Rotation-Based Quantization

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4 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

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Latest papers 36

Oct 6, 2026cs.LG

ApexQuant: Data-Free Elastic Quantization by Residual Re-Isotropization

We introduce ApexQuant, a calibration-free quantization method that recursively re-quantizes the residual error, serving as a refinement layer on top of existing quantizers. We establish that a fresh random rotation returns each residual to the uniform distribution on the hypersphere, which characterizes the rate of progressive error decay across successive passes. This result lets us determine, before any weight is read, how many passes a layer needs for a target weight-space error. Every prefix is itself a valid lower-rate model, so one artifact serves several precisions. We instantiate ApexQuant with three interchangeable stages, scalar,

E_8

and trellis, and validate it on four open-weight LLMs and on Earth-observation and medical domains where in-distribution data is often unattainable as imagery arrives under restrictive licences or due to patient material under privacy constraints. Progressive re-isotropization comes within a few percent of full precision at four bits and gives the best two-bit arm we measure, in a completely data-free setting.

Aksel Fristrup, Sumit Pandey, Ankit Kariryaa

Henselian (henselian.com) · Department of Computer Science University of Copenhagen Denmark · Towards Deep Learning

LLM Quantization Rotation-Based Quantization Low-Bit Quantization Neural Network Quantization

Sep 28, 2026cs.LG

ThinQuant: Scalable Rotation Learning for Weight and Activation Quantization of LLMs

Learned rotations play an important role in enabling low-bit weight and activation quantization of large language models by smoothing outliers in the activation distribution. State-of-the-art approaches include gradient-based procedures such as SpinQuant and computationally friendlier gradient-free approaches such as DartQuant, but both remain hard to scale to the largest architectures. To address the computational bottlenecks in gradient-free rotation learning, we introduce two ideas for efficiency, (i) a data selection procedure which reduces the required number of calibration data points, and (ii) an exact reduction of the associated optimization on this reduced calibration set. Our data selection procedure exploits the geometric structure of the convex hull of the activations. Using this idea, we show that a carefully selected calibration set with several orders of magnitude fewer activations than state-of-the-art rotation-based methods can match their performance in low-bit quantization settings. Under this extreme data efficiency, the selected activations span an

r

-dimensional subspace with

r<d

, making optimization over a

d\times d

rotation equivalent to optimizing a

d\times r

matrix on the Stiefel manifold. We solve this reduced problem using an efficient ADMM algorithm that iteratively employs thin matrix updates at every step, hence the name ThinQuant. For Llama-3-70B with W4A4KV4 quantization, ThinQuant completes the entire rotation calibration in under 12 minutes and achieves a WikiText-2 perplexity of 5.63, compared with 7.55 for DartQuant, which requires 111 minutes. Unlike SpinQuant and DartQuant, ThinQuant also scales to Llama-3.1-405B on a single H200 GPU, completing rotation calibration in just over 2 hours and achieving WikiText-2 perplexity of 2.97 at W4A4, compared with 3.48 for GPTAQ+QuaRoT.

Mehdi Makni, Ryan Lucas, Rahul Mazumder

Operations Research Center Massachusetts Institute of Technology

LLM Quantization Rotation-Based Quantization Activation Quantization Low-Bit Quantization

Sep 28, 2026cs.LG

TORQUE: Optimizing What (not) to Quantize Before and After Rotation

Uniform random rotations are an effective preprocessing step for quantization: they make normalized coordinate distributions approximately Gaussian, enabling the use of codebooks optimized offline. We introduce TORQUE, a framework that improves on previous quantization works that use random rotations by jointly optimizing how many and which coordinates to preserve at high precision both before and after rotation, under a fixed overall expected bit budget. Intuitively, before rotation, preserving large input coordinates at high precision can reduce overall error by preventing the rotation from spreading their values across many coordinates. Likewise, after rotation, preserving a small fraction of the largest-magnitude coordinates at high precision allows the remaining values to be quantized more accurately using codebooks optimized offline for the resulting truncated Gaussian distribution. We derive a quantization error upper bound and prove that top-

k

pre-rotation retention minimizes it for each

k

. This reduces the search over coordinate subsets to an optimization over

k

, enabling a fast optimizer that uses offline codebooks and parallel parameter selection for practical implementation. We demonstrate an improved tradeoff between reconstruction accuracy and storage cost through numerical evaluation under the Gaussian model and experiments on nearest-neighbor retrieval, KV-cache compression, and activation compression.

