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生成模型与 LLM 推理优化

XFP: Quality-Targeted Adaptive Codebook Quantization with Sparse Outlier Separation for LLM Inference

arXiv 2026-05-14

We introduce XFP, a dynamic weight quantizer for LLM inference that inverts the conventional workflow: the operator specifies reconstruction quality floors on per-channel cosine similarity (one strict floor for attention and shared experts, one lazy floor for routed-expert MoE); XFP determines codebook size, outlier budget, and packing per layer automatically -- no Hessian, no calibration data, no manual bit-width selection. Each weight matrix is decomposed into a sparse fp16 outlier residual and a dense sub-byte index tensor into a per-group learned codebook. Two storage modes share one auto-select frontend and one fused decode kernel: V2 (per-channel Lloyd) and V2a (shared library of L=32 codebooks per layer). On Qwen3.5-122B-A10B under V2, XFP reaches 138 tok/s single-stream decode on workstation hardware (RTX PRO 6000 Blackwell, TP=2) at 94.49% GSM8K strict-match (3 seeds, n=3957), and is 49% faster than Marlin INT4 at TP=1. For models that do not fit in the target memory envelope, we present the H-Process: a quality-driven iteration over the two cosine thresholds that finds the operating point at which the model just fits while still producing sensible output. Three constraints define its search space: the operator-set thresholds, an OOM boundary at quantize-on-load, and a garbage boundary in generation (cosine similarity steers; benches verify). On Qwen3.5-397B-A17B (512 routed experts/layer), the H-Process fits the full expert population into 2x96 GB at ~3.4 effective bits and delivers 100.9 tok/s long-output decode at 66.72% GSM8K strict-match on the full 1319-problem set (single seed at submission; multi-seed evaluation in progress), exceeding INT4 with routed-expert pruning on memory, throughput, and accuracy simultaneously.

HeatKV: Head-tuned KV-cache Compression for Visual Autoregressive Modeling

arXiv 2026-05-14

Visual Autoregressive (VAR) models have recently demonstrated impressive image generation quality while maintaining low latency. However, they suffer from severe KV-cache memory constraints, often requiring gigabytes of memory per generated image. We introduce HeatKV, a novel compression method that adapts cache allocation in each head based on its attention to previously generated scales. Using a small offline calibration set, the attention heads are ranked according to their attention scores over prior scales. Based on this ranking, we construct a static pruning schedule tailored to a given memory budget. Applied to the Infinity-2B model, HeatKV achieves \(2 \times\) higher compression ratio in memory allocation for KV cache compared to existing methods, while maintaining similar or better image fidelity, prompt alignment and human perception score. Our method achieves a new state-of-the-art (SOTA) for VAR model KV-cache compression, showcasing the effectiveness of fine-grained, head-specific cache allocation.

A Hardware-Aware, Per-Layer Methodology for Post-Training Quantization of Large Language Models

arXiv 2026-05-14

Scaled Outer Product (SOP) is a post-training quantization methodology for large language model weights, designed to deliver near-lossless fidelity at 4.5--6 bits per weight on hardware with per-layer LUT decode. The methodology combines per-layer search of fixed and dynamic codebook pairs selected by a per-block selection bit, signed per-block scales, activation-weighted cosine selection, and multiple-choice knapsack promotion of sensitive layers with outlier and sparse-residual correction. Fixed codebooks include NF4, BOF4, Split87, and SH4; per-layer optimized codebooks (DD4) are hosted in LUT SRAM. A new hardware-efficient LUT output format (HIF) is proposed to improve performance, energy, and cost. Across six open model families, the recommended FP6 operating point (E2M3sUE4M4, 6.5 bpw) achieves lower weight reconstruction error than the conventional per-layer-POT FP8 baseline (E4M3, 8.0 bpw) at 1.5 bpw lower storage cost, demonstrating that block-scaled small atoms with carefully chosen scale precision can replace conventionally-deployed FP8. Full evaluation across the 4.5--6 bpw range, including layer promotion and sparse residual correction, is reported in a companion paper.

