlier-aware rotations based on activation fluctuation, effectively mitigating the impact of both types of outliers. Extensive experiments on various text-to-image and text-to-video DiT models demonstrate that LRQ-DiT preserves high generation quality.

Mixture-of-Experts (MoE) models face deployment challenges due to their large parameter counts and computational demands. We explore quantization for MoE models and highlight two key insights: 1) linear blocks exhibit varying quantization sensitivity, and 2) divergent expert activation frequencies create heterogeneous computational characteristics. Based on these observations, we introduce MxMoE, a mixed-precision optimization framework for MoE models that considers both algorithmic and system perspectives. MxMoE navigates the design space defined by parameter sensitivity, expert activation dynamics, and hardware resources to derive efficient mixed-precision configurations. Additionally, MxMoE automatically generates optimized mixed-precision GroupGEMM kernels, enabling parallel execution of GEMMs with different precisions. Evaluations show that MxMoE outperforms existing methods, achieving 2.4 lower Wikitext-2 perplexity than GPTQ at 2.25-bit and delivering up to 3.4x speedup over full precision, as well as up to 29.4% speedup over uniform quantization at equivalent accuracy with 5-bit weight-activation quantization. Our code is available at https://github.com/cat538/MxMoE.

Mixture-of-Experts (MoE) large language models incur substantial memory costs due to their large expert parameter counts. Mixed-precision quantization reduces these costs by allocating different bit-widths to experts or linear blocks according to their importance. However, assigning a single precision within each expert or linear block overlooks its internal structural heterogeneity. This limitation motivates two key questions: (1) how to define a fine-grained unit for quantization within a linear transformation; and (2) how to characterize the quantization cost of each unit under actual activation patterns and different bit-widths. To address these two questions, we propose BitsMoE, a cost-aware mixed-precision quantization framework built on two complementary techniques: (1) Shared-basis Spectral Decomposition (SSD) separates expert weights into a shared basis and expert-specific spectral components, defining structural quantization units while exploiting cross-expert redundancy. (2) Factorized Quantization Cost Modeling (FQCM) estimates component-wise costs from output reconstruction loss by combining intrinsic spectral importance, activation-dependent importance, and bit-width-dependent distortion. Using these component-wise costs, we formulate bit allocation as an integer linear program (ILP) that minimizes total modeled quantization cost under a fixed memory budget. On Qwen3-30B-A3B at 2-bit, BitsMoE achieves 64.29% average accuracy over seven downstream tasks, outperforming the evaluated MoE-specific methods, including those using ILP-based bit allocation, and exceeding GEMQ by 2.80 percentage points. Under the same setting, it achieves a 16.47times end-to-end offline quantization speedup over GEMQ. It also achieves up to 6.46times the decode throughput of GPTQ.

Mixture-of-Experts Multimodal Large Language Models (MoE-MLLMs) offer remarkable performance but incur prohibitive GPU memory costs, making compression essential. Among PTQ methods, expert-level mixed-precision quantization has proven effective for MoE-LLMs, yet suffers notable degradation on MoE-MLLMs due to two overlooked biases in expert importance estimation. (1) At the cross-modal level, the numerical dominance of vision tokens causes expert selection frequency to be dominated by vision tokens, masking experts that are critical to the text modality; (2) at the intra-vision level, the large proportion of redundant vision tokens further skew frequency statistics, obscuring experts critical for informative visual content. To bridge gaps, we propose MODE, a modality-decomposed expert-level mixed-precision quantization framework for MoE-MLLMs that decomposes expert selection frequency by modality, filters redundant vision tokens to obtain denoised visual frequency, and further evaluates quantization sensitivity per modality as a complementary signal to frequency-based estimation. These signals are integrated into an Integer Linear Programming formulation to assign per-expert bit-widths under a given budget. Extensive experiments show that MODE is particularly well-suited for MoE-MLLMs, limiting average performance loss to within 2.9% at W3A16, with larger gains at the extreme 2-bit setting.

Hybrid LLMs pair softmax attention with linear-attention layers such as Gated DeltaNet (GDN), whose recurrent state summarizes the context in fixed size. Early community 4-bit quantizations of Qwen3.8-27B (48 GDN layers, 16 attention layers) left the GDN block in 8- or 16-bit precision -- especially its decay and write-strength gates -- on the intuition that errors in a recurrence accumulate over long contexts. We test that intuition by building Minima: NVFP4 W4A4 on all 496 linear layers, GDN included. Across perplexity at 4K/32K, MMLU-Pro, GSM8K, AIME'25, GPQA-Diamond, LiveCodeBench, and RULER retrieval to 64K, Minima matches BF16 within seed noise (5-task average -0.52) while being the smallest (17.5 GiB) and fastest-prefill (+14-19%) recipe we compare, and its 32K perplexity gap shrinks with position. A four-part mechanism study explains why: (i) NVFP4's 16-element block scaling localizes the residual stream's extreme outliers, equalizing activation error across layer roles; (ii) the supposedly fragile gate projections are the least sensitive -- softplus/exponential and sigmoid parameterizations compress ~11% GEMM error to ~2% output error; (iii) the delta-rule recurrence holds injected noise at a flat plateau over 32K tokens and forgets a state impulse within hundreds of steps, because each write overwrites the state along the current key direction; (iv) the per-token quantization cost washes out with context instead of compounding. We also repair a global-scale mismatch that arises when per-module-calibrated NVFP4 checkpoints are served by kernels that fuse those modules into one GEMM, and show calibrated FP8 KV-cache scales are performance-free. The result: a practical recipe -- quantize everything, ship KV scales -- and a mechanistic account of why the recurrent half of a hybrid LLM is the easy half to quantize. Checkpoint: https://huggingface.co/minima-ai/mnma_qwen3.8_27b_nvfp4

The complicated architecture and high training cost of vision transformers urge the exploration of post-training quantization. However, the heavy-tailed distribution of vision transformer activations hinders the effectiveness of previous post-training quantization methods, even with advanced quantizer designs. Instead of tuning the quantizer to better fit the complicated activation distribution, this paper proposes NoisyQuant, a quantizer-agnostic enhancement for the post-training activation quantization performance of vision transformers. We make a surprising theoretical discovery that for a given quantizer, adding a fixed Uniform noisy bias to the values being quantized can significantly reduce the quantization error under provable conditions. Building on the theoretical insight, NoisyQuant achieves the first success on actively altering the heavy-tailed activation distribution with additive noisy bias to fit a given quantizer. Extensive experiments show NoisyQuant largely improves the post-training quantization performance of vision transformer with minimal computation overhead. For instance, on linear uniform 6-bit activation quantization, NoisyQuant improves SOTA top-1 accuracy on ImageNet by up to 1.7%, 1.1% and 0.5% for ViT, DeiT, and Swin Transformer respectively, achieving on-par or even higher performance than previous nonlinear, mixed-precision quantization.

Current low-precision quantization algorithms often have the hidden cost of conversion back and forth from floating point to quantized integer values. This hidden cost limits the latency improvement realized by quantizing Neural Networks. To address this, we present HAWQV3, a novel mixed-precision integer-only quantization framework. The contributions of HAWQV3 are the following: (i) An integer-only inference where the entire computational graph is performed only with integer multiplication, addition, and bit shifting, without any floating point operations or even integer division; (ii) A novel hardware-aware mixed-precision quantization method where the bit-precision is calculated by solving an integer linear programming problem that balances the trade-off between model perturbation and other constraints, e.g., memory footprint and latency; (iii) Direct hardware deployment and open source contribution for 4-bit uniform/mixed-precision quantization in TVM, achieving an average speed up of 1.45times for uniform 4-bit, as compared to uniform 8-bit for ResNet50 on T4 GPUs; and (iv) extensive evaluation of the proposed methods on ResNet18/50 and InceptionV3, for various model compression levels with/without mixed precision. For ResNet50, our INT8 quantization achieves an accuracy of 77.58%, which is 2.68% higher than prior integer-only work, and our mixed-precision INT4/8 quantization can reduce INT8 latency by 23% and still achieve 76.73% accuracy. Our framework and the TVM implementation have been open sourced.

Vector Quantized Variational AutoEncoders (VQ-VAEs) are designed to compress a continuous input to a discrete latent space and reconstruct it with minimal distortion. They operate by maintaining a set of vectors -- often referred to as the codebook -- and quantizing each encoder output to the nearest vector in the codebook. However, as vector quantization is non-differentiable, the gradient to the encoder flows around the vector quantization layer rather than through it in a straight-through approximation. This approximation may be undesirable as all information from the vector quantization operation is lost. In this work, we propose a way to propagate gradients through the vector quantization layer of VQ-VAEs. We smoothly transform each encoder output into its corresponding codebook vector via a rotation and rescaling linear transformation that is treated as a constant during backpropagation. As a result, the relative magnitude and angle between encoder output and codebook vector becomes encoded into the gradient as it propagates through the vector quantization layer and back to the encoder. Across 11 different VQ-VAE training paradigms, we find this restructuring improves reconstruction metrics, codebook utilization, and quantization error. Our code is available at https://github.com/cfifty/rotation_trick.

Recent years have witnessed the success of foundation models pre-trained with self-supervised learning (SSL) in various music informatics understanding tasks, including music tagging, instrument classification, key detection, and more. In this paper, we propose a self-supervised music representation learning model for music understanding. Distinguished from previous studies adopting random projection or existing neural codec, the proposed model, named MuQ, is trained to predict tokens generated by Mel Residual Vector Quantization (Mel-RVQ). Our Mel-RVQ utilizes residual linear projection structure for Mel spectrum quantization to enhance the stability and efficiency of target extraction and lead to better performance. Experiments in a large variety of downstream tasks demonstrate that MuQ outperforms previous self-supervised music representation models with only 0.9K hours of open-source pre-training data. Scaling up the data to over 160K hours and adopting iterative training consistently improve the model performance. To further validate the strength of our model, we present MuQ-MuLan, a joint music-text embedding model based on contrastive learning, which achieves state-of-the-art performance in the zero-shot music tagging task on the MagnaTagATune dataset. Code and checkpoints are open source in https://github.com/tencent-ailab/MuQ.

Post-training quantization (PTQ) has emerged as a widely adopted technique for compressing and accelerating Large Language Models (LLMs). The major challenge in LLM quantization is that uneven and heavy-tailed data distributions can expand the quantization range, thereby reducing bit precision for most values. Recent methods attempt to eliminate outliers and balance inter-channel differences by employing linear transformations; however, they remain heuristic and are often overlook optimizing the data distribution across the entire quantization space.In this paper, we introduce Quantization Space Utilization Rate (QSUR), a novel metric that effectively assesses the quantizability of transformed data by measuring the space utilization of the data in the quantization space. We complement QSUR with mathematical derivations that examine the effects and limitations of various transformations, guiding our development of Orthogonal and Scaling Transformation-based Quantization (OSTQuant). OSQuant employs a learnable equivalent transformation, consisting of an orthogonal transformation and a scaling transformation, to optimize the distributions of weights and activations across the entire quantization space. Futhermore, we propose the KL-Top loss function, designed to mitigate noise during optimization while retaining richer semantic information within the limited calibration data imposed by PTQ. OSTQuant outperforms existing work on various LLMs and benchmarks. In the W4-only setting, it retains 99.5\% of the floating-point accuracy. In the more challenging W4A4KV4 configuration, OSTQuant reduces the performance gap by 32\% on the LLaMA-3-8B model compared to state-of-the-art methods. https://github.com/BrotherHappy/OSTQuant{https://github.com/BrotherHappy/OSTQuant}.

Quantization has been widely used to compress and accelerate inference of large language models (LLMs). Existing methods focus on exploring the per-token dynamic calibration to ensure both inference acceleration and model accuracy under 4-bit quantization. However, in autoregressive generation inference of long sequences, the overhead of repeated dynamic quantization and dequantization steps becomes considerably expensive. In this work, we propose MergeQuant, an accurate and efficient per-channel static quantization framework. MergeQuant integrates the per-channel quantization steps with the corresponding scalings and linear mappings through a Quantization Step Migration (QSM) method, thereby eliminating the quantization overheads before and after matrix multiplication. Furthermore, in view of the significant differences between the different channel ranges, we propose dimensional reconstruction and adaptive clipping to address the non-uniformity of quantization scale factors and redistribute the channel variations to the subsequent modules to balance the parameter distribution under QSM. Within the static quantization setting of W4A4, MergeQuant reduces the accuracy gap on zero-shot tasks compared to FP16 baseline to 1.3 points on Llama-2-70B model. On Llama-2-7B model, MergeQuant achieves up to 1.77x speedup in decoding, and up to 2.06x speedup in end-to-end compared to FP16 baseline.