Ran Ben Basat, Michael Mitzenmacher, Shay Vargaftik

University College London · Harvard University · VMware Research by Broadcom

Rotation-Based Quantization Vector Quantization Activation Quantization Low-Bit Quantization Neural Network Quantization

Sep 28, 2026cs.CV

SubRot: Signed Gradient Subspace Calibration for VLM Rotation Quantization

Post-training quantization reduces the deployment cost of vision-language models (VLMs), but preserving multimodal capabilities at low bit widths remains challenging. Existing methods rely on modality- or token-level gradient statistics, which are susceptible to cross-sample variations in visual-to-textual token ratios and the positions of visual information, limiting statistical stability. Moreover, overly coarse aggregation through absolute values and averaging discards gradient signs and channel-wise differences, limiting the separation of modality-specific sensitivities. In contrast, the channel space provides a shared coordinate system across samples, making it a more natural basis for capturing stable task-sensitive structures. We therefore propose SubRot, a signed gradient subspace calibration method for VLM rotation quantization. Through eigendecomposition of the empirical Fisher matrix of activation gradients, SubRot identifies a sensitive channel subspace with three properties: cross-sample stability, clear sensitivity separation, and consistent signed effects on the autoregressive loss along certain directions. Guided by a local Taylor expansion, SubRot combines signed first-order guidance along sign-stable directions with second-order constraints along the remaining sensitive directions, while retaining MSE for overall reconstruction quality. This objective steers quantization errors toward loss-decreasing directions while controlling their magnitude. Experiments on five VLMs across five benchmarks show consistent average-score improvements over FlatQuant under W4A6 and W4A4, reaching 1.4 percentage points on LLaVA-NeXT-7B. Under W4A4, average accuracy degradation from FP16 remains within 1.4 percentage points across all evaluated models, while LLaVA-v1.5-13B exceeds its FP16 average score by 0.4 percentage points.

Zhenhao Shang, Haizhao Jing, Haokui Zhang +4

Northwest Polytechnical University · Nanjing University of Science and Technology · Intellifusion +1

VLM Quantization Rotation-Based Quantization VLM Calibration Post-Training Quantization

Sep 8, 2026cs.IT

A Note on Scaling in Randomly Rotated Quantization and Its Connection to the CDEF +1 Pythagorean Relation

Quantization schemes based on randomized rotations have recently received renewed attention, including the roles of MMSE and unbiased reconstruction scalings. In this note, we point out the connection to classical results in statistical signal processing and communication theory. Specifically, the two reconstruction scales used in the EDEN line of work admit a natural interpretation as finite-dimensional, realization-dependent counterparts of the Wiener and unbiased coefficients in the classical CDEF formulation. At finite blocklength, the CDEF +1 relation holds pointwise for each rotation realization as an exact geometric (Pythagorean) identity, but does not hold after averaging the distortions over the rotation. The classical SNR relation

\sf{SNR}_{\rm MMSE}=\sf{SNR}_{\rm MMSE,U}+1

is recovered as

d\to\infty

: once the overall scale is handled separately, the empirical coordinate statistics of a randomly rotated vector approach their i.i.d. Gaussian counterparts, and the rotation-dependent quantities concentrate. Importantly, EDEN goes beyond this classical correspondence: for every finite

d

, its Haar-rotation formulation guarantees exact conditional unbiasedness, a stronger property than the second-order notion of unbiasedness in CDEF. We further comment on two distinct roles random rotations play in quantization: one is approximate Gaussianization of the coordinates; the other is decorrelation of reconstruction errors across quantization branches.