An Interpretable Latency Model for Speculative Decoding in LLM Serving

arXiv 2026-05-14

Speculative decoding (SD) accelerates large language model (LLM) inference by using a smaller draft model to propose multiple tokens that are verified by a larger target model in parallel. While prior work demonstrates substantial speedups in isolated or fixed-batch settings, the behavior of SD in production serving systems remains poorly understood: request load varies over time, and effective batch size emerges from the serving system rather than being directly controlled or observed. In this work, we develop a simple and interpretable latency model for SD in LLM serving. We infer effective batch size from request rate using Little's Law and decompose per-request demand into load-independent and load-dependent components for prefill, drafting, and verification. We validate our model using extensive measurements from vLLM across verifier and drafter model sizes, prefill and decode lengths, request rates, draft lengths, and acceptance probabilities. The model accurately describes observed latency, explains why speedups often diminish as server load increases, and characterizes how draft length, acceptance rate, and verifier-drafter size shape latency across serving conditions, with implications for configuring SD in deployed systems. We further show how the framework extends to mixture of experts models, where sparse expert activation changes the effective service costs across load regimes. Together, our results provide a structured framework for understanding SD in real LLM serving systems.

HASTE: Training-Free Video Diffusion Acceleration via Head-Wise Adaptive Sparse Attention

arXiv 2026-05-14

Diffusion-based video generation has advanced substantially in visual fidelity and temporal coherence, but practical deployment remains limited by the quadratic complexity of full attention. Training-free sparse attention is attractive because it accelerates pretrained models without retraining, yet existing online top-\(p\) sparse attention still spends non-negligible cost on mask prediction and applies shared thresholds despite strong head-level heterogeneity. We show that these two overlooked factors limit the practical speed-quality trade-off of training-free sparse attention in Video DiTs. To address them, we introduce a head-wise adaptive framework with two plug-in components: Temporal Mask Reuse, which skips unnecessary mask prediction based on query-key drift, and Error-guided Budgeted Calibration, which assigns per-head top-\(p\) thresholds by minimizing measured model-output error under a global sparsity budget. On Wan2.1-1.3B and Wan2.1-14B, our method consistently improves XAttention and SVG2, achieving up to 1.93 times speedup at 720P while maintaining competitive video quality and similarity metrics.

Causal Forcing++: Scalable Few-Step Autoregressive Diffusion Distillation for Real-Time Interactive Video Generation

arXiv 2026-05-14

Real-time interactive video generation requires low-latency, streaming, and controllable rollout. Existing autoregressive (AR) diffusion distillation methods have achieved strong results in the chunk-wise 4-step regime by distilling bidirectional base models into few-step AR students, but they remain limited by coarse response granularity and non-negligible sampling latency. In this paper, we study a more aggressive setting: frame-wise autoregression with only 1--2 sampling steps. In this regime, we identify the initialization of a few-step AR student as the key bottleneck: existing strategies are either target-misaligned, incapable of few-step generation, or too costly to scale. We propose \textbf{Causal Forcing++}, a principled and scalable pipeline that uses \emph{causal consistency distillation} (causal CD) for few-step AR initialization. The core idea is that causal CD learns the same AR-conditional flow map as causal ODE distillation, but obtains supervision from a single online teacher ODE step between adjacent timesteps, avoiding the need to precompute and store full PF-ODE trajectories. This makes the initialization both more efficient and easier to optimize. The resulting pipeline, \ours, surpasses the SOTA 4-step chunk-wise Causal Forcing under the \textit{\textbf{frame-wise 2-step setting}} by 0.1 in VBench Total, 0.3 in VBench Quality, and 0.335 in VisionReward, while reducing first-frame latency by 50\% and Stage 2 training cost by \(\sim\)\(4\times\). We further extend the pipeline to action-conditioned world model generation in the spirit of Genie3. Project Page: https://github.com/thu-ml/Causal-Forcing and https://github.com/shengshu-ai/minWM .