Vision-language-action (VLA) models unify perception, language, and control for embodied agents but face significant challenges in practical deployment due to rapidly increasing compute and memory demands, especially as models scale to longer horizons and larger backbones. To address these bottlenecks, we introduce QuantVLA, a training-free post-training quantization (PTQ) framework that, to our knowledge, is the first PTQ approach for VLA systems and the first to successfully quantize a diffusion transformer (DiT) action head. QuantVLA incorporates three scale-calibrated components: (1) a selective quantization layout that integerizes all linear layers in both the language backbone and the DiT while keeping attention projections in floating point to preserve the original operator schedule; (2) attention temperature matching, a lightweight per-head scaling mechanism that stabilizes attention logits and is folded into the dequantization scales at inference; and (3) output head balancing, a per-layer residual interface calibration that mitigates post-projection energy drift. The framework requires no additional training, uses only a small unlabeled calibration buffer, and supports integer kernels for low-bit weights and activations while leaving the architecture unchanged. Across representative VLA models on LIBERO, QuantVLA exceeds the task success rates of full-precision baselines, achieves about 70% relative memory savings on the quantized components, and delivers a 1.22x speedup in end-to-end inference latency, providing a practical pathway toward scalable low-bit embodied intelligence under strict compute, memory, and power constraints.

Quantization is the key method for reducing inference latency, power and memory footprint of generative AI models. However, accuracy often degrades sharply when activations are quantized below eight bits. Recent work suggests that invertible linear transformations (e.g. rotations) can aid quantization, by reparameterizing feature channels and weights. In this paper, we propose Sequence Transformation and Mixed Precision (STaMP) quantization, a novel strategy that applies linear transformations along the sequence dimension to exploit the strong local correlation in language and visual data. By keeping a small number of tokens in each intermediate activation at higher precision, we can maintain model accuracy at lower (average) activations bit-widths. We evaluate STaMP on recent LVM and LLM architectures, demonstrating that it significantly improves low bit width activation quantization and complements established activation and weight quantization methods including recent feature transformations.

Most competitive 4-bit LLM research pipelines now open the same way: apply a linear, function-preserving transform (rotation, scaling, permutation, non-orthogonal affine) so the outlier mass sits more favorably against the group scales, and only then round. Yet we are aware of no survey dedicated to this transform stage, and its literature is quietly re-deriving an older theory. We identify and formalize the principle that organizes it, the Great Inversion: allocation-flexible coding rewards energy concentration, whereas the grouped shared-scale quantization a deployed matrix instruction performs rewards within-group flattening. Classical transform coding (1963: decorrelate, allocate bits, quantize) spends different bits per coordinate at a fixed total rate; for a Gaussian source at high rate the Karhunen-Loeve transform's concentration minimizes distortion. A deployed operand tile instead carries one absolute-maximum scale per group and equal bits everywhere, with no allocation; on a uniform grid that objective rewards flattening, approached by Hadamard incoherence. We prove that opposition under within-group majorization: the prescriptions point in opposite directions, each backed by a proof against its own objective, and for a generic spectrum no optimality guarantee transfers. A second axis is the number format: the non-uniform FP4 grid makes flattening buy less, MXFP4's power-of-two block scale still rewards a rotation confined to that block, and NVFP4's mantissa-carrying scale largely removes that pull, so the target pole depends jointly on allocation regime and format. We survey 200 works to a June 2026 cutoff; classify 43 transform methods by structure, data-awareness, searched-versus-constructed, and runtime cost; record, where reported, how they compose with GPTQ rounding; distill a first-choice guide by deployment regime; and close with the open problems it exposes.

Softmax attention stores key and value vectors for every preceding token, causing inference memory to grow with sequence length. Recent language models incorporating Gated DeltaNet (GDN) or Kimi Delta Attention (KDA) reduce this cost by replacing the KV cache in most layers with fixed-size recurrent states. However, these recurrent states are commonly stored in FP32 and consume substantial GPU memory; their updates are memory-bandwidth bound and contribute significantly to decoding latency. To our knowledge, we are the first to study post-training quantization of recurrent states in GDN and KDA based language models. We find that uniform quantization provides a poor accuracy--storage trade-off: INT8 and FP8 already degrade accuracy on complex reasoning tasks, while INT4 and NVFP4 reduce it to near zero. We further find that most quantization-error energy is concentrated in a small subset of channels and that the relative decay strength of state channels remains stable across prompts and tasks. Motivated by these findings, DAMP uses both quantization-error energy and decay-based persistence to identify high-risk channels during offline calibration. It stores these channels at higher precision and the remainder in INT8. We evaluate DAMP on Qwen3.6-35B and Kimi-Linear-48B across six benchmarks covering mathematical reasoning, general reasoning, and code generation. At 9.9 bits per state value, DAMP maintains average accuracy close to the FP32 baseline. DAMP reduces recurrent-state storage by 69.1%, accelerates the recurrent-state update kernel by up to 2.01x, and lowers full-model TPOT by up to 10.9%.

Large language models (LLMs) have demonstrated state-of-the-art performance across various tasks. However, the latency of inference and the large GPU memory consumption of LLMs restrict their deployment performance. Recently, there have been some efficient attempts to quantize LLMs, yet inference with large batch size or long sequence still has the issue of being compute-bound. Fine-grained quantization methods have showcased their proficiency in achieving low-bit quantization for LLMs, while requiring FP16 data type for linear layer computations, which is time-consuming when dealing with large batch size or long sequence. In this paper, we introduce a method called FlattenQuant, which significantly reduces the maximum value of the tensor by flattening the large channels in the tensor, to achieve low bit per-tensor quantization with minimal accuracy loss. Our experiments show that FlattenQuant can directly use 4 bits to achieve 48.29% of the linear layer calculation in LLMs, with the remaining layers using 8 bits. The 4-bit matrix multiplication introduced in the FlattenQuant method can effectively address the compute-bound caused by large matrix calculation. Our work achieves up to 2times speedup and 2.3times memory reduction for LLMs with negligible loss in accuracy.

Post-training quantization has emerged as the most widely used strategy for deploying large language models at low precision. Still, current methods show perplexity degradation at bit-widths less than or equal to 4, partly because representing outliers causes precision issues in parameters that share the same scales as these outliers. This problem is especially pronounced for calibration-free, uniform quantization methods. We introduce SINQ to augment existing post-training quantizers with an additional second-axis scale factor and a fast Sinkhorn-Knopp-style algorithm that finds scales to normalize per-row and per-column variances, thereby minimizing a novel per-matrix proxy target for quantization: the matrix imbalance. Our method has no interactions between layers and can be trivially applied to new architectures to quantize any linear layers. We evaluate our method on the Qwen3 model family and DeepSeek-V2.5. SINQ improves WikiText2 and C4 perplexity significantly against uncalibrated uniform quantization baselines and can be further enhanced by combining it with calibration and non-uniform quantization levels. Code to reproduce the results of this work and to easily quantize models using SINQ is available at https://github.com/huawei-csl/SINQ.

Large Language Models (LLMs) demonstrate exceptional performance but entail significant memory and computational costs, restricting their practical deployment. While existing INT4/INT8 quantization reduces these costs, they often degrade accuracy or lack optimal efficiency. INT6 quantization offers a superior trade-off between model accuracy and inference efficiency, but lacks hardware support in modern GPUs, forcing emulation via higher-precision arithmetic units that limit acceleration. In this paper, we propose FlexQ, a novel post-training INT6 quantization framework combining algorithmic innovation with system-level optimizations. FlexQ employs uniform 6-bit weight quantization across all layers, with adaptive retention of 8-bit activations in layers identified through layer-wise sensitivity analysis. To maximize hardware efficiency, we develop a specialized high-performance GPU kernel supporting matrix multiplication for W6A6 and W6A8 representations via Binary Tensor Core (BTC) equivalents, effectively bypassing the lack of native INT6 tensor cores. Evaluations on LLaMA models show FlexQ maintains near-FP16 accuracy, with perplexity increases of no more than 0.05. The proposed kernel achieves an average 1.39times speedup over ABQ-LLM on LLaMA-2-70B linear layers. End-to-end, FlexQ delivers 1.33times inference acceleration and 1.21times memory savings over SmoothQuant. Code is released at https://github.com/FlyFoxPlayer/FlexQ.

We present HyperQuant (Hadamard, optimallY Packing, Entropy Rice-coding), a unified post-training quantization pipeline for the weights and the KV cache of large language and diffusion transformers. Across a suite of self-contained experiments (Table 1), HyperQuant outperforms the recent HIGGS scheme at every operating point from 3 to 5 bits per scalar (bps) on weights, and beats both TurboQuant and OCTOPUS on KV quantization down to 1.7 bps. Beyond the LLM setting, HyperQuant quantizes the 19B-parameter LTX-2 DiT video model with no observable per-frame artifacts. End-to-end on an H100 at 4 bps, HyperQuant compresses the linear weights ~3.9x and the KV cache ~3.79x at near-lossless quality. HyperQuant combines four known ideas into a single construction: (i) a per-tile Randomized Hadamard Transform that makes the per-coordinate distribution of weights and activations approximately Gaussian; (ii) quantization to a low-dimensional optimal lattice (E8, D4, A2, or Z); (iii) lossless bit-stripping and near-entropy-optimal variable-length Rice coding of the lattice indices; and (iv) bias-correction methods for the KV cache that keep the reconstruction unbiased under inner products, preserving attention semantics. We further integrate the pipeline with 8-bit and 4-bit Tensor-Core MMA paths (fp8-e4m3, int8, nvfp4, mxfp4), and find that int8 beats fp8 on the post-RHT lattice output. Project page: https://moonmath.ai/hyperquant/

Post-training quantization (PTQ) has emerged as a prevailing technique for deploying large language models (LLMs) efficiently in terms of both memory and computation, across edge devices and server platforms. Existing PTQ methods primarily aim to reduce precision in weights and activations by mitigating quantization errors caused by channel-wise outlier activations (e.g., pre-quantization scaling, online transformations, or low-rank error reconstruction). Among these approaches, error reconstruction with low-rank adaptation (LoRA) has proven particularly effective, as it introduces a lightweight auxiliary computation path without requiring heavy optimization or additional online layers. However, prior studies reveal severe accuracy degradation under W4A4 settings, and conventional low-rank adaptations rely on two sequential factors, necessitating intermediate quantization during inference and thereby limiting low-precision efficiency. In this work, we propose SERQ, a saliency-aware error reconstruction method for low-bit LLM inference that employs a single low-rank compensation matrix. SERQ preserves efficient 4-bit matrix multiplication in linear layers by jointly mitigating quantization errors arising from both activation and weight saliency through three stages: (1) static activation flattening, (2) saliency-aware error reconstruction, and (3) offline weight permutation. The method incurs additional computation only for low-rank error reconstruction via a single decomposition, while all other operations are performed offline, thereby keeping latency overhead minimal. Empirically, SERQ outperforms prior error reconstruction methods under both W4A8 and W4A4 settings, and achieves higher accuracy than state-of-the-art rotation-based W4A4 approaches, while substantially reducing calibration complexity.

Deep neural networks (DNNs) continue to make significant advances, solving tasks from image classification to translation or reinforcement learning. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. This paper focuses on this problem, and proposes two new compression methods, which jointly leverage weight quantization and distillation of larger teacher networks into smaller student networks. The first method we propose is called quantized distillation and leverages distillation during the training process, by incorporating distillation loss, expressed with respect to the teacher, into the training of a student network whose weights are quantized to a limited set of levels. The second method, differentiable quantization, optimizes the location of quantization points through stochastic gradient descent, to better fit the behavior of the teacher model. We validate both methods through experiments on convolutional and recurrent architectures. We show that quantized shallow students can reach similar accuracy levels to full-precision teacher models, while providing order of magnitude compression, and inference speedup that is linear in the depth reduction. In sum, our results enable DNNs for resource-constrained environments to leverage architecture and accuracy advances developed on more powerful devices.

The emergence of LLMs has ignited a fresh surge of breakthroughs in NLP applications, particularly in domains such as question-answering systems and text generation. As the need for longer context grows, a significant bottleneck in model deployment emerges due to the linear expansion of the Key-Value (KV) cache with the context length. Existing methods primarily rely on various hypotheses, such as sorting the KV cache based on attention scores for replacement or eviction, to compress the KV cache and improve model throughput. However, heuristics used by these strategies may wrongly evict essential KV cache, which can significantly degrade model performance. In this paper, we propose QAQ, a Quality Adaptive Quantization scheme for the KV cache. We theoretically demonstrate that key cache and value cache exhibit distinct sensitivities to quantization, leading to the formulation of separate quantization strategies for their non-uniform quantization. Through the integration of dedicated outlier handling, as well as an improved attention-aware approach, QAQ achieves up to 10x the compression ratio of the KV cache size with a neglectable impact on model performance. QAQ significantly reduces the practical hurdles of deploying LLMs, opening up new possibilities for longer-context applications. The code is available at github.com/ClubieDong/KVCacheQuantization.

Transformer models have been successful in various sequence processing tasks, but the self-attention mechanism's computational cost limits its practicality for long sequences. Although there are existing attention variants that improve computational efficiency, they have a limited ability to abstract global information effectively based on their hand-crafted mixing strategies. On the other hand, state-space models (SSMs) are tailored for long sequences but cannot capture complicated local information. Therefore, the combination of them as a unified token mixer is a trend in recent long-sequence models. However, the linearized attention degrades performance significantly even when equipped with SSMs. To address the issue, we propose a new method called LongVQ. LongVQ uses the vector quantization (VQ) technique to compress the global abstraction as a length-fixed codebook, enabling the linear-time computation of the attention matrix. This technique effectively maintains dynamic global and local patterns, which helps to complement the lack of long-range dependency issues. Our experiments on the Long Range Arena benchmark, autoregressive language modeling, and image and speech classification demonstrate the effectiveness of LongVQ. Our model achieves significant improvements over other sequence models, including variants of Transformers, Convolutions, and recent State Space Models.