Uri Erez

School of Electrical Engineering Tel Aviv University Tel Aviv, Israel

Rotation-Based Quantization

Aug 31, 2026cs.LG

RSLM: Training-Free Vector Quantization for Approximate Nearest Neighbor Search

By introducing RSLM (Rotated Scaled Lloyd-Max), a family of training-free vector quantization codecs compressing embeddings to 1--4 bits per dimension, we reduce memory cost and memory bandwidth of a typical large-scale Approximate Nearest Neighbor (ANN) search system, while reducing its complexity and keeping or improving recall across multiple benchmark datasets. State-of-the-art systems filter candidates using coarse partitions, approximately score them to narrow the set, and then rescore the best with higher precision representations (often >=8 bits per dimension). Our relativized codecs can bring this down to 2--4 bits per dimension. We use the properties of the ANN system to encode residual vectors instead of full vectors, both for the approximate scoring phase and the rescoring phase. Since Maximum Inner Product Search (MIPS) is very sensitive to vector norms, we correct the

L_2

norms of quantized vectors. Our major innovation is that we correct the

L_2

norm of the final reconstructed vector rather than just the residual. Our rescaling replaces more complicated schemes, such as Anisotropic loss. The residualization scheme gives us a more favorable quality vs size trade-off than generic quantization methods. Our high-performance implementation leverages a block-wise cascaded Fast Walsh-Hadamard Transform (FWHT) with linear-like complexity, AVX SIMD-optimized codebooks, and a steganographic encoding of scaling factors for perfect cache-line alignment.

Rastislav Lenhardt, Teodora Dobos, Thomas Vecchiato +2

Google Zurich, Switzerland · Technical University of Munich Munich, Germany · University of Copenhagen Copenhagen, Denmark +1

Rotation-Based Quantization Vector Quantization Embedding Compression Low-Bit Quantization Approximate Nearest Neighbor Search

Aug 13, 2026cs.LG

When Local Variance Optimality Is Not Enough: RoPE-Aligned Q/K Rotations for Dynamic 4-Bit Quantisation

Rotation-based post-training quantisation commonly applies an orthogonal transform across an entire attention head to reduce outlier-induced error. RoPE instead partitions each head into two-dimensional frequency pairs, raising the question of whether a transform respecting this decomposition can improve on full-head mixing. Prior work has established the per-pair rotations that commute with RoPE. We state the converse result that, for distinct frequencies, no other single-head orthogonal map commutes with RoPE. For the head-shared parameterisation used in our experiments, we then derive the rotation angle that minimises the larger channel variance under a pooled-covariance, position-averaged surrogate and verify that the implementation attains its analytic minimum. The evaluated head-shared pairwise configuration does not improve accuracy in the tested dynamic W4A4KV4 setting. Across four checkpoints, replacing the full-head Hadamard with this configuration increases perplexity at both short and long context lengths. Composing the pairwise rotation with the Hadamard satisfies the selected

\pm0.05

-PPL interval criterion under the default estimator. Estimating the shared angle from K alone improves pairwise-only on every checkpoint but does not close its gap to full-head mixing. The analytic objective controls a position-averaged second moment of a pooled calibration covariance, whereas the dynamic quantiser sets its step from a tokenwise group range. The pairwise transform also has only two-channel mixing support. Along a controlled interpolation from two-channel to full-head mixing, K range, relative quantisation error, and perplexity degradation decrease as support increases. These results show that optimality for a structured surrogate need not reduce quantisation error when the surrogate and mixing support are misaligned with the quantiser's scale-setting statistic.

Shuhan Wang, Yilin Luo, Nan Xu +1

LLM Quantization 4-Bit Quantization Rotation-Based Quantization Post-Training Quantization Neural Network Quantization

Aug 8, 2026cs.NE

RotaryQuant: Fitting 120B MoE Models on Consumer Hardware via Fused Compressed-Space Attention

Large mixture-of-experts (MoE) language models with 26--120 billion parameters exceed the memory capacity of consumer devices through three simultaneous pressures: resident weight matrices, key-value (KV) cache state that grows linearly with context, and dozens of expert sublayers that must be paged on demand. We present RotaryQuant, a three-axis compression system that addresses all three. Mixed-precision weight quantization assigns bit-widths by architectural role: 4-bit for dense layers, 2-bit for routed experts, and 8-bit for the shared expert whose high activation kurtosis resists aggressive compression. LRU expert offloading pages non-resident experts to disk under genuine memory pressure. The novel axis is IsoQuant, a KV cache compression method that applies a Walsh--Hadamard transform followed by block-diagonal SO(4) rotations to isotropize activation distributions before 3-bit scalar quantization, requiring