CoReDiT: Spatial Coherence-Guided Token Pruning and Reconstruction for Efficient Diffusion Transformers

arXiv 2026-05-13

Diffusion Transformers (DiTs) deliver remarkable image and video generation quality but incur high computational cost, limiting scalability and on-device deployment. We introduce CoReDiT, a structured token pruning framework for DiTs across vision tasks. CoReDiT uses a linear-time spatial coherence score to estimate local redundancy in the latent token lattice and skips high coherence (redundant) tokens in self-attention. To maintain a dense representation and avoid visual discontinuities, we reconstruct skipped attention outputs via coherence-guided aggregation of spatially neighboring retained tokens. We further introduce a progressive, block-adaptive pruning schedule that increases pruning gradually and allocates larger budgets to blocks and denoising steps with higher redundancy. Across state-of-the-art diffusion backbones including PixArt-α and MagicDrive-V2, CoReDiT achieves up to 55% self-attention FLOPs reduction and inference speedups of 1.33x on cloud GPUs and 1.72x on mobile NPUs, while maintaining high visual quality. Notably, CoReDiT also increases on-device memory head-room, enabling higher-resolution generation.

Mistletoe: Stealthy Acceleration-Collapse Attacks on Speculative Decoding

arXiv 2026-05-13

Speculative decoding has become a widely adopted technique for accelerating large language model (LLM) inference by drafting multiple candidate tokens and verifying them with a target model in parallel. Its efficiency, however, critically depends on the average accepted length \(τ\), i.e., how many draft tokens survive each verification step. In this work, we identify a new mechanism-level vulnerability in model-based speculative decoding: the drafter is trained to approximate the target model distribution, but this approximation is inevitably imperfect. Such a drafter-target mismatch creates a hidden attack surface where small perturbations can preserve the target model's visible behavior while substantially reducing draft-token acceptability. We propose Mistletoe, a stealthy acceleration-collapse attack against speculative decoding. Mistletoe directly targets the acceptance mechanism of speculative decoding. It jointly optimizes a degradation objective that decreases drafter-target agreement and a semantic-preservation objective that constrains the target model's output distribution. To resolve the conflict between these objectives, we introduce a null-space projection mechanism, where degradation gradients are projected away from the local semantic-preserving direction, suppressing draft acceptance while minimizing semantic drift. Experiments on various speculative decoding systems show that Mistletoe substantially reduces average accepted length \(τ\), collapses speedup, and lowers averaged token throughput, while preserving output quality and perplexity. Our work highlights that speculative decoding introduces a mechanism-level attack surface beyond existing output robustness, calling for more robust designs of LLM acceleration systems.

Multi-Scale Dequant: Eliminating Dequantization Bottleneck via Activation Decomposition for Efficient LLM Inference

arXiv 2026-05-13

Quantization is essential for efficient large language model (LLM) inference, yet the dequantization step-converting low-bit weights back to high-precision for matrix multiplication has become a critical bottleneck on modern AI accelerators. On architectures with decoupled compute units (e.g., Ascend NPUs), dequantization operations can consume more cycles than the matrix multiplication itself, leaving the high-throughput tensor cores underutilized. This paper presents Multi-Scale Dequant (MSD), a quantization framework that removes weight/KV dequantization from the GEMM critical path. Instead of lifting low-bit weights to BF16 precision, MSD decomposes high-precision BF16 activations into multiple low-precision components, each of which can be multiplied directly with quantized weights via native hardware-accelerated GEMM. This approach shifts the computational paradigm from precision conversion to multi-scale approximation, avoiding INT8-to-BF16 weight conversion before GEMM. We instantiate MSD for two weight formats and derive tight error bounds for each. For INT8 weights (W4A16), two-pass INT8 decomposition achieves near 16 effective bits. For MXFP4 weights (W4A16), two-pass MXFP4 decomposition yields near 6.6 effective bits with error bound 1/64 per block surpassing single-pass MXFP8(5.24 bits) while maintaining the same effective GEMM compute time. We further derive closed-form latency and HBM traffic models showing that MSD avoids the Vector-Cube pipeline stall caused by dequantization and reduces KV cache HBM traffic by up to 2.5 times in attention. Numerical simulations on matrix multiplication and Flash Attention kernels confirm that MSD does not degrade accuracy compared to dequantization baselines, and in many settings achieves lower L2 error.