Recently, vision transformers (ViTs) have superseded convolutional neural networks in numerous applications, including classification, detection, and segmentation. However, the high computational requirements of ViTs hinder their widespread implementation. To address this issue, researchers have proposed efficient hybrid transformer architectures that combine convolutional and transformer layers with optimized attention computation of linear complexity. Additionally, post-training quantization has been proposed as a means of mitigating computational demands. For mobile devices, achieving optimal acceleration for ViTs necessitates the strategic integration of quantization techniques and efficient hybrid transformer structures. However, no prior investigation has applied quantization to efficient hybrid transformers. In this paper, we discover that applying existing post-training quantization (PTQ) methods for ViTs to efficient hybrid transformers leads to a drastic accuracy drop, attributed to the four following challenges: (i) highly dynamic ranges, (ii) zero-point overflow, (iii) diverse normalization, and (iv) limited model parameters (<5M). To overcome these challenges, we propose a new post-training quantization method, which is the first to quantize efficient hybrid ViTs (MobileViTv1, MobileViTv2, Mobile-Former, EfficientFormerV1, EfficientFormerV2). We achieve a significant improvement of 17.73% for 8-bit and 29.75% for 6-bit on average, respectively, compared with existing PTQ methods (EasyQuant, FQ-ViT, PTQ4ViT, and RepQ-ViT)}. We plan to release our code at https://gitlab.com/ones-ai/q-hyvit.

Learned Image Compression (LIC) has achieved dramatic progress regarding objective and subjective metrics. MSE-based models aim to improve objective metrics while generative models are leveraged to improve visual quality measured by subjective metrics. However, they all suffer from blurring or deformation at low bit rates, especially at below 0.2bpp. Besides, deformation on human faces and text is unacceptable for visual quality assessment, and the problem becomes more prominent on small faces and text. To solve this problem, we combine the advantage of MSE-based models and generative models by utilizing region of interest (ROI). We propose Hierarchical-ROI (H-ROI), to split images into several foreground regions and one background region to improve the reconstruction of regions containing faces, text, and complex textures. Further, we propose adaptive quantization by non-linear mapping within the channel dimension to constrain the bit rate while maintaining the visual quality. Exhaustive experiments demonstrate that our methods achieve better visual quality on small faces and text with lower bit rates, e.g., 0.7X bits of HiFiC and 0.5X bits of BPG.

State Space Models (SSMs) have emerged as an appealing alternative to Transformers for large language models, achieving state-of-the-art accuracy with constant memory complexity which allows for holding longer context lengths than attention-based networks. The superior computational efficiency of SSMs in long sequence modeling positions them favorably over Transformers in many scenarios. However, improving the efficiency of SSMs on request-intensive cloud-serving and resource-limited edge applications is still a formidable task. SSM quantization is a possible solution to this problem, making SSMs more suitable for wide deployment, while still maintaining their accuracy. Quantization is a common technique to reduce the model size and to utilize the low bit-width acceleration features on modern computing units, yet existing quantization techniques are poorly suited for SSMs. Most notably, SSMs have highly sensitive feature maps within the selective scan mechanism (i.e., linear recurrence) and massive outliers in the output activations which are not present in the output of token-mixing in the self-attention modules. To address this issue, we propose a static 8-bit per-tensor SSM quantization method which suppresses the maximum values of the input activations to the selective SSM for finer quantization precision and quantizes the output activations in an outlier-free space with Hadamard transform. Our 8-bit weight-activation quantized Mamba 2.8B SSM benefits from hardware acceleration and achieves a 1.72x lower generation latency on an Nvidia Orin Nano 8G, with only a 0.9% drop in average accuracy on zero-shot tasks. The experiments demonstrate the effectiveness and practical applicability of our approach for deploying SSM-based models of all sizes on both cloud and edge platforms.

State space models (SSMs) like Mamba have recently attracted much attention. Compared to Transformer-based large language models (LLMs), Mamba achieves linear computation complexity with the sequence length and demonstrates superior performance. However, Mamba is hard to accelerate due to the scattered activation outliers and the complex computation dependency, rendering existing LLM accelerators inefficient. In this paper, we propose LightMamba that co-designs the quantization algorithm and FPGA accelerator architecture for efficient Mamba inference. We first propose an FPGA-friendly post-training quantization algorithm that features rotation-assisted quantization and power-of-two SSM quantization to reduce the majority of computation to 4-bit. We further design an FPGA accelerator that partially unrolls the Mamba computation to balance the efficiency and hardware costs. Through computation reordering as well as fine-grained tiling and fusion, the hardware utilization and memory efficiency of the accelerator get drastically improved. We implement LightMamba on Xilinx Versal VCK190 FPGA and achieve 4.65x to 6.06x higher energy efficiency over the GPU baseline. When evaluated on Alveo U280 FPGA, LightMamba reaches 93 tokens/s, which is 1.43x that of the GPU baseline.

To bridge the ever increasing gap between deep neural networks' complexity and hardware capability, network quantization has attracted more and more research attention. The latest trend of mixed precision quantization takes advantage of hardware's multiple bit-width arithmetic operations to unleash the full potential of network quantization. However, this also results in a difficult integer programming formulation, and forces most existing approaches to use an extremely time-consuming search process even with various relaxations. Instead of solving a problem of the original integer programming, we propose to optimize a proxy metric, the concept of network orthogonality, which is highly correlated with the loss of the integer programming but also easy to optimize with linear programming. This approach reduces the search time and required data amount by orders of magnitude, with little compromise on quantization accuracy. Specifically, we achieve 72.08% Top-1 accuracy on ResNet-18 with 6.7Mb, which does not require any searching iterations. Given the high efficiency and low data dependency of our algorithm, we used it for the post-training quantization, which achieve 71.27% Top-1 accuracy on MobileNetV2 with only 1.5Mb. Our code is available at https://github.com/MAC-AutoML/OMPQ.

The rapid scaling of Large Language Models (LLMs) elevates inference costs and compounds substantial deployment barriers. While quantization to 8 or 4 bits mitigates this, sub-3-bit methods face severe accuracy, scalability, and efficiency degradation. We propose Convolutional Code Quantization (CCQ), an inference-optimized quantization approach compressing LLMs to 2.0-2.75 bits with minimal accuracy loss. Departing from error-prone scalar quantization or slow vector quantization, CCQ integrates a hardware-aware bit-shift encoding and decoding solution with Convolutional Code, Hybrid Encoding, and Code Cluster, jointly overcoming accuracy-speed bottlenecks. We construct a lookup-free encoding space, enabling a linear mapping between the codebook and weight vectors, thereby optimizing inference performance. Meanwhile, by drawing on the concept of data mapping from vector quantization, we minimize the performance degradation of the model under extremely low-bit conditions. Experiments demonstrate that CCQ achieves outstanding performance on LLMs across various benchmarks. We compress DeepSeek-V3 (671B total parameters) to 184GB and ERNIE-4.5-300B-A47B to 89GB, enabling single-GPU deployment of ERNIE 4.5 and eliminating inter-card communication. The 2-bit ERNIE-4.5-300B-A47B model and inference engine have been open-sourced.

Quantizing the weights of large language models (LLMs) from 16-bit to lower bitwidth is the de facto approach to deploy massive transformers onto more affordable accelerators. GPTQ emerged as one of the standard methods for one-shot post-training quantization at LLM scale. Yet, its inner workings are described as a sequence of ad-hoc algebraic updates that obscure any geometric meaning or worst-case guarantees. In this work, we show that, when executed back-to-front (from the last to first dimension) for a linear layer, GPTQ is mathematically identical to Babai's nearest plane algorithm for the classical closest vector problem (CVP) on a lattice defined by the Hessian matrix of the layer's inputs. This equivalence is based on a sophisticated mathematical argument, and has two analytical consequences: (i) the GPTQ error propagation step gains an intuitive geometric interpretation; (ii) GPTQ inherits the error upper bound of Babai's algorithm under the no-clipping condition. Taken together, these results place GPTQ on firm theoretical footing and open the door to importing decades of progress in lattice algorithms towards the design of future quantization algorithms for billion-parameter models.

Mixture-of-Experts (MoE) is a promising way to scale up the learning capacity of large language models. It increases the number of parameters while keeping FLOPs nearly constant during inference through sparse activation. Yet, it still suffers from significant memory overheads due to the vast parameter size, necessitating model compression techniques. Post-training quantization offers a powerful approach for model compression. Existing methods adopt a fixed quantization precision for the entire MoE model. This rigid setup can lead to suboptimal performance, without considering the inherent sparse structure. For example, MoE's sparse routing mechanism leads to different activation patterns, where shared experts are accessed by all tokens while token-conditioned experts are selectively activated. This activation disparity suggests different quantization requirements, with consistently activated shared experts potentially needing higher precision to maintain model quality. In this paper, we study a fine-grained precision setup for MoE quantization. We explore MoE structure-aware quantization heuristics, ranging from coarse (e.g., MoE layers) to fine granularity (e.g., linear layers). Our investigations reveal critical principles, where different MoE structures require varying numbers of bits for effective quantization. Conclusions are supported by extensive benchmarking across two representative MoE models and six tasks including commonsense reasoning and natural language understanding. We further show that an MoE quantized in a fined-grained mixed precision achieved state-of-the-art 65.35% performance on average compared to the baseline 64.30% (i.e., GPTQ). Moreover, based on the findings, we introduce novel data-driven techniques for optimizing bit allocation in MoE quantization, including the outlier-aware linear layer scorer and MoE block importance predictor.

Segment Anything Model (SAM) has achieved impressive performance in many computer vision tasks. However, as a large-scale model, the immense memory and computation costs hinder its practical deployment. In this paper, we propose a post-training quantization (PTQ) framework for Segment Anything Model, namely PTQ4SAM. First, we investigate the inherent bottleneck of SAM quantization attributed to the bimodal distribution in post-Key-Linear activations. We analyze its characteristics from both per-tensor and per-channel perspectives, and propose a Bimodal Integration strategy, which utilizes a mathematically equivalent sign operation to transform the bimodal distribution into a relatively easy-quantized normal distribution offline. Second, SAM encompasses diverse attention mechanisms (i.e., self-attention and two-way cross-attention), resulting in substantial variations in the post-Softmax distributions. Therefore, we introduce an Adaptive Granularity Quantization for Softmax through searching the optimal power-of-two base, which is hardware-friendly. Extensive experimental results across various vision tasks (instance segmentation, semantic segmentation and object detection), datasets and model variants show the superiority of PTQ4SAM. For example, when quantizing SAM-L to 6-bit, we achieve lossless accuracy for instance segmentation, about 0.5\% drop with theoretical 3.9times acceleration. The code is available at https://github.com/chengtao-lv/PTQ4SAM.

Sparse-Linear Attention (SLA) combines sparse and linear attention to accelerate diffusion models and has shown strong performance in video generation. However, (i) SLA relies on a heuristic split that assigns computations to the sparse or linear branch based on attention-weight magnitude, which can be suboptimal. Additionally, (ii) after formally analyzing the attention error in SLA, we identify a mismatch between SLA and a direct decomposition into sparse and linear attention. We propose SLA2, which introduces (I) a learnable router that dynamically selects whether each attention computation should use sparse or linear attention, (II) a more faithful and direct sparse-linear attention formulation that uses a learnable ratio to combine the sparse and linear attention branches, and (III) a sparse + low-bit attention design, where low-bit attention is introduced via quantization-aware fine-tuning to reduce quantization error. Experiments show that on video diffusion models, SLA2 can achieve 97% attention sparsity and deliver an 18.6x attention speedup while preserving generation quality.

We give an overview of the light-front holographic approach to strongly coupled QCD, whereby a confining gauge theory, quantized on the light front, is mapped to a higher-dimensional anti de Sitter (AdS) space. The framework is guided by the AdS/CFT correspondence incorporating a gravitational background asymptotic to AdS space which encodes the salient properties of QCD, such as the ultraviolet conformal limit at the AdS boundary at z to 0, as well as modifications of the geometry in the large z infrared region to describe confinement and linear Regge behavior. There are two equivalent procedures for deriving the AdS/QCD equations of motion: one can start from the Hamiltonian equation of motion in physical space time by studying the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a light-front Hamiltonian equation which describes the bound state dynamics of light hadrons in terms of an invariant impact variable ζ which measures the separation of the partons within the hadron at equal light-front time. Alternatively, one can start from the gravity side by studying the propagation of hadronic modes in a fixed effective gravitational background. Both approaches are equivalent in the semiclassical approximation. This allows us to identify the holographic variable z in AdS space with the impact variable ζ. Light-front holography thus allows a precise mapping of transition amplitudes from AdS to physical space-time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.