O(d \log d)

operations and 256 stored parameters per head versus

O(d^2)

and 16{,}384 for dense rotation methods. A fused four-kernel Metal GPU pipeline performs attention directly on packed 3-bit tensors without materializing full-precision KV state---a different execution model, not just a quantization scheme. The combined system fits Gemma 4-26B-A4B and Qwen3-30B-A3B within a 16,GB budget and Nemotron-H 120B within 32,GB, running interactively at 9--19 tok/s with near-zero perplexity degradation (

Δ

PPL

\leq +0.0012

) and 100% retrieval accuracy at 32K context.

Anthony. Lui, Mohamed. Elsaied, N. P. Savani

Cognizant AI & Analytics, London, UB8 3PH, UK · Southern Methodist University (SMU), Engineering Management, Lyle School of Engineering, Dallas, TX, USA · Cognizant AI Lab, Responsible AI Office, San Francisco, USA +1

Expert Offloading Mixture-of-Experts Language Models Rotation-Based Quantization LLM Inference Acceleration Mixture-of-Experts Quantization Attention Quantization+1

Aug 5, 2026cs.LG

Beyond Rotations: AuroOFT for Expressive Quantized Orthogonal Fine-Tuning

Quantized orthogonal fine-tuning (qoft) enables parameter-efficient adaptation of low-bit language models by learning structured activation rotations before frozen quantized weights. However, its task-specific updates remain constrained to linear orthogonal transformations, limiting input-dependent nonlinear corrections. We introduce AuroOFT, which keeps qoft as a stable quantization-compatible branch while attaching a zero-start gated low-rank nonlinear residual to each adapted linear layer. AuroOFT maps activations into an RMS-normalized compact latent space and uses adaptive nonlinear bases with bounded or token-dependent gating. The zero-initialized up projection makes AuroOFT functionally identical to qoft at initialization, while orthogonality remains a branch-level stability property rather than a property of the combined nonlinear layer. Under matched data, optimization, decoding, and parser protocols, AuroOFT improves Macro-6 over matched qoft by 1.30-2.70% on the 1.5B/3B Qwen2.5 settings, exceeds QLoRA by 6.52-10.62%, and saves 32.3-44.7% trainable parameters relative to QLoRA in representative scales. The small exam-style multiple-choice math set is treated only as a protocol-sensitivity diagnostic. Our code is available at the anonymous repository: https://anonymous.4open.science/r/AuroOFT-F3FD.

Yue Han, Dianlin Wang

College of Systems Engineering, National University of Defense Technology · College of Computer Science and Technology, National University of Defense Technology

LLM Quantization Fine-Tuning Rotation-Based Quantization Adapter Tuning Parameter-Efficient Fine-Tuning

Aug 3, 2026cs.LG

Output-Aware Rotation for INT2 KV-Cache Quantization

The key-value (KV) cache has become a major memory and bandwidth bottleneck in long-context large language model inference, making ultra-low-bit quantization increasingly important. However, existing rotation-based INT2 methods optimize cache statistics or proxy errors before the complete attention readout, even though the model is ultimately affected by the error propagated through attention and the output projection

W_O

. To address this mismatch, we propose \textit{OptR}, an output-aware rotation method that minimizes post-

W_O

attention-output error. OptR decomposes the post-

W_O

attention-output error into key- and value-induced terms and learns per-head orthogonal corrections through the full INT2 quantization and attention path. OptR further applies an attention-equivalent key reparameterization to reduce large channel-wise offsets without changing the softmax distribution. Across three models and five reasoning and coding benchmarks, OptR consistently improves both QuaRot and OSCAR and strengthens long-context retrieval, while preserving the paged KV-cache format with negligible inference overhead.