STOP: Structured On-Policy Pruning of Long-Form Reasoning in Low-Data Regimes

arXiv 2026-05-13

Long chain-of-thought (Long CoT) reasoning improves performance on multi-step problems, but it also induces overthinking: models often generate low-yield reasoning that increases inference cost and latency. This inefficiency is especially problematic in low-data fine-tuning regimes, where real applications adapt reasoning models with limited supervision and cannot rely on large-scale teacher distillation or heavy test-time control. To address this, we propose STOP (Structured On-policy Pruning), an on-policy algorithm for analyzing and pruning long-form reasoning traces. STOP constructs self-distilled traces from the model. Then it maps each trace into a structured reasoning interface through node segmentation, taxonomy annotation, and reasoning-tree construction. On top of this interface, we introduce ECN (Earliest Correct Node), which retains the shortest prefix ending at the earliest node that both functions as an answering conclusion and yields the correct final answer, removing redundant post-solution reasoning while preserving semantic continuity. Experiments on DeepSeek-R1-Distill-Qwen-7B and DeepSeek-R1-Distill-LLaMA-3-8B across GSM8K, Math 500, and AIME 2024 show that STOP reduces generated tokens by 19.4-42.4% while largely preserving accuracy in low-data fine-tuning. Beyond efficiency, our analyses show that STOP induces much smaller distributional shift than teacher-guided pruning, improves the structural efficiency of generated reasoning, and reallocates reasoning effort away from redundant verification and backtracking toward more productive exploration.

AdaFocus: Adaptive Relevance-Diversity Sampling with Zero-Cache Look-back for Efficient Long Video Understanding

arXiv 2026-05-13

Long video understanding is heavily bottlenecked by a rigid one-shot paradigm: existing methods either densely encode videos at prohibitive memory and latency costs, or aggressively compress them into sparse frame sets that irreversibly discard fine-grained evidence needed for downstream reasoning. Consequently, current models struggle to simultaneously balance temporal coverage, visual details, and computational efficiency. We propose AdaFocus, an efficient framework that rethinks long-video understanding as progressive evidence acquisition rather than one-pass encoding. AdaFocus relies on two tightly coupled components. First, a Query-Aware Adaptive Relevance-Diversity sampler (AdaRD) produces a compact yet informative video preview, adaptively switching to global clustering when the query lacks reliable local grounding. Second, instead of caching exhaustive frame sequences in memory, AdaFocus introduces an uncertainty-triggered refinement mechanism. It performs targeted look-back only when the model is not confident, retrieving high-resolution evidence directly from disk via a zero-cache I/O design. This turns discarded visual details from an irreversible loss into on-demand recoverable evidence without paying the cost of exhaustive preloading. Experiments on seven standard long-video benchmarks show that AdaFocus delivers a substantially better efficiency-accuracy trade-off than strong baselines. Compared with conventional dense encoding, AdaFocus achieves improved task performance (e.g., +2.59 accuracy on VideoMME, +8.39 mIoU on Charades-STA over single-pass inference) while reducing visual token consumption by ~33x and eliminating the need for in-memory frame pre-caching through its zero-cache disk retrieval design. These findings suggest that progressive preview combined with zero-cache evidence refinement is a highly effective paradigm for scalable multimedia reasoning.