Diffusion transformers (DiTs) achieve state-of-the-art image and video generation, but their multi-step sampling and growing parameter count make inference expensive. Post-training quantization (PTQ) is the natural remedy, yet DiT activations shift across timesteps, prompts, and guidance branches, forcing prior methods to re-fit calibration data for every new checkpoint or modality. We present OrbitQuant, a data-agnostic weight-activation quantizer that bypasses range estimation by quantizing in a normalized, rotated basis. In this basis, a randomized permuted block-Hadamard (RPBH) rotation concentrates each coordinate around one fixed, known marginal regardless of the input, so a single Lloyd-Max codebook serves all timesteps, prompts, and layers of a given input dimension. We extend the same quantizer to weight rows offline, absorbing the rotation into the weights so that it cancels inside each linear layer and only a forward rotation on the activations remains at runtime. The same recipe transfers from image to video with no per-modality tuning. Across FLUX.1, Z-Image-Turbo, Wan 2.1, and CogVideoX, it sets the state of the art for PTQ at several low-bit settings. It also pushes PTQ of image diffusion transformers to W2A4 with usable generation quality.

Large-scale language models (LLMs) have demonstrated impressive performance, but their deployment presents challenges due to their significant memory usage. This issue can be alleviated through quantization. In this paper, we identify that the challenge in quantizing activations in LLMs arises from varying ranges across channels, rather than solely the presence of outliers. To address this challenge, we introduce a quantization method called RPTQ, which utilizes a reorder-based approach. By rearranging the channels and quantizing them in clusters, RPTQ effectively mitigates the impact of range differences between channels. To minimize the overhead of the reorder operation, we fuse it into the layer norm operation and weights in linear layers. In our experiments, RPTQ achieved a significant breakthrough by utilizing 3-bit activation in LLMs for the first time, resulting in a substantial reduction in memory usage. For instance, quantizing OPT-175b can lead to a memory consumption reduction of up to 80%.

Post-training quantization (PTQ) is a practical way to reduce the memory footprint of large language models, but low-bit quantization is sensitive to mismatches between the quantization codebook and the empirical weight/activation distributions. We revisit Benford-like leading-digit statistics as a lightweight diagnostic of scale-broad behavior in transformer tensors. Across several model families, we observe a consistent functional dichotomy: transformational nn.Linear weights tend to be Benford-like, whereas LayerNorm parameters systematically deviate. Motivated by this observation, we propose BenQ, a data-free PTQ codebook that uses a simple log-spaced grid as a proxy for scale-broad distributions and applies it selectively to transformational layers while keeping stability-critical parameters in higher precision. In 4-bit group-wise PTQ, BenQ consistently improves over uniform RTN and trades wins with NF4 across architectures and tasks, while remaining substantially simpler than optimization-based methods. We additionally report dynamic activation quantization as an exploratory stress test: the results show that log-spaced grids can reduce RTN failures in some families, but also reveal that outlier handling remains essential for reliable low-bit activation PTQ. Code is available at https://github.com/ufopcsilab/benford-quant.

Stateful optimizers maintain gradient statistics over time, e.g., the exponentially smoothed sum (SGD with momentum) or squared sum (Adam) of past gradient values. This state can be used to accelerate optimization compared to plain stochastic gradient descent but uses memory that might otherwise be allocated to model parameters, thereby limiting the maximum size of models trained in practice. In this paper, we develop the first optimizers that use 8-bit statistics while maintaining the performance levels of using 32-bit optimizer states. To overcome the resulting computational, quantization, and stability challenges, we develop block-wise dynamic quantization. Block-wise quantization divides input tensors into smaller blocks that are independently quantized. Each block is processed in parallel across cores, yielding faster optimization and high precision quantization. To maintain stability and performance, we combine block-wise quantization with two additional changes: (1) dynamic quantization, a form of non-linear optimization that is precise for both large and small magnitude values, and (2) a stable embedding layer to reduce gradient variance that comes from the highly non-uniform distribution of input tokens in language models. As a result, our 8-bit optimizers maintain 32-bit performance with a small fraction of the memory footprint on a range of tasks, including 1.5B parameter language modeling, GLUE finetuning, ImageNet classification, WMT'14 machine translation, MoCo v2 contrastive ImageNet pretraining+finetuning, and RoBERTa pretraining, without changes to the original optimizer hyperparameters. We open-source our 8-bit optimizers as a drop-in replacement that only requires a two-line code change.

Structured pruning and quantization are promising approaches for reducing the inference time and memory footprint of neural networks. However, most existing methods require the original training dataset to fine-tune the model. This not only brings heavy resource consumption but also is not possible for applications with sensitive or proprietary data due to privacy and security concerns. Therefore, a few data-free methods are proposed to address this problem, but they perform data-free pruning and quantization separately, which does not explore the complementarity of pruning and quantization. In this paper, we propose a novel framework named Unified Data-Free Compression(UDFC), which performs pruning and quantization simultaneously without any data and fine-tuning process. Specifically, UDFC starts with the assumption that the partial information of a damaged(e.g., pruned or quantized) channel can be preserved by a linear combination of other channels, and then derives the reconstruction form from the assumption to restore the information loss due to compression. Finally, we formulate the reconstruction error between the original network and its compressed network, and theoretically deduce the closed-form solution. We evaluate the UDFC on the large-scale image classification task and obtain significant improvements over various network architectures and compression methods. For example, we achieve a 20.54% accuracy improvement on ImageNet dataset compared to SOTA method with 30% pruning ratio and 6-bit quantization on ResNet-34.

Quantization emerges as one of the most promising approaches for deploying advanced deep models on resource-constrained hardware. Mixed-precision quantization leverages multiple bit-width architectures to unleash the accuracy and efficiency potential of quantized models. However, existing mixed-precision quantization suffers exhaustive search space that causes immense computational overhead. The quantization process thus relies on separate high-performance devices rather than locally, which also leads to a significant gap between the considered hardware metrics and the real deployment.In this paper, we propose an On-chip Hardware-aware Quantization (OHQ) framework that performs hardware-aware mixed-precision quantization without accessing online devices. First, we construct the On-chip Quantization Awareness (OQA) pipeline, enabling perceive the actual efficiency metrics of the quantization operator on the hardware.Second, we propose Mask-guided Quantization Estimation (MQE) technique to efficiently estimate the accuracy metrics of operators under the constraints of on-chip-level computing power.By synthesizing network and hardware insights through linear programming, we obtain optimized bit-width configurations. Notably, the quantization process occurs on-chip entirely without any additional computing devices and data access. We demonstrate accelerated inference after quantization for various architectures and compression ratios, achieving 70% and 73% accuracy for ResNet-18 and MobileNetV3, respectively. OHQ improves latency by 15~30% compared to INT8 on deployment.

State Space Models (SSMs) are emerging as a compelling alternative to Transformers because of their consistent memory usage and high performance. Despite this, scaling up SSMs on cloud services or limited-resource devices is challenging due to their storage requirements and computational power. To overcome this, quantizing SSMs with low bit-width data formats can reduce model size and benefit from hardware acceleration. As SSMs are prone to quantization-induced errors, recent efforts have focused on optimizing a particular model or bit-width for efficiency without sacrificing performance. However, distinct bit-width configurations are essential for different scenarios, like W4A8 for boosting large-batch decoding speed, and W4A16 for enhancing generation speed in short prompt applications for a single user. To this end, we present Quamba2, compatible with W8A8, W4A8, and W4A16 for both Mamba1 and Mamba2 backbones, addressing the growing demand for SSM deployment on various platforms. Based on the channel order preserving and activation persistence of SSMs, we propose an offline approach to quantize inputs of a linear recurrence in 8-bit by sorting and clustering for input x, combined with a per-state-group quantization for input-dependent parameters B and C. To ensure compute-invariance in the SSM output, we rearrange weights offline according to the clustering sequence. The experiments show that Quamba2-8B outperforms several state-of-the-art SSM quantization methods and delivers 1.3times and 3times speed-ups in the pre-filling and generation stages, respectively, while offering 4times memory reduction with only a 1.6% average accuracy drop. The evaluation on MMLU shows the generalizability and robustness of our framework. The code and quantized models will be released at: https://github.com/enyac-group/Quamba.

The energy levels of hydrogen-like atoms are obtained from the phase-space quantization, one of the pillars of the old quantum theory, by three different methods - (i) direct integration, (ii) Sommerfeld's original method, and (iii) complex integration. The difficulties come from the imposition of elliptical orbits to the electron, resulting in a variable radial component of the linear momentum. Details of the calculation, which constitute a recurrent gap in textbooks that deal with phase-space quantization, are shown in depth in an accessible fashion for students of introductory quantum mechanics courses.

Mixture-of-Experts Large Language Models (MoE-LLMs) achieve strong performance but incur substantial memory overhead due to massive expert parameters. Mixed-precision quantization mitigates this cost by allocating expert-wise bit-widths based on their importance, approaching the accuracy-memory Pareto frontier and enabling extreme low-bit quantization. However, existing methods rely on layer-wise importance estimation and overlook router shifts induced by quantization, resulting in suboptimal allocation and routing. In this work, we propose Global Expert-level Mixed-precision Quantization (GEMQ) to overcome these limitations via (1) a global linear-programming formulation that captures model-wide expert importance based on quantization error analysis, and (2) efficient router fine-tuning to adapt routing to quantized experts. These components are integrated into a progressive quantization framework that iteratively refines importance estimation and allocation. Experiments demonstrate that GEMQ significantly reduces memory and accelerates inference with minimal accuracy degradation. Source code is available at https://github.com/jndeng/GEMQ .

Post-training model compression is essential for enhancing the portability of Large Language Models (LLMs) while preserving their performance. While several compression approaches have been proposed, less emphasis has been placed on selecting the most suitable set of data (the so-called calibration data) for finding the compressed model configuration. The choice of calibration data is a critical step in preserving model capabilities both intra- and inter-tasks. In this work, we address the challenge of identifying high-performance calibration sets for both pruning and quantization by analyzing intrinsic data properties rather than model-specific signals. We introduce \textbf{ZipCal}, a model-agnostic data curation strategy that maximizes lexical diversity based on Zipfian power laws. Experiments demonstrate that our method consistently outperforms standard uniform random sampling across various pruning benchmarks. Notably, it also performs on par, in terms of downstream performance, with a state-of-the-art method that relies on model perplexity. The latter becomes prohibitively expensive at large-scale models and datasets, while \textbf{ZipCal} is on average sim240times faster due to its tractable linear complexityWe make the code and the experiments available at https://anonymous.4open.science/r/zipcal-71CD/..

We introduce SANA-WM, an efficient 2.6B-parameter open-source world model natively trained for one-minute generation, synthesizing high-fidelity, 720p, minute-scale videos with precise camera control. SANA-WM achieves visual quality comparable to large-scale industrial baselines such as LingBot-World and HY-WorldPlay, while significantly improving efficiency. Four core designs drive our architecture: (1) Hybrid Linear Attention combines frame-wise Gated DeltaNet (GDN) with softmax attention for memory-efficient long-context modeling. (2) Dual-Branch Camera Control ensures precise 6-DoF trajectory adherence. (3) Two-Stage Generation Pipeline applies a long-video refiner to stage-1 outputs, improving quality and consistency across sequences. (4) Robust Annotation Pipeline extracts accurate metric-scale 6-DoF camera poses from public videos to yield high-quality, spatiotemporally consistent action labels. Driven by these designs, SANA-WMdemonstrates remarkable efficiency across data, training compute, and inference hardware: it uses only sim213K public video clips with metric-scale pose supervision, completes training in 15 days on 64 H100s, and generates each 60s clip on a single GPU; its distilled variant can be deployed on a single RTX 5090 with NVFP4 quantization to denoise a 60s 720p clip in 34s. On our one-minute world-model benchmark, SANA-WM demonstrates stronger action-following accuracy than prior open-source baselines and achieves comparable visual quality at 36times higher throughput for scalable world modeling.

We propose a simple approach for memory-efficient adaptation of pretrained language models. Our approach uses an iterative algorithm to decompose each pretrained matrix into a high-precision low-rank component and a memory-efficient quantized component. During finetuning, the quantized component remains fixed and only the low-rank component is updated. We present an integer linear programming formulation of the quantization component which enables dynamic configuration of quantization parameters (e.g., bit-width, block size) for each matrix given an overall target memory budget. We further explore a data-aware version of the algorithm which uses an approximation of the Fisher information matrix to weight the reconstruction objective during matrix decomposition. Experiments on adapting RoBERTa and LLaMA-2 (7B and 70B) demonstrate that our low-rank plus quantized matrix decomposition approach (LQ-LoRA) outperforms strong QLoRA and GPTQ-LoRA baselines and moreover enables more aggressive quantization. For example, on the OpenAssistant benchmark LQ-LoRA is able to learn a 2.5-bit LLaMA-2 model that is competitive with a model finetuned with 4-bit QLoRA. When finetuned on a language modeling calibration dataset, LQ-LoRA can also be used for model compression; in this setting our 2.75-bit LLaMA-2-70B model (which has 2.85 bits on average when including the low-rank components and requires 27GB of GPU memory) is competitive with the original model in full precision.