Vincent-Daniel Yun, Woosang Lim, Minsoo Cheong +4

University of Southern California · Seoul National University · Inha University

LLM Inference KV Caching Rotation-Based Quantization Attention Quantization KV-Cache Quantization Low-Bit Quantization+1

Jul 30, 2026cs.AR

LightRot: A Light-Weighted Rotation Scheme and Architecture for Accurate Low-Bit Large Language Model Inference

As large language models (LLMs) continue to demonstrate exceptional capabilities across various domains, the challenge of achieving energy-efficient and accurate inference becomes increasingly critical. This work presents LightRot, a lightweight rotation scheme and dedicated hardware accelerator designed for low-bit LLM inference. The proposed architecture integrates Grouped Local Rotation (GLR) and Outlier Direction Aligning (ODA) algorithms with a hierarchical Fast Hadamard Transform (FHT)-based rotation unit to address key challenges in low-bit quantization, including the energy overhead of rotation operations. The proposed accelerator, implemented in a 28nm CMOS process, achieves a peak energy efficiency of 27.4 TOPS/W for 4-bit inference, surpassing prior state-of-the-art designs. Unlike conventional approaches that rely on higher-precision inference or evaluate on basic language modeling tasks like GPT-2, LightRot is optimized for advanced models such as LLaMA2-13B and LLaMA3-8B. Its performance is further validated on MT-Bench, demonstrating robust applicability to real-world conversational scenarios and redefining benchmarks for chat-based AI systems. By synergizing algorithmic innovations and hardware efficiency, this work sets a new paradigm for scalable, low-bit LLM inference, paving the way for sustainable AI advancements.

Sangjin Kim, Yuseon Choi, Jungjun Oh +2

PIM Semiconductor Design Research Center (AI-PIM), Daejeon 34141, South Korea

LLM Quantization AI Accelerator Inference Rotation-Based Quantization LLM Inference Acceleration Low-Bit Quantization

Jul 30, 2026cs.AR

GyRot: Leveraging Hidden Synergy between Rotation and Fine-grained Group Quantization for Low-bit LLM Inference

Low-bit quantization is essential for efficient LLM inference, and both rotation and fine-grained group quantization have shown individual promise. However, their combination often leads to accuracy degradation or hardware overhead due to a mismatch between the global nature of rotation and the localized behavior of group scaling. We propose GyRot, a quantization framework and hardware accelerator that bridges this gap through algorithm-hardware co-design. GyRot introduces Coarse Rotation, Fine Grouping (CoRFiG) and Harmonic-Aligned Permutation (HAP) to enable cooperative integration of rotation and group quantization, enhancing quantizability while relaxing scaling factor precision. To further reduce hardware cost, we reformulate asymmetric quantization and introduce a zero-point rounding strategy that enables fully integer dequantization. Implemented on an INT4-based tensor PE architecture, GyRot achieves state-of-the-art 4-bit accuracy across LLaMA-family models, while delivering up to 3.4x speedup and 3.6x energy efficiency over baseline LLM accelerators. These results validate GyRot's practical effectiveness for scalable and energy-efficient LLM deployment.

Sangjin Kim, Yuseon Choi, Byeongcheol Kim +2

School of Electrical Engineering, Korea Advanced Institue of Science and Technology (KAIST)

AI Accelerator Inference Rotation-Based Quantization LLM Inference Acceleration Low-Bit Quantization Neural Network Quantization

Jul 22, 2026cs.LG

GaugeQuant: Online Learning of Quantization-Optimal Bases from LLM Symmetries

Transformers are known to have internal continuous symmetries that leave outputs invariant, while modifying quantization. GaugeQuant leverages this in-training by introducing a LogSumExp term to the loss that breaks the symmetries, thus selecting a basis that minimizes activation outliers. A stop-gradient operator ensures that only rotation matrices are updated, yielding the language modeling objective completely unaltered. Our requires no specific calibration data, no quantization simulation, and adds negligible training overhead. With the LLaMA-2 7B model under W4A4 quantization with group size 128, perplexity drops from 8.22 to 6.73, competing with post-training methods that require frozen models and calibration datasets. Under W4A16, perplexity drops from 11.16 to 5.45. Code is available at https://github.com/MPedraBento/gauge-quant.