Test-time Sparsity for Extreme Fast Action Diffusion

arXiv 2026-05-13

Action diffusion excels at high-fidelity action generation but incurs heavy computational costs owing to its iterative denoising nature. Despite current technologies showing promise in accelerating diffusion transformers by reusing the cached features, they struggle to adapt to policy dynamics arising from diverse perceptions and multi-round rollout iterations in open environments. We propose test-time sparsity to tackle this challenge, which aims to accelerate action diffusion by dynamically predicting prunable residual computations for each model forward at test time. However, two bottlenecks remain in this paradigm: 1) repetitive conditional encoding and pruning offset most potential speed gains, and 2) the features cached from previous denoising timesteps cannot constrain large pruning errors under aggressive sparsity. To address the first bottleneck, we design a highly parallelized inference pipeline that minimizes the non-decoder delay to milliseconds. Specifically, we first design a lightweight pruner that shares the encoder with the diffusion transformer. Then, we decouple the encoding and pruning from the autoregressive denoising loop by processing all denoising timesteps in parallel, and overlap the pruner with the decoder forward inference through asynchronism. To overcome the second bottleneck, we introduce an omnidirectional reusing strategy, which achieves 95% sparsity by selectively reusing features cached from the current forward, previous denoising timesteps, and earlier rollout iterations. To learn the rollout-level reusing strategies, we sample a few action trajectories to supervise the sparsified diffusion step by step. Extensive experiments demonstrate that our method reduces FLOPs by 92% and accelerates action generation by 5x, achieving lossless performance with an inference frequency of 47.5 Hz. Our code is available at https://github.com/ky-ji/Test-time-Sparsity.

Provable Quantization with Randomized Hadamard Transform

arXiv 2026-05-13

Vector quantization via random projection followed by scalar quantization is a fundamental primitive in machine learning, with applications ranging from similarity search to federated learning and KV cache compression. While dense random rotations yield clean theoretical guarantees, they require \(Θ(d^2)\) time. The randomized Hadamard transform \(HD\) reduces this cost to \(O(d \log d)\), but its discrete structure complicates analysis and leads to weaker or purely empirical compression guarantees. In this work, we study a variant of this approach: dithered quantization with a single randomized Hadamard transform. Specifically, the quantizer applies \(HD\) to the input vector and subtracts a random scalar offset before quantizing, injecting additional randomness at negligible cost. We prove that this approach is unbiased and provides mean squared error bounds that asymptotically match those achievable with truly random rotation matrices. In particular, we prove that a dithered version of TurboQuant achieves mean squared error \(\bigl(π\sqrt{3}/2 + o(1)\bigr) \cdot 4^{-b}\) at \(b\) bits per coordinate, where the \(o(1)\) term vanishes uniformly over all unit vectors and all dimensions as the number of quantization levels grows.

KVServe: Service-Aware KV Cache Compression for Communication-Efficient Disaggregated LLM Serving

arXiv 2026-05-13

LLMs are widely adopted in production, pushing inference systems to their limits. Disaggregated LLM serving (e.g., PD separation and KV state disaggregation) improves scalability and cost efficiency, but it also turns KV into an explicit payload crossing network and storage boundaries, making KV a dominant end-to-end bottleneck. Existing KV compression are typically static runtime configurations, despite production service context varies over time in workload mix, bandwidth, and SLO/quality budgets. As a result, a fixed choice can be suboptimal or even increase latency. We present \emph{KVServe}, the first service-aware and adaptive KV communication compression framework for disaggregated LLM serving: KVServe (1) unifies KV compression into a modular strategy space with new components and cross-method recomposition; (2) introduces Bayesian Profiling Engine that efficiently searches this space and distills a 3D Pareto candidate set, reducing \(50\times\) offline search overhead; and (3) deploys a Service-Aware Online Controller that combines an analytical latency model with a lightweight bandit to select profiles under constraints and correct offline-to-online mismatch. Integrated into vLLM and evaluated across datasets, models, GPUs and networks, KVServe achieves up to \(9.13\times\) JCT speedup in PD-separated serving and up to \(32.8\times\) TTFT reduction in KV-disaggregated serving.