We introduce TurboDiffusion, a video generation acceleration framework that can speed up end-to-end diffusion generation by 100-200x while maintaining video quality. TurboDiffusion mainly relies on several components for acceleration: (1) Attention acceleration: TurboDiffusion uses low-bit SageAttention and trainable Sparse-Linear Attention (SLA) to speed up attention computation. (2) Step distillation: TurboDiffusion adopts rCM for efficient step distillation. (3) W8A8 quantization: TurboDiffusion quantizes model parameters and activations to 8 bits to accelerate linear layers and compress the model. In addition, TurboDiffusion incorporates several other engineering optimizations. We conduct experiments on the Wan2.2-I2V-14B-720P, Wan2.1-T2V-1.3B-480P, Wan2.1-T2V-14B-720P, and Wan2.1-T2V-14B-480P models. Experimental results show that TurboDiffusion achieves 100-200x speedup for video generation even on a single RTX 5090 GPU, while maintaining comparable video quality. The GitHub repository, which includes model checkpoints and easy-to-use code, is available at https://github.com/thu-ml/TurboDiffusion.

The transformer architecture predominates across various models. As the heart of the transformer, attention has a computational complexity of O(N^2), compared to O(N) for linear transformations. When handling large sequence lengths, attention becomes the primary time-consuming component. Although quantization has proven to be an effective method for accelerating model inference, existing quantization methods primarily focus on optimizing the linear layer. In response, we first analyze the feasibility of quantization in attention detailedly. Following that, we propose SageAttention, a highly efficient and accurate quantization method for attention. The OPS (operations per second) of our approach outperforms FlashAttention2 and xformers by about 2.1 times and 2.7 times, respectively. SageAttention also achieves superior accuracy performance over FlashAttention3. Comprehensive experiments confirm that our approach incurs almost no end-to-end metrics loss across diverse models, including those for large language processing, image generation, and video generation.

Reinforcement learning (RL) for large language models (LLMs) is increasingly bottlenecked by rollout (generation), where long output sequence lengths make attention and KV-cache memory dominate end-to-end step time. FP8 offers an attractive lever for accelerating RL by reducing compute cost and memory traffic during rollout, but applying FP8 in RL introduces unique engineering and algorithmic challenges: policy weights change every step (requiring repeated quantization and weight synchronization into the inference engine) and low-precision rollouts can deviate from the higher-precision policy assumed by the trainer, causing train-inference mismatch and potential instability. This report presents a practical FP8 rollout stack for LLM RL, implemented in the veRL ecosystem with support for common training backends (e.g., FSDP/Megatron-LM) and inference engines (e.g., vLLM/SGLang). We (i) enable FP8 W8A8 linear-layer rollout using blockwise FP8 quantization, (ii) extend FP8 to KV-cache to remove long-context memory bottlenecks via per-step QKV scale recalibration, and (iii) mitigate mismatch using importance-sampling-based rollout correction (token-level TIS/MIS variants). Across dense and MoE models, these techniques deliver up to 44% rollout throughput gains while preserving learning behavior comparable to BF16 baselines.

The NVFP4 lower-precision format, supported in hardware by NVIDIA Blackwell GPUs, promises to allow, for the first time, end-to-end fully-quantized pre-training of massive models such as LLMs. Yet, existing quantized training methods still sacrifice some of the representation capacity of this format in favor of more accurate unbiased quantized gradient estimation by stochastic rounding (SR), losing noticeable accuracy relative to standard FP16 and FP8 training. In this paper, improve the state of the art for quantized training in NVFP4 via a novel unbiased quantization routine for micro-scaled formats, called MS-EDEN, that has more than 2x lower quantization error than SR. We integrate it into a novel fully-NVFP4 quantization scheme for linear layers, called Quartet II. We show analytically that Quartet II achieves consistently better gradient estimation across all major matrix multiplications, both on the forward and on the backward passes. In addition, our proposal synergizes well with recent training improvements aimed specifically at NVFP4. We further validate Quartet II on end-to-end LLM training with up to 1.9B parameters on 38B tokens. We provide kernels for execution on NVIDIA Blackwell GPUs with up to 4.2x speedup over BF16. Our code is available at https://github.com/IST-DASLab/Quartet-II .

Modern deep learning models have the ability to generate high-dimensional vectors whose similarity reflects semantic resemblance. Thus, similarity search, i.e., the operation of retrieving those vectors in a large collection that are similar to a given query, has become a critical component of a wide range of applications that demand highly accurate and timely answers. In this setting, the high vector dimensionality puts similarity search systems under compute and memory pressure, leading to subpar performance. Additionally, cross-modal retrieval tasks have become increasingly common, e.g., where a user inputs a text query to find the most relevant images for that query. However, these queries often have different distributions than the database embeddings, making it challenging to achieve high accuracy. In this work, we present LeanVec, a framework that combines linear dimensionality reduction with vector quantization to accelerate similarity search on high-dimensional vectors while maintaining accuracy. We present LeanVec variants for in-distribution (ID) and out-of-distribution (OOD) queries. LeanVec-ID yields accuracies on par with those from recently introduced deep learning alternatives whose computational overhead precludes their usage in practice. LeanVec-OOD uses a novel technique for dimensionality reduction that considers the query and database distributions to simultaneously boost the accuracy and the performance of the framework even further (even presenting competitive results when the query and database distributions match). All in all, our extensive and varied experimental results show that LeanVec produces state-of-the-art results, with up to 3.7x improvement in search throughput and up to 4.9x faster index build time over the state of the art.

Low Rank Decomposition of matrix - splitting a large matrix into a product of two smaller matrix offers a means for compression that reduces the parameters of a model without sparsification, and hence delivering more speedup on modern hardware. Moreover, unlike quantization, the compressed linear layers remain fully differentiable and all the parameters trainable, while being able to leverage the existing highly efficient kernels over floating point matrices. We study the potential to compress Large Language Models (LLMs) for monolingual Code generation via Low Rank Decomposition (LoRD) and observe that ranks for the linear layers in these models can be reduced by upto 39.58% with less than 1% increase in perplexity. We then use Low Rank Decomposition (LoRD) to compress StarCoder 16B to 13.2B parameter with no drop and to 12.3B with minimal drop in HumanEval Pass@1 score, in less than 10 minutes on a single A100. The compressed models speeds up inference by up to 22.35% with just a single line of change in code over huggingface's implementation with pytorch backend. Low Rank Decomposition (LoRD) models remain compatible with state of the art near-lossless quantization method such as SpQR, which allows leveraging further compression gains of quantization. Lastly, QLoRA over Low Rank Decomposition (LoRD) model further reduces memory requirements by as much as 21.2% over vanilla QLoRA while offering similar gains from parameter efficient fine tuning. Our work shows Low Rank Decomposition (LoRD) as a promising new paradigm for LLM compression.

We present the Power Law Graph Transformer, a transformer model with well defined deductive and inductive tasks for prediction and representation learning. The deductive task learns the dataset level (global) and instance level (local) graph structures in terms of learnable power law distribution parameters. The inductive task outputs the prediction probabilities using the deductive task output, similar to a transductive model. We trained our model with Turkish-English and Portuguese-English datasets from TED talk transcripts for machine translation and compared the model performance and characteristics to a transformer model with scaled dot product attention trained on the same experimental setup. We report BLEU scores of 17.79 and 28.33 on the Turkish-English and Portuguese-English translation tasks with our model, respectively. We also show how a duality between a quantization set and N-dimensional manifold representation can be leveraged to transform between local and global deductive-inductive outputs using successive application of linear and non-linear transformations end-to-end.

Foundation models trained with self-supervised objectives are increasingly applied to brain recordings, but autoregressive generation of realistic multichannel neural time series remains comparatively underexplored, particularly for Magnetoencephalography (MEG). We study (i) modified multichannel WaveNet variants and (ii) a GPT-2-style Transformer, autoregressively trained by next-step prediction on unlabelled MEG. For the Transformer, we propose a simple quantization/tokenization and embedding scheme (channel, subject, and task-condition embeddings) that repurposes a language-model architecture for continuous, high-rate multichannel time series and enables conditional simulation of task-evoked activity. Across forecasting, long-horizon generation, and downstream decoding, GPT2MEG more faithfully reproduces temporal, spectral, and task-evoked statistics of real MEG than WaveNet variants and linear autoregressive baselines, and scales to multiple subjects via subject embeddings. Code available at https://github.com/ricsinaruto/MEG-transfer-decoding.

Large language models (LLMs) have revolutionized artificial intelligence, yet their massive memory and computational demands necessitate aggressive quantization, increasingly pushing representations toward the theoretical limit of a single bit. While complex-valued LLMs, such as iFairy, offer a superior chance for low-bit representation compared to real-valued counterparts, they require training from scratch, preventing the utilization of the vast ecosystem of pre-trained real-valued foundation models. Here we present Fairy2i, a universal framework that transforms pre-trained real-valued layers into an equivalent widely-linear complex form, enabling extremely low-bit quantization while reusing existing checkpoints. By proving a lossless mathematical equivalence between real and widely-linear maps, we convert standard Transformers into the complex domain and employ a phase-aware quantization scheme with a highly efficient codebook of fourth roots of unity. Furthermore, we introduce a recursive residual quantization mechanism that iteratively minimizes quantization error, allowing inference to proceed via efficient multiplication-free accumulation. We demonstrate that Fairy2i restores the performance of LLaMA-2 7B at an effective 2-bit precision to levels nearly comparable with full-precision baselines, significantly outperforming state-of-the-art real-valued binary and ternary quantization methods. This work bridges the gap between the representational efficiency of complex-valued arithmetic and the practical utility of pre-trained models, paving a new way for efficient inference on commodity hardware.

Neural audio codecs provide promising acoustic features for speech synthesis, with representative streaming codecs like Mimi providing high-quality acoustic features for real-time Text-to-Speech (TTS) applications. However, Mimi's decoder, which employs a hybrid transformer and convolution architecture, introduces significant latency bottlenecks on edge devices due to the the compute intensive nature of deconvolution layers which are not friendly for mobile-CPUs, such as the most representative framework XNNPACK. This paper introduces T-Mimi, a novel modification of the Mimi codec decoder that replaces its convolutional components with a purely transformer-based decoder, inspired by the TS3-Codec architecture. This change dramatically reduces on-device TTS latency from 42.1ms to just 4.4ms. Furthermore, we conduct quantization aware training and derive a crucial finding: the final two transformer layers and the concluding linear layers of the decoder, which are close to the waveform, are highly sensitive to quantization and must be preserved at full precision to maintain audio quality.

The main goal of post-training quantization (PTQ) is to produced a compressed model whose output distribution is as close to the original model's as possible. To do this tractably, almost all LLM PTQ algorithms quantize linear layers by independently minimizing the immediate activation error. However, this localized objective ignores the effect of subsequent layers, so reducing it does not necessarily give a closer model. In this work, we introduce Yet Another Quantization Algorithm (YAQA), an adaptive rounding algorithm that uses Kronecker-factored approximations of each linear layer's Hessian with respect to the full model KL divergence. YAQA consists of two components: Kronecker-factored sketches of the full layerwise Hessian that can be tractably computed for hundred-billion parameter LLMs, and a quantizer-independent rounding algorithm that uses these sketches and comes with theoretical guarantees. Across a wide range of models and quantizers, YAQA empirically reduces the KL divergence to the original model by approx 30% while achieving state of the art performance on downstream tasks.

Unified vision-language models (VLMs) that tokenize images through a vector-quantized (VQ) codebook routinely hallucinate objects on grounded yes/no benchmarks, yet existing decoding-time fixes treat this as generic miscalibration without an architectural account. Using activation patching across twenty-five models spanning eight LLM families, we identify an early-layer (L_0) attention routing circuit shared across VQ-tokenized VLMs and propose a three-gate diagnostic that distinguishes the models carrying it from those that do not. The diagnostic isolates ten positive models (five natural unified-VQ VLMs across three LLM families and five induced variants) and rejects the remaining fifteen. A single-variable architectural swap (LLaVA-1.6 CLIP+MLP rightarrow VQ+Linear) installs the circuit, while a matched-compute MLP control on identical data does not, isolating vector quantization as the source of the pathological signal; the routing pathway that carries it is one that the backbone already provides. Against tuned VCD and DoLA baselines, tuned DoLA wins on binary calibration, but only L_0 ablation reduces object hallucination in open-ended generation (CHAIR_i reduces by 31,% relatively, whereas tuned DoLA and VCD leave it unchanged or worsen it). These results recast object hallucination in unified VQ VLMs as a property of architecture and pretraining, and yield a targeted intervention that mechanism-agnostic decoding cannot replicate.

Diffusion and flow matching models have made significant progress in text-to-image generation, yet high computation, quadratic complexity, and large memory footprint hinder high-resolution synthesis and edge deployment. We propose Nexus, which integrates sparse architecture, linear complexity, and low-bit quantization. It combines MoE feed-forward layers, gated DeltaNet attention, and per-expert low-bit training to reduce computation and memory. Their joint optimization allows Nexus to achieve generation quality comparable to mainstream models such as SDXL and SD3 while delivering markedly higher inference efficiency. Experiments on COCO and LAION validate its effectiveness.

We introduce a novel class of regularization functions, called Cauchy-Schwarz (CS) regularizers, which can be designed to induce a wide range of properties in solution vectors of optimization problems. To demonstrate the versatility of CS regularizers, we derive regularization functions that promote discrete-valued vectors, eigenvectors of a given matrix, and orthogonal matrices. The resulting CS regularizers are simple, differentiable, and can be free of spurious stationary points, making them suitable for gradient-based solvers and large-scale optimization problems. In addition, CS regularizers automatically adapt to the appropriate scale, which is, for example, beneficial when discretizing the weights of neural networks. To demonstrate the efficacy of CS regularizers, we provide results for solving underdetermined systems of linear equations and weight quantization in neural networks. Furthermore, we discuss specializations, variations, and generalizations, which lead to an even broader class of new and possibly more powerful regularizers.