Miguel P. Bento, João F. Seabra

Independent Researcher · Lisbon, Portugal

LLM Quantization Rotation-Based Quantization Activation Quantization Low-Bit Quantization

Jul 8, 2026cs.LG

KronQ: LLM Quantization via Kronecker-Factored Hessian

Post-training quantization (PTQ) is a widely adopted technique for compressing large language models (LLMs) without retraining. Existing second-order PTQ methods, including GPTQ, construct quantization objectives exclusively from input activation statistics, effectively assuming that all output channels contribute equally to the layer-wise reconstruction objective. We propose KronQ, a PTQ framework that challenges this assumption by introducing the gradient covariance into the quantization pipeline. Under the Kronecker-factored Hessian approximation, the quantization loss depends jointly on both the activation and gradient covariances, and KronQ exploits this at two complementary levels. (1) KronQ introduces bidirectional incoherence processing, extending the existing input-side random rotation to the output dimension using the gradient covariance, reducing weight magnitude variance across both input and output dimensions. (2) KronQ derives a new sensitivity metric for inter-layer mixed-precision allocation, driven by the gradient and activation Hessian traces. Notably, in the case of 2-bit weight-only quantization on LLaMA-3-70B, while GPTQ and GPTAQ diverge or produce degenerate quantizations (>2000 perplexity on WikiText-2), KronQ achieves 7.93 perplexity.

Donghyun Lee, Yuhang Li, Ruokai Yin +1

University of Southern California · Yale University

Mixed-Precision Quantization LLM Quantization Rotation-Based Quantization Weight-Only Quantization Post-Training Quantization Neural Network Quantization

Jul 2, 2026cs.CV

OrbitQuant: Data-Agnostic Quantization for Image and Video Diffusion Transformers

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.

Donghyun Lee, Jitesh Chavan, Duy Nguyen +5

Cantina Labs · University of Southern California · *Work done during an internship at Cantina Labs. +1

Video Diffusion Models Diffusion Transformer Diffusion Model Quantization Rotation-Based Quantization Activation Quantization Post-Training Quantization+1

Jul 1, 2026cs.CV

RotateAttention: RoPE-Aware Rotation and Range Rectification for INT4 Quantized Attention in Video Generation

In

\textbf{DiT-based video generation models equipped with 3D Rotary Position Embeddings (3D RoPE)}

, the attention mechanism remains a primary computational bottleneck due to its quadratic complexity with respect to sequence length. While quantized

\textbf{FlashAttention}

offers a promising path toward hardware acceleration, existing low-bit quantization methods overlook two critical challenges in this setting:

\textbf{1)}

applying online rotation matrices -- a widely used technique for mitigating outliers in Queries (

Q

) and Keys (

K

) -- is difficult to reconcile with

\textbf{RoPE}

; and

\textbf{2)}

the non-negative attention matrix

P = \exp(QK - \max(QK))

makes symmetric quantization waste half of the 4-bit dynamic range. In this work, we observe that the outlier distributions of

Q

and

K

are strongly affected by the dimensional partitioning of

\textbf{3D RoPE}

. Based on this finding, we propose

\textbf{RotateAttention}

, an efficient

\textbf{mixed-precision INT4 FlashAttention}

framework tailored for

\textbf{DiT-based video generation models with 3D RoPE}

, using selective

\textbf{FP16 fallback}

for accuracy-sensitive attention blocks and denoising steps. RotateAttention introduces two core techniques:

\textbf{1) RoPE-aware Rotation}

, which employs either mergeable rotation matrices that can be fused into RoPE or negligible-overhead matrices to mitigate RoPE-induced outliers in

Q

and

K

; and

\textbf{2) Range-optimized

P

Quantization}

, which uses fixed scales and zero-points to fully exploit the

\textbf{INT4 numerical range}

with minimal computational overhead. Experiments show that

\textbf{RotateAttention}

preserves video generation quality nearly identical to full-precision baselines while achieving up to 1.68

\times

end-to-end speedup and 2.2

\times

kernel-level acceleration.