AnyFlow: Any-Step Video Diffusion Model with On-Policy Flow Map Distillation

arXiv 2026-05-13

Few-step video generation has been significantly advanced by consistency distillation. However, the performance of consistency-distilled models often degrades as more sampling steps are allocated at test time, limiting their effectiveness for any-step video diffusion. This limitation arises because consistency distillation replaces the original probability-flow ODE trajectory with a consistency-sampling trajectory, weakening the desirable test-time scaling behavior of ODE sampling. To address this limitation, we introduce AnyFlow, the first any-step video diffusion distillation framework based on flow maps. Instead of distilling a model for only a few fixed sampling steps, AnyFlow optimizes the full ODE sampling trajectory. To this end, we shift the distillation target from endpoint consistency mapping \((z_{t}\rightarrow z_{0})\) to flow-map transition learning \((z_{t}\rightarrow z_{r})\) over arbitrary time intervals. We further propose Flow Map Backward Simulation, which decomposes a full Euler rollout into shortcut flow-map transitions, enabling efficient on-policy distillation that reduces test-time errors (i.e., discretization error in few-step sampling and exposure bias in causal generation). Extensive experiments across both bidirectional and causal architectures, at scales ranging from 1.3B to 14B parameters, demonstrate that AnyFlow achieves performance matches or surpasses consistency-based counterparts in the few-step regime, while scaling with sampling step budgets.

Pyramid Forcing: Head-Aware Pyramid KV Cache Policy for High-Quality Long Video Generation

arXiv 2026-05-13

Autoregressive video generation enables streaming and open-ended long video synthesis, but still suffers from long-term degradation caused by accumulated errors. Existing KVCache strategies usually apply unified historical-frame retention, implicitly assuming homogeneous historical dependencies across attention heads. We revisit historical-frame attention and reveal three distinct head types: Anchor Heads require broad long-range context, Wave Heads exhibit periodic temporal dependencies, and Veil Heads focus on initial and adjacent frames. Based on this finding, we propose Pyramid Forcing, a head-aware pyramidal KVCache framework that identifies head types offline, assigns behavior-specific cache policies, and supports heterogeneous cache lengths via efficient ragged-cache attention. Experiments on Self Forcing and Causal Forcing show that Pyramid Forcing consistently improves long-horizon generation quality on VBench-Long, increasing the 60-second Self Forcing score from 77.87 to 81.21 while enhancing motion dynamics, visual fidelity, and semantic consistency. Project: https://if-lab-pku.github.io/Pyramid-Forcing/.

Kairos: A Scalable Serving System for Physical AI

arXiv 2026-05-12

Physical AI is experiencing rapid growth with frontier foundation models increasing its capabilities across general environments. Physical AI tasks are characterized by inference properties that are markedly different from digital AI. They consist of multiple rounds of inference and action execution, generating a chunk of actions in each inference round, and asynchronously interleaving inference and execution. This makes existing digital AI serving systems unsuited for physical AI; a shortcoming that is critical for enabling their wide adoption, considering their size and the scale of the robot fleets they have to serve. To fill this gap, we design Kairos, the first multi-robot serving system that makes the generate-execute loop a first-class citizen, with active involvement in the execution phase. Across a wide range of physical AI models and robots, Kairos reduces the average end-to-end task latency by 31.8--66.5% over state-of-the-art digital AI serving practices, with gains scaling with the robot fleet size.