Mixture-of-Experts (MoE) effectively scales large language models (LLMs) and vision-language models (VLMs) by increasing capacity through sparse activation. However, preloading all experts into memory and activating multiple experts per input introduces significant computational and memory overhead, making the expert module a major contributor to model size and inference cost. To address this, we propose MC# (Mixture-Compressor-sharp), a framework that combines static quantization and dynamic expert pruning by leveraging the significance of experts and tokens for aggressive compression of MoE-LLMs/VLMs. To reduce storage and loading costs, we introduce Pre-Loading Mixed-Precision Quantization (PMQ), which optimizes bit allocation via linear programming, balancing expert importance and quantization error for a Pareto-optimal trade-off between size and performance. To reduce runtime computation, Online Top-any Pruning (OTP) uses Gumbel-Softmax sampling to dynamically select a subset of experts per token, enabling fine-grained control over activation. By combining PMQ's static bit-width optimization with OTP's dynamic routing, MC# achieves extreme compression with minimal accuracy loss. On DeepSeek-VL2, MC# achieves a 6.2 times weight reduction at 2.57 average bits with only a 1.7% accuracy drop across five multimodal benchmarks. Additionally, OTP reduces expert activation over 20% with less than 1% performance degradation, demonstrating strong potential for efficient MoE-based model deployment.

Transformer-based 3D reconstruction has emerged as a powerful paradigm for recovering geometry and appearance from multi-view observations, offering strong performance across challenging visual conditions. As these models scale to larger backbones and higher-resolution inputs, improving their efficiency becomes increasingly important for practical deployment. However, modern 3D transformer pipelines face two coupled challenges: dense multi-view attention creates substantial token-mixing overhead, and low-precision execution can destabilize geometry-sensitive representations and degrade depth, pose, and 3D consistency. To address the first challenge, we propose Lite3R, a model-agnostic teacher-student framework that replaces dense attention with Sparse Linear Attention to preserve important geometric interactions while reducing attention cost. To address the second challenge, we introduce a parameter-efficient FP8-aware quantization-aware training (FP8-aware QAT) strategy with partial attention distillation, which freezes the vast majority of pretrained backbone parameters and trains only lightweight linear-branch projection layers, enabling stable low-precision deployment while retaining pretrained geometric priors. We further evaluate Lite3R on two representative backbones, VGGT and DA3-Large, over BlendedMVS and DTU64, showing that it substantially reduces latency (1.7-2.0x) and memory usage (1.9-2.4x) while preserving competitive reconstruction quality overall. These results demonstrate that Lite3R provides an effective algorithm-system co-design approach for practical transformer-based 3D reconstruction. Code: https://github.com/AIGeeksGroup/Lite3R. Website: https://aigeeksgroup.github.io/Lite3R.

Diffusion Transformers (DiTs) have been widely used in many tasks, including image synthesis, video generation, and content editing. However, their multi-iteration inference process leads to performance inefficiency and high energy consumption. Existing acceleration methods primarily focus on reducing temporal redundancy between adjacent timesteps, but often overlook the specific features of DiTs. As a result, these approaches either suffer from great accuracy degradation or fail to achieve high efficiency. We present DSTAR, a software-hardware co-design framework that accelerates DiT inference by reducing spatial and temporal redundancy. At the algorithmic level, DSTAR introduces a fine-grained mixed-precision quantization method for differential activations in linear operations, significantly increasing the proportion of low-bit computations. Additionally, DSTAR incorporates a sparse attention reuse mechanism to minimize redundant computation in attention layers. For architectural support, we design a specialized hardware accelerator which achieves high efficiency in both latency and energy consumption. Evaluation on seven typical DiTs demonstrates that DSTAR achieves up to 7.33x latency speedup and 41.89x energy savings compared to an NVIDIA A100 GPU, and achieves up to 2.54x latency speedup and 3.68x energy savings compared to SOTA accelerators, without accuracy degradation.

Mixture-of-Experts large language models (MoE-LLMs) marks a significant step forward of language models, however, they encounter two critical challenges in practice: 1) expert parameters lead to considerable memory consumption and loading latency; and 2) the current activated experts are redundant, as many tokens may only require a single expert. Motivated by these issues, we investigate the MoE-LLMs and make two key observations: a) different experts exhibit varying behaviors on activation reconstruction error, routing scores, and activated frequencies, highlighting their differing importance, and b) not all tokens are equally important -- only a small subset is critical. Building on these insights, we propose MC-MoE, a training-free Mixture-Compressor for MoE-LLMs, which leverages the significance of both experts and tokens to achieve an extreme compression. First, to mitigate storage and loading overheads, we introduce Pre-Loading Mixed-Precision Quantization, which formulates the adaptive bit-width allocation as a Linear Programming problem, where the objective function balances multi-factors reflecting the importance of each expert. Additionally, we develop Online Dynamic Pruning, which identifies important tokens to retain and dynamically select activated experts for other tokens during inference to optimize efficiency while maintaining performance. Our MC-MoE integrates static quantization and dynamic pruning to collaboratively achieve extreme compression for MoE-LLMs with less accuracy loss, ensuring an optimal trade-off between performance and efficiency. Extensive experiments confirm the effectiveness of our approach. For instance, at 2.54 bits, MC-MoE compresses 76.6% of the model, with only a 3.8% average accuracy loss. During dynamic inference, we further reduce activated parameters by 15%, with a performance drop of less than 0.6%.

Zero-Input AI (ZIA) introduces a novel framework for human-computer interaction by enabling proactive intent prediction without explicit user commands. It integrates gaze tracking, bio-signals (EEG, heart rate), and contextual data (time, location, usage history) into a multi-modal model for real-time inference, targeting <100 ms latency. The proposed architecture employs a transformer-based model with cross-modal attention, variational Bayesian inference for uncertainty estimation, and reinforcement learning for adaptive optimization. To support deployment on edge devices (CPUs, TPUs, NPUs), ZIA utilizes quantization, weight pruning, and linear attention to reduce complexity from quadratic to linear with sequence length. Theoretical analysis establishes an information-theoretic bound on prediction error and demonstrates how multi-modal fusion improves accuracy over single-modal approaches. Expected performance suggests 85-90% accuracy with EEG integration and 60-100 ms inference latency. ZIA provides a scalable, privacy-preserving framework for accessibility, healthcare, and consumer applications, advancing AI toward anticipatory intelligence.

Large language models (LLMs) have transformed natural-language processing, yet their scale makes real-world deployment costly. Post-training quantization reduces memory and computation but often degrades accuracy, while quantization-aware training can recover performance at the cost of extra training. Pushing quantization to the ternary (2-bit) regime yields even larger savings but is notoriously unstable. Building on recent work showing that a bias-free, RMS-normalized Transformer with straight-through estimation can reach 1.58-bit precision, we demonstrate that simply inserting RMS normalization before every linear projection and applying a gradual, layer-wise quantization schedule stably fine-tunes full-precision checkpoints into ternary LLMs. Our approach matches or surpasses more elaborate knowledge-distillation pipelines on standard language-modeling benchmarks without adding model complexity. These results indicate that careful normalization alone can close much of the accuracy gap between ternary and full-precision LLMs, making ultra-low-bit inference practical.

Modern optical mouse sensors, with their advanced precision and high responsiveness, possess an often overlooked vulnerability: they can be exploited for side-channel attacks. This paper introduces Mic-E-Mouse, the first-ever side-channel attack that targets high-performance optical mouse sensors to covertly eavesdrop on users. We demonstrate that audio signals can induce subtle surface vibrations detectable by a mouse's optical sensor. Remarkably, user-space software on popular operating systems can collect and broadcast this sensitive side channel, granting attackers access to raw mouse data without requiring direct system-level permissions. Initially, the vibration signals extracted from mouse data are of poor quality due to non-uniform sampling, a non-linear frequency response, and significant quantization. To overcome these limitations, Mic-E-Mouse employs a sophisticated end-to-end data filtering pipeline that combines Wiener filtering, resampling corrections, and an innovative encoder-only spectrogram neural filtering technique. We evaluate the attack's efficacy across diverse conditions, including speaking volume, mouse polling rate and DPI, surface materials, speaker languages, and environmental noise. In controlled environments, Mic-E-Mouse improves the signal-to-noise ratio (SNR) by up to +19 dB for speech reconstruction. Furthermore, our results demonstrate a speech recognition accuracy of roughly 42% to 61% on the AudioMNIST and VCTK datasets. All our code and datasets are publicly accessible on https://sites.google.com/view/mic-e-mouse.

Long context capability is a crucial competency for large language models (LLMs) as it mitigates the human struggle to digest long-form texts. This capability enables complex task-solving scenarios such as book summarization, code assistance, and many more tasks that are traditionally manpower-intensive. However, transformer-based LLMs face significant challenges with long context input due to the growing size of the KV cache and the intrinsic complexity of attending to extended inputs; where multiple schools of efficiency-driven approaches -- such as KV cache quantization, token dropping, prompt compression, linear-time sequence models, and hybrid architectures -- have been proposed to produce efficient yet long context-capable models. Despite these advancements, no existing work has comprehensively benchmarked these methods in a reasonably aligned environment. In this work, we fill this gap by providing a taxonomy of current methods and evaluating 10+ state-of-the-art approaches across seven categories of long context tasks. Our work reveals numerous previously unknown phenomena and offers insights -- as well as a friendly workbench -- for the future development of long context-capable LLMs. The source code will be available at https://github.com/henryzhongsc/longctx_bench

Long-context LLMs have enabled numerous downstream applications but also introduced significant challenges related to computational and memory efficiency. To address these challenges, optimizations for long-context inference have been developed, centered around the KV cache. However, existing benchmarks often evaluate in single-request, neglecting the full lifecycle of the KV cache in real-world use. This oversight is particularly critical, as KV cache reuse has become widely adopted in LLMs inference frameworks, such as vLLM and SGLang, as well as by LLM providers, including OpenAI, Microsoft, Google, and Anthropic. To address this gap, we introduce SCBench(SharedContextBench), a comprehensive benchmark for evaluating long-context methods from a KV cachecentric perspective: 1) KV cache generation, 2) KV cache compression, 3) KV cache retrieval, 4) KV cache loading. Specifically, SCBench uses test examples with shared context, ranging 12 tasks with two shared context modes, covering four categories of long-context capabilities: string retrieval, semantic retrieval, global information, and multi-task. With it, we provide an extensive KV cache-centric analysis of eight categories long-context solutions, including Gated Linear RNNs, Mamba-Attention hybrids, and efficient methods such as sparse attention, KV cache dropping, quantization, retrieval, loading, and prompt compression. The evaluation is conducted on 8 long-context LLMs. Our findings show that sub-O(n) memory methods suffer in multi-turn scenarios, while sparse encoding with O(n) memory and sub-O(n^2) pre-filling computation perform robustly. Dynamic sparsity yields more expressive KV caches than static patterns, and layer-level sparsity in hybrid architectures reduces memory usage with strong performance. Additionally, we identify attention distribution shift issues in long-generation scenarios. https://aka.ms/SCBench.

We introduce Helios, the first 14B video generation model that runs at 19.5 FPS on a single NVIDIA H100 GPU and supports minute-scale generation while matching the quality of a strong baseline. We make breakthroughs along three key dimensions: (1) robustness to long-video drifting without commonly used anti-drifting heuristics such as self-forcing, error-banks, or keyframe sampling; (2) real-time generation without standard acceleration techniques such as KV-cache, sparse/linear attention, or quantization; and (3) training without parallelism or sharding frameworks, enabling image-diffusion-scale batch sizes while fitting up to four 14B models within 80 GB of GPU memory. Specifically, Helios is a 14B autoregressive diffusion model with a unified input representation that natively supports T2V, I2V, and V2V tasks. To mitigate drifting in long-video generation, we characterize typical failure modes and propose simple yet effective training strategies that explicitly simulate drifting during training, while eliminating repetitive motion at its source. For efficiency, we heavily compress the historical and noisy context and reduce the number of sampling steps, yielding computational costs comparable to -- or lower than -- those of 1.3B video generative models. Moreover, we introduce infrastructure-level optimizations that accelerate both inference and training while reducing memory consumption. Extensive experiments demonstrate that Helios consistently outperforms prior methods on both short- and long-video generation. We plan to release the code, base model, and distilled model to support further development by the community.

Quantizing large language models has become a standard way to reduce their memory and computational costs. Typically, existing methods focus on breaking down the problem into individual layer-wise sub-problems, and minimizing per-layer error, measured via various metrics. Yet, this approach currently lacks theoretical justification and the metrics employed may be sub-optimal. In this paper, we present a "linearity theorem" establishing a direct relationship between the layer-wise ell_2 reconstruction error and the model perplexity increase due to quantization. This insight enables two novel applications: (1) a simple data-free LLM quantization method using Hadamard rotations and MSE-optimal grids, dubbed HIGGS, which outperforms all prior data-free approaches such as the extremely popular NF4 quantized format, and (2) an optimal solution to the problem of finding non-uniform per-layer quantization levels which match a given compression constraint in the medium-bitwidth regime, obtained by reduction to dynamic programming. On the practical side, we demonstrate improved accuracy-compression trade-offs on Llama-3.1 and 3.2-family models, as well as on Qwen-family models. Further, we show that our method can be efficiently supported in terms of GPU kernels at various batch sizes, advancing both data-free and non-uniform quantization for LLMs.

Model quantification uses low bit-width values to represent the weight matrices of models, which is a promising approach to reduce both storage and computational overheads of deploying highly anticipated LLMs. However, existing quantization methods suffer severe performance degradation when the bit-width is extremely reduced, and thus focus on utilizing 4-bit or 8-bit values to quantize models. This paper boldly quantizes the weight matrices of LLMs to 1-bit, paving the way for the extremely low bit-width deployment of LLMs. For this target, we introduce a 1-bit quantization-aware training (QAT) framework named OneBit, including a novel 1-bit parameter representation method to better quantize LLMs as well as an effective parameter initialization method based on matrix decomposition to improve the convergence speed of the QAT framework. Sufficient experimental results indicate that OneBit achieves good performance (at least 83% of the non-quantized performance) with robust training processes when only using 1-bit weight matrices.

Conventional model compression techniques for LLMs address high memory consumption and slow inference challenges but typically require computationally expensive retraining to preserve accuracy. In contrast, one-shot compression methods eliminate retraining cost, but struggle to achieve accuracy comparable to dense models. This paper presents SLIM, a new one-shot compression framework that holistically integrates hardware-friendly quantization, sparsity, and low-rank approximation into a unified process. First, we formulate the quantization process using a probabilistic approach (SLIM-Quant) that enables us to apply uniform quantization. Then, we use an existing one-shot pruning method to apply semi-structured sparsity on top of the quantized weights. Finally, to compensate for the introduced aggregated quantization and sparsity error, we use a novel saliency function with unique invertible and additive features that enables us to mathematically compute the value of low-rank adapters. SLIM improves model accuracy by up to 5.66% (LLaMA-2-7B) for 2:4 sparsity with 4-bit weight quantization, outperforming prior methods. Models compressed with SLIM achieve up to 4.3x and 3.8x on Nvidia RTX3060 and A100 GPUs, respectively. Additionally, they achieve up to 0.23x end-to-end memory reduction in comparison to their dense counterparts. We also propose an optional PEFT recipe that further improves accuracy by up to 1.66% (LLaMA-2-13B) compared to SLIM without fine-tuning.

Quantization is a widely-used compression technology to reduce the overhead of serving large language models (LLMs) on terminal devices and in cloud data centers. However, prevalent quantization methods, such as 8-bit weight-activation or 4-bit weight-only quantization, achieve limited performance improvements due to poor support for low-precision (e.g., 4-bit) activation. This work, for the first time, realizes practical W4A4KV4 serving for LLMs, fully utilizing the INT4 tensor cores on modern GPUs and reducing the memory bottleneck caused by the KV cache. Specifically, we propose a novel fine-grained mixed-precision quantization algorithm (FMPQ) that compresses most activations into 4-bit with negligible accuracy loss. To support mixed-precision matrix multiplication for W4A4 and W4A8, we develop a highly optimized W4Ax kernel. Our approach introduces a novel mixed-precision data layout to facilitate access and fast dequantization for activation and weight tensors, utilizing the GPU's software pipeline to hide the overhead of data loading and conversion. Additionally, we propose fine-grained streaming multiprocessor (SM) scheduling to achieve load balance across different SMs. We integrate the optimized W4Ax kernel into our inference framework, COMET, and provide efficient management to support popular LLMs such as LLaMA-3-70B. Extensive evaluations demonstrate that, when running LLaMA family models on a single A100-80G-SMX4, COMET achieves a kernel-level speedup of 2.88times over cuBLAS and a 2.02 times throughput improvement compared to TensorRT-LLM from an end-to-end framework perspective.

Large Language Models (LLMs) have revolutionized natural language processing tasks. However, their practical application is constrained by substantial memory and computational demands. Post-training quantization (PTQ) is considered an effective method to accelerate LLM inference. Despite its growing popularity in LLM model compression, PTQ deployment faces two major challenges. First, low-bit quantization leads to performance degradation. Second, restricted by the limited integer computing unit type on GPUs, quantized matrix operations with different precisions cannot be effectively accelerated. To address these issues, we introduce a novel arbitrary-bit quantization algorithm and inference framework, ABQ-LLM. It achieves superior performance across various quantization settings and enables efficient arbitrary-precision quantized inference on the GPU. ABQ-LLM introduces several key innovations: (1) a distribution correction method for transformer blocks to mitigate distribution differences caused by full quantization of weights and activations, improving performance at low bit-widths. (2) the bit balance strategy to counteract performance degradation from asymmetric distribution issues at very low bit-widths (e.g., 2-bit). (3) an innovative quantization acceleration framework that reconstructs the quantization matrix multiplication of arbitrary precision combinations based on BTC (Binary TensorCore) equivalents, gets rid of the limitations of INT4/INT8 computing units. ABQ-LLM can convert each component bit width gain into actual acceleration gain, maximizing performance under mixed precision(e.g., W6A6, W2A8). Based on W2*A8 quantization configuration on LLaMA-7B model, it achieved a WikiText2 perplexity of 7.59 (2.17downarrow vs 9.76 in AffineQuant). Compared to SmoothQuant, we realized 1.6times acceleration improvement and 2.7times memory compression gain.

As the size of large language models (LLMs) continues to grow, model compression without sacrificing accuracy has become a crucial challenge for deployment. While some quantization methods, such as GPTQ, have made progress in achieving acceptable 4-bit weight-only quantization, attempts at lower bit quantization often result in severe performance degradation. In this paper, we introduce a technique called norm tweaking, which can be used as a plugin in current PTQ methods to achieve high precision while being cost-efficient. Our approach is inspired by the observation that rectifying the quantized activation distribution to match its float counterpart can readily restore accuracy for LLMs. To achieve this, we carefully design a tweaking strategy that includes calibration data generation and channel-wise distance constraint to update the weights of normalization layers for better generalization. We conduct extensive experiments on various datasets using several open-sourced LLMs. Our method demonstrates significant improvements in both weight-only quantization and joint quantization of weights and activations, surpassing existing PTQ methods. On GLM-130B and OPT-66B, our method even achieves the same level of accuracy at 2-bit quantization as their float ones. Our simple and effective approach makes it more practical for real-world applications.

Recent generative models have become increasingly powerful, but their inference cost continues to grow. Model quantization offers a promising way to compress these models and accelerate inference. However, at 4 bits, activation quantization is substantially more challenging than weight quantization. Recent post-training quantization (PTQ) and quantization-aware training (QAT) methods have made progress in 4-bit activation quantization by introducing smoothing, SVD branches, rotations, mixed precision, or advanced formats such as NVFP4. These additional operators and data types impose demanding requirements on inference engines and hardware, limiting the broad adoption of low-precision models. Can quantization be achieved using only plain low-bit operators? To answer this question, we propose JustQuant, a simple yet effective framework that moves the complexity of low-bit quantization from deployment-time operators into the training process. We first revisit model quantization from the perspective of knowledge distillation and show that a key reason existing PTQ and QAT methods fail is that they typically exploit supervision at only a single level. We then introduce Theseus QAD, a quantization-aware distillation method that progressively applies multi-level supervision, analogous to the gradual replacement process in the Ship of Theseus. Extensive experiments on DiT and diffusion large language models show two distinct regimes. For smaller models, Theseus QAD can serve as a lightweight warm-up stage that substantially improves subsequent QAT with plain operators, while naive QAD may collapse in the same setting. For larger models, Theseus QAD provides a stronger distillation training path than ordinary QAD. Across both regimes, JustQuant improves low-bit quantization quality while avoiding the complex operators required by many existing PTQ methods.

Network quantization generally converts full-precision weights and/or activations into low-bit fixed-point values in order to accelerate an inference process. Recent approaches to network quantization further discretize the gradients into low-bit fixed-point values, enabling an efficient training. They typically set a quantization interval using a min-max range of the gradients or adjust the interval such that the quantization error for entire gradients is minimized. In this paper, we analyze the quantization error of gradients for the low-bit fixed-point training, and show that lowering the error for large-magnitude gradients boosts the quantization performance significantly. Based on this, we derive an upper bound of quantization error for the large gradients in terms of the quantization interval, and obtain an optimal condition for the interval minimizing the quantization error for large gradients. We also introduce an interval update algorithm that adjusts the quantization interval adaptively to maintain a small quantization error for large gradients. Experimental results demonstrate the effectiveness of our quantization method for various combinations of network architectures and bit-widths on various tasks, including image classification, object detection, and super-resolution.

Prevailing quantization techniques in Learned Image Compression (LIC) typically employ a static, uniform bit-width across all layers, failing to adapt to the highly diverse data distributions and sensitivity characteristics inherent in LIC models. This leads to a suboptimal trade-off between performance and efficiency. In this paper, we introduce DynaQuant, a novel framework for dynamic mixed-precision quantization that operates on two complementary levels. First, we propose content-aware quantization, where learnable scaling and offset parameters dynamically adapt to the statistical variations of latent features. This fine-grained adaptation is trained end-to-end using a novel Distance-aware Gradient Modulator (DGM), which provides a more informative learning signal than the standard Straight-Through Estimator. Second, we introduce a data-driven, dynamic bit-width selector that learns to assign an optimal bit precision to each layer, dynamically reconfiguring the network's precision profile based on the input data. Our fully dynamic approach offers substantial flexibility in balancing rate-distortion (R-D) performance and computational cost. Experiments demonstrate that DynaQuant achieves rd performance comparable to full-precision models while significantly reducing computational and storage requirements, thereby enabling the practical deployment of advanced LIC on diverse hardware platforms.

Recent advancements in large language models (LLMs) are propelling us toward artificial general intelligence with their remarkable emergent abilities and reasoning capabilities. However, the substantial computational and memory requirements limit the widespread adoption. Quantization, a key compression technique, can effectively mitigate these demands by compressing and accelerating LLMs, albeit with potential risks to accuracy. Numerous studies have aimed to minimize the accuracy loss associated with quantization. However, their quantization configurations vary from each other and cannot be fairly compared. In this paper, we present LLMC, a plug-and-play compression toolkit, to fairly and systematically explore the impact of quantization. LLMC integrates dozens of algorithms, models, and hardwares, offering high extensibility from integer to floating-point quantization, from LLM to vision-language (VLM) model, from fixed-bit to mixed precision, and from quantization to sparsification. Powered by this versatile toolkit, our benchmark covers three key aspects: calibration data, algorithms (three strategies), and data formats, providing novel insights and detailed analyses for further research and practical guidance for users. Our toolkit is available at https://github.com/ModelTC/llmc.

Post-training quantization (PTQ) and quantization-aware training (QAT) methods are gaining popularity in mitigating the high memory and computational costs associated with Large Language Models (LLMs). In resource-constrained scenarios, PTQ, with its reduced training overhead, is often preferred over QAT, despite the latter's potential for higher accuracy. Meanwhile, parameter-efficient fine-tuning (PEFT) methods like low-rank adaptation (LoRA) have been introduced, and recent efforts have explored quantization-aware PEFT techniques. However, these approaches may lack generality due to their reliance on the pre-quantized model's configuration. Their effectiveness may be compromised by non-linearly quantized or mixed-precision weights, and the retraining of specific quantization parameters might impede optimal performance. To address these challenges, we propose L4Q, an algorithm for parameter-efficient quantization-aware training. L4Q leverages LoRA-wise learned quantization step size for LLMs, aiming to enhance generality. The simultaneous quantization-and-fine-tuning process of L4Q is applicable to high-precision models, yielding linearly quantized weights with superior accuracy. Our experiments, conducted on the LLaMA and LLaMA2 model families using an instructional dataset, showcase L4Q's capabilities in language comprehension and few-shot in-context learning, achieving sub-4-bit precision while maintaining comparable training times to applying PEFT on a quantized model.

Large Language Models (LLMs) have demonstrated remarkable capabilities but typically require extensive computational resources and memory for inference. Post-training quantization (PTQ) can effectively reduce these demands by storing weights in lower bit-width formats. However, standard uniform quantization often leads to notable performance degradation, particularly in low-bit scenarios. In this work, we introduce a Grouped Lattice Vector Quantization (GLVQ) framework that assigns each group of weights a customized lattice codebook, defined by a learnable generation matrix. To address the non-differentiability of the quantization process, we adopt Babai rounding to approximate nearest-lattice-point search during training, which enables stable optimization of the generation matrices. Once trained, decoding reduces to a simple matrix-vector multiplication, yielding an efficient and practical quantization pipeline. Experiments on multiple benchmarks show that our approach achieves a better trade-off between model size and accuracy compared to existing post-training quantization baselines, highlighting its effectiveness in deploying large models under stringent resource constraints. Our source code is available on GitHub repository: https://github.com/xzhang9308/GLVQ.