SOAR: Scale Optimization for Accurate Reconstruction in NVFP4 Quantization

arXiv 2026-05-12

NVFP4 has recently emerged as an efficient 4-bit microscaling format for large language models (LLMs), offering superior numerical fidelity with native hardware support. However, existing methods often yield suboptimal performance due to inflexible scale selection and the coupled treatment of quantization and dequantization scales. To address these issues, we propose Scale Optimization for Accurate Reconstruction (SOAR), a novel post-training quantization framework that improves the accuracy of NVFP4 quantization. At its core, SOAR features Closed-form Joint Scale Optimization (CJSO), which jointly optimizes global and block-wise scales via analytical solutions derived from reconstruction error minimization. Furthermore, it incorporates Decoupled Scale Search (DSS). DSS decouples the high-precision quantization scale from its constrained dequantization counterpart, and performs discrete search to mitigate precision loss from scale quantization. Extensive experiments across multiple LLMs show that our method consistently outperforms existing NVFP4 quantization baselines, achieving superior accuracy under the same memory footprint with no additional hardware overhead. The code and models will be available at https://github.com/steven-bao1/SOAR.

Enhancing Instruction Prefetching via Cache and TLB Management

arXiv 2026-05-12

Modern server workloads exhibit massive instruction footprints that heavily pressure the processor front-end, making L1 instruction (L1I) prefetching critical for sustaining performance. However, this paper shows that current L1I prefetchers fail to reach their full potential due to two key limitations. First, L1I prefetches crossing page boundaries require address translation before issuance, and translation latency reduces prefetch timeliness. Second, the reuse behavior of code lines fetched by L1I prefetches is highly heterogeneous: while some lines are reused many times, others are dead-on-arrival. This paper introduces Instruction Prefetch-Centric Cache and TLB Management (IP-CaT), the first microarchitectural framework jointly optimizing TLB and cache management for L1I prefetching. IP-CaT consists of two components: (i) the translation Prefetch Buffer (tPB), a small structure colocated with the second-level TLB (sTLB) that stores page table entries fetched by page-crossing L1I prefetches, reducing translation overheads; and (ii) the Trimodal Instruction Prefetch Replacement Policy (TIPRP), a decision-tree-based L2 cache replacement policy specialized for lines fetched by L1I prefetches. We evaluate IP-CaT with three state-of-the-art L1I prefetchers: EPI, FNL+MMA, and Barca. Across 105 contemporary server workloads, IP-CaT consistently improves performance. For example, IP-CaT+EPI achieves an 8.7% geomean speedup over EPI alone. We further show that IP-CaT outperforms state-of-the-art instruction TLB prefetching, advanced TLB replacement (CHiRP), and state-of-the-art code-aware, prefetch-aware, and general-purpose cache replacement policies, including Emissary, SHiP++, and Mockingjay.

MuonQ: Enhancing Low-Bit Muon Quantization via Directional Fidelity Optimization

arXiv 2026-05-12

The Muon optimizer has emerged as a compelling alternative to Adam for training large language models, achieving remarkable computational savings through gradient orthogonalization. However, Muon's optimizer state is more sensitive to quantization errors: because the orthogonalization discards the magnitudes of singular values and retains only directional information, even small quantization errors in singular vector directions are amplified in the update. In this work, we propose MuonQ, a low-bit Muon training framework built on the principle of directional fidelity optimization. First, we apply a pre-quantization normalization so that each step introduces quantization errors of the same magnitude, preventing the accumulated error from developing a preferred direction. Second, we introduce a structural decomposition that separately quantizes the dominant singular components via power iteration, ensuring that quantization errors perturb only singular value magnitudes rather than rotating singular vector directions. Third, we adopt \(μ\)-law companding quantization to allocate higher resolution to densely packed momentum values, shifting the quantization objective from outlier preservation to dense-region distinguishability. Together, these techniques enable stable 4-bit quantization of Muon's optimizer states. Pre-training experiments on GPT-style and LLaMA-style models demonstrate that MuonQ at 4-bit precision closely matches full-precision Muon in both training loss and downstream task accuracy, while reducing optimizer state memory by up to 7.3 \(\times\). Our code is available at https://github.com/YupengSu/MuonQ.