Quantization is a promising approach for reducing the inference time and memory footprint of neural networks. However, most existing quantization methods require access to the original training dataset for retraining during quantization. This is often not possible for applications with sensitive or proprietary data, e.g., due to privacy and security concerns. Existing zero-shot quantization methods use different heuristics to address this, but they result in poor performance, especially when quantizing to ultra-low precision. Here, we propose ZeroQ , a novel zero-shot quantization framework to address this. ZeroQ enables mixed-precision quantization without any access to the training or validation data. This is achieved by optimizing for a Distilled Dataset, which is engineered to match the statistics of batch normalization across different layers of the network. ZeroQ supports both uniform and mixed-precision quantization. For the latter, we introduce a novel Pareto frontier based method to automatically determine the mixed-precision bit setting for all layers, with no manual search involved. We extensively test our proposed method on a diverse set of models, including ResNet18/50/152, MobileNetV2, ShuffleNet, SqueezeNext, and InceptionV3 on ImageNet, as well as RetinaNet-ResNet50 on the Microsoft COCO dataset. In particular, we show that ZeroQ can achieve 1.71\% higher accuracy on MobileNetV2, as compared to the recently proposed DFQ method. Importantly, ZeroQ has a very low computational overhead, and it can finish the entire quantization process in less than 30s (0.5\% of one epoch training time of ResNet50 on ImageNet). We have open-sourced the ZeroQ frameworkhttps://github.com/amirgholami/ZeroQ.

Post-training quantization at the 2-bit level enables low-cost deployment and inference acceleration for large language models (LLMs). Scalar quantization (SQ) and vector quantization (VQ) are two primary quantization methods, however, the former suffers from significant performance degradation, and the latter incurs computational and storage overhead. We propose UniSVQ, a unified 2-bit quantization framework that bridges scalar and vector quantization by parameterizing codewords as an affine transform of integer lattices. This structure preserves compatibility with optimized integer kernels while retaining much of VQ's flexibility. We further introduce a data-driven block-wise fine-tuning strategy to directly minimize quantization reconstruction error. Extensive experiments across multiple LLM families and zero-shot benchmarks demonstrate that UniSVQ consistently outperforms state-of-the-art SQ methods and achieves performance comparable to advanced VQ methods, while providing higher inference throughput. Codes are publicly available at https://github.com/AI9Stars/UniSVQ.

With the commercialization of large language models (LLMs), weight-activation quantization has emerged to compress and accelerate LLMs, achieving high throughput while reducing inference costs. However, existing post-training quantization (PTQ) techniques for quantizing weights and activations of LLMs still suffer from non-negligible accuracy drops, especially on massive multitask language understanding. To address this issue, we propose Low-Rank Quantization (LRQ) - a simple yet effective post-training weight quantization method for LLMs that reconstructs the outputs of an intermediate Transformer block by leveraging low-rank weight-scaling matrices, replacing the conventional full weight-scaling matrices that entail as many learnable scales as their associated weights. Thanks to parameter sharing via low-rank structure, LRQ only needs to learn significantly fewer parameters while enabling the individual scaling of weights, thus boosting the generalization capability of quantized LLMs. We show the superiority of LRQ over prior LLM PTQ works under (i) 8-bit weight and per-tensor activation quantization, (ii) 4-bit weight and 8-bit per-token activation quantization, and (iii) low-bit weight-only quantization schemes. Our code is available at https://github.com/onliwad101/FlexRound_LRQ to inspire LLM researchers and engineers.

Large language models (LLMs) require immense resources for training and inference. Quantization, a technique that reduces the precision of model parameters, offers a promising solution for improving LLM efficiency and sustainability. While post-training quantization methods typically achieve 4-8 bits per parameter, recent research suggests that training LLMs with 1.58 bits per weight parameter from scratch can maintain model accuracy while greatly reducing memory requirements and energy consumption at inference time. Here, we investigate a training strategy for quantization-aware pre-training, where the models are first trained with 16-bit precision and then transition into 1.58-bit quantization-aware training. Our results on 11 downstream tasks show that this 16-to-1.58-bit training strategy is preferable over full 1.58-bit training and leaves models closer to those which have undergone 16-bit training. We further investigate the effects of retaining the optimizer state at the transition point and gradually phasing in quantization strength -- finding that both techniques alleviate the magnitude of loss spikes, but also that these effects can be compensated through further training.

Recent years have witnessed an increasing interest in deploying LLMs on resource-constrained devices, among which quantization has emerged as a promising lightweight technique that converts full-precision model weights and activations into lower-bit formats. Existing weight quantization approaches can be roughly divided into three categories: Post-Training Quantization (PTQ) that calibrates quantized parameters on a small dataset without retraining but suffers from severe performance degradation below 4-bit, Quantization-Aware Training (QAT) that searches low-bit parameters using surrogate gradients but demands substantial computational resources, and Quantization-Aware Distillation that integrates QAT with knowledge transfer from a full-precision teacher but manually selects features to distill and relies heavily on teacher-specific data. In this paper, we propose EdgeRazor, a lightweight framework for LLMs with mixed-precision and extremely low-bit weight quantization. The EdgeRazor framework contains three modules: Mixed-Precision Quantization-Aware Distillation for the fine-grained control of precision, Adaptive Feature Distillation that derives an n-bit student from its 16-bit teacher, and Entropy-Aware KL Divergence on both human-annotated and distilled datasets, whose forward-reverse balance is determined solely by the teacher's output distribution. Empirical investigations of EdgeRazor are conducted on base, instruction-tuned, and multimodal LLMs. Notably, EdgeRazor with 1.88-bit surpasses all contenders with the 3-bit precision, especially outperforms the leading 2-bit PTQ methods by 11.3 points, within a 4-10times lower training budget than the leading QAT approach. EdgeRazor delivers higher compression ratios at all bit width; the 1.58-bit Qwen3-0.6B reduces storage from 1.41 GB to 0.28 GB while accelerating decoding by 15.1times relative to the 16-bit baseline.

Recent advancements in machine learning achieved by Deep Neural Networks (DNNs) have been significant. While demonstrating high accuracy, DNNs are associated with a huge number of parameters and computations, which leads to high memory usage and energy consumption. As a result, deploying DNNs on devices with constrained hardware resources poses significant challenges. To overcome this, various compression techniques have been widely employed to optimize DNN accelerators. A promising approach is quantization, in which the full-precision values are stored in low bit-width precision. Quantization not only reduces memory requirements but also replaces high-cost operations with low-cost ones. DNN quantization offers flexibility and efficiency in hardware design, making it a widely adopted technique in various methods. Since quantization has been extensively utilized in previous works, there is a need for an integrated report that provides an understanding, analysis, and comparison of different quantization approaches. Consequently, we present a comprehensive survey of quantization concepts and methods, with a focus on image classification. We describe clustering-based quantization methods and explore the use of a scale factor parameter for approximating full-precision values. Moreover, we thoroughly review the training of a quantized DNN, including the use of a straight-through estimator and quantization regularization. We explain the replacement of floating-point operations with low-cost bitwise operations in a quantized DNN and the sensitivity of different layers in quantization. Furthermore, we highlight the evaluation metrics for quantization methods and important benchmarks in the image classification task. We also present the accuracy of the state-of-the-art methods on CIFAR-10 and ImageNet.

Deploying large language models (LLMs) in resource-constrained environments is hindered by heavy computational and memory requirements. We present LBLLM, a lightweight binarization framework that achieves effective W(1+1)A4 quantization through a novel three-stage quantization strategy. The framework proceeds as follows: (1) initialize a high-quality quantized model via PTQ; (2) quantize binarized weights, group-wise bitmaps, and quantization parameters through layer-wise distillation while keeping activations in full precision; and (3) training learnable activation quantization factors to dynamically quantize activations to 4 bits. This decoupled design mitigates interference between weight and activation quantization, yielding greater training stability and better inference accuracy. LBLLM, trained only using 0.016B tokens with a single GPU, surpasses existing state-of-the-art binarization methods on W2A4 quantization settings across tasks of language modeling, commonsense QA, and language understanding. These results demonstrate that extreme low-bit quantization of LLMs can be both practical and highly effective without introducing any extra high-precision channels or rotational matrices commonly used in recent PTQ-based works, offering a promising path toward efficient LLM deployment in resource-limited situations.

Quantization has become one of the most effective methodologies to compress LLMs into smaller size. However, the existing quantization solutions still show limitations of either non-negligible accuracy drop or system inefficiency. In this paper, we make a comprehensive analysis of the general quantization principles on their effect to the triangle of accuracy, memory consumption and system efficiency. We propose MixLLM that explores the new optimization space of mixed-precision quantization between output features based on the insight that different output features matter differently in the model. MixLLM identifies the output features with high salience in the global view rather than within each single layer, effectively assigning the larger bit-width to output features that need it most to achieve good accuracy with low memory consumption. We present the sweet spot of quantization configuration of algorithm-system co-design that leads to high accuracy and system efficiency. To address the system challenge, we design the two-step dequantization to make use of the int8 Tensor Core easily and fast data type conversion to reduce dequantization overhead significantly, and present the software pipeline to overlap the memory access, dequantization and the MatMul to the best. Extensive experiments show that with only 10% more bits, the PPL increasement can be reduced from about 0.5 in SOTA to within 0.2 for Llama 3.1 70B, while on average MMLU-Pro improves by 0.93 over the SOTA of three popular models. In addition to its superior accuracy, MixLLM also achieves state-of-the-art system efficiency.

Quantization is a practical technique for making large language models easier to deploy by reducing the precision used to store and operate on model weights. This can lower memory use and improve runtime feasibility on constrained hardware, which is especially relevant for users running models locally. Quantization in llama.cpp enables large language models to run on commodity hardware, but available formats are often evaluated inconsistently, making it hard to choose among schemes. We present a unified empirical study of the llama.cpp quantization on a single modern model, Llama-3.1-8B-Instruct (FP16, GGUF), covering 3-8 bit K-quant and legacy formats. We evaluate downstream task performance across standard reasoning, knowledge, instruction-following, and truthfulness benchmarks, and also measure perplexity and CPU throughput (prefill/decoding) alongside model size, compression, and quantization time. Ultimately, this work is a practical guide for choosing a llama.cpp quantization scheme, helping readers make informed, context-aware decisions for their intended use and resource budget.

Quantization has been widely adopted in LLM training and inference to reduce cost and improve efficiency. However, low-bit quantization of the attention module often introduces large errors at very low bit-widths, causing performance degradation. Existing methods mainly rely on smoothing techniques to handle outliers, while we propose a hybrid quantization design to better balance accuracy and efficiency. Specifically, we propose HyQuant, an efficient hybrid quantization framework for LLM attention. HyQuant quantizes most attention states into low-bit formats while retaining a small set of vertical-line tokens and local-window states in high precision. These accuracy-critical regions are selected using lightweight vertical-line-aware attention-pattern signals, reducing quantization error with limited overhead. In the Prefill stage, HyQuant uses a hybrid-precision quantized attention operator that preserves vertical-line tokens and a local sliding window in full precision while quantizing the remaining context. In the Decode stage, HyQuant applies the same principle to KV-cache compression and fuses KV dequantization with attention computation to improve memory and hardware efficiency. Across diverse tasks, models, and datasets, HyQuant maintains nearly lossless accuracy with an extremely simple design, demonstrating the efficiency and practical feasibility of hybrid quantization for LLM attention. Code is available at: https://github.com/jerrysfls/HyQuant .

Optimizer states are a major source of memory consumption for training neural networks, limiting the maximum trainable model within given memory budget. Compressing the optimizer states from 32-bit floating points to lower bitwidth is promising to reduce the training memory footprint, while the current lowest achievable bitwidth is 8-bit. In this work, we push optimizer states bitwidth down to 4-bit through a detailed empirical analysis of first and second moments. Specifically, we find that moments have complicated outlier patterns, that current block-wise quantization cannot accurately approximate. We use a smaller block size and propose to utilize both row-wise and column-wise information for better quantization. We further identify a zero point problem of quantizing the second moment, and solve this problem with a linear quantizer that excludes the zero point. Our 4-bit optimizers are evaluated on a wide variety of benchmarks including natural language understanding, machine translation, image classification, and instruction tuning. On all the tasks our optimizers can achieve comparable accuracy with their full-precision counterparts, while enjoying better memory efficiency.

Quantization has become a crucial step for the efficient deployment of deep neural networks, where floating point operations are converted to simpler fixed point operations. In its most naive form, it simply consists in a combination of scaling and rounding transformations, leading to either a limited compression rate or a significant accuracy drop. Recently, Gradient-based post-training quantization (GPTQ) methods appears to be constitute a suitable trade-off between such simple methods and more powerful, yet expensive Quantization-Aware Training (QAT) approaches, particularly when attempting to quantize LLMs, where scalability of the quantization process is of paramount importance. GPTQ essentially consists in learning the rounding operation using a small calibration set. In this work, we challenge common choices in GPTQ methods. In particular, we show that the process is, to a certain extent, robust to a number of variables (weight selection, feature augmentation, choice of calibration set). More importantly, we derive a number of best practices for designing more efficient and scalable GPTQ methods, regarding the problem formulation (loss, degrees of freedom, use of non-uniform quantization schemes) or optimization process (choice of variable and optimizer). Lastly, we propose a novel importance-based mixed-precision technique. Those guidelines lead to significant performance improvements on all the tested state-of-the-art GPTQ methods and networks (e.g. +6.819 points on ViT for 4-bit quantization), paving the way for the design of scalable, yet effective quantization methods.