Yaofu Liu, Wanli Lan, Jinxi Li +2

The Hong Kong University of Science and Technology, Hong Kong SAR, China · Independent Researcher, China

Mixed-Precision Quantization Rotary Positional Embeddings Video Diffusion Models 4-Bit Quantization Rotation-Based Quantization Attention Quantization+1

Jun 19, 2026cs.LG

Fast-TurboQuant: A Multiplier-Free Online Vector Quantization Approach

As large language models scale, memory bandwidth for key-value caches and retrieval-augmented generation systems becomes a critical bottleneck. While 1-bit quantization addresses this constraint, recent TurboQuant relies on dense random rotation matrices to condition the vector distribution before quantization. This projection demands millions of floating-point multiplications per embedding, making it difficult to deploy on constrained edge silicon. We introduce Fast-TurboQuant, a multiplier-free projection architecture that replaces the dense matrix with a structured fast Johnson-Lindenstrauss transform. By applying a Rademacher phase inversion followed by a fast Walsh-Hadamard transform (FWHT), the method leverages sub-Gaussian concentration to satisfy the prerequisites of scalar Lloyd-Max quantization without Gaussian projections. This substitution reduces the arithmetic complexity to only additions, eliminating hardware multipliers. Evaluation on DBpedia OpenAI-3 Large embeddings demonstrates a 19.7 times algorithmic speedup under sequential execution. Furthermore, the dimension expansion due to the FWHT zero-padding reduces the mean squared error and improves Recall@10.

Pedro M. R. Pereira, Felipe A. P. de Figueiredo, Rausley A. A. de Souza

National Institute of Telecommunications (Inatel), Santa Rita do Sapucaí, MG 37536-001, Brazil

LLM Quantization Rotation-Based Quantization Vector Quantization Randomized Sketching Embedding Compression

Jun 14, 2026cs.LG

Ablation, Statistical Inference, and Validation for KV-Cache Compression

This study systematically compares Turbo-Quant and SpectralQuant KV-cache compression, evaluating non-dominated schemes, including WHT rotation with Beta Lloyd-Max and QJL, through a statistical validation methodology that separates systematic codec differences from implementation variance. Key findings reveal that while eigenbasis-based methods fail on heavy-tailed data due to covariance instability, they excel in structured regimes, with the effective semantic dimension (

d_{eff}

) adapting to calibration budgets rather than true data rank. (this is an abstract of the abstract thank you )

Paolo D'Alberto, Ashish Siarasao, Elliott Delaye +1

Advanced Micro Devices, Inc.

KV Caching Rotation-Based Quantization KV-Cache Compression Covariance Estimation KV-Cache Quantization Statistical Hypothesis Testing

Jun 7, 2026cs.LG

Trainable Smooth-Rotation Transforms with Learned Channel Scales for LLM Quantization

Post-training quantization (PTQ) is one of the most practical ways to reduce the serving cost of Large Language Models (LLMs), but activation quantization remains difficult because outlier-dominated channels lead to large quantization errors. This paper investigates whether part of this degradation is caused by over-migration in scaling-based equivalent transformations. We introduce a quantile-robust scaling policy for SmoothRot-style transforms by replacing max-based activation statistics with high quantiles, and we complement it with constrained gradient-based optimization of channel scales. On LLaMA-3.2-1B under W4A4 quantization, quantile-only policy search improves selected-layer error by 11.1% over the SmoothRot baseline, joint (alpha, q) search improves it by 12%, and training reaches 18.5%. Replaying the best selected-layer policy on all decoder-block down-projection layers reduces the corresponding full-layer mean error from 97.51 to 78.08 (19.9%). The results show that robust migration control and lightweight scale learning provide consistent gains over max-based fixed policies while preserving the equivalent-transform framework.

Patrik Czakó, Gábor Kertész, Sándor Szénási

Doctoral School of Applied Informatics and Applied Mathematics, Obuda University Budapest, Hungary · John von Neumann Faculty of Informatics, Obuda University Budapest, Hungary

LLM Quantization 4-Bit Quantization Rotation-Based Quantization Activation Quantization Post-Training Quantization

Jun 1, 2026cs.LG

Qift: Shift-Friendly No-Zero W2 Post-Training Quantization for Rotated W2A4/KV4 LLM Inference

Two-bit weight quantization is attractive for memory-efficient LLM inference, but the standard W2 level set {-2,-1,0,+1} often collapses under aggressive W2A4/KV4 settings. We study the scalar level-set geometry of two-bit weights in a Hadamard-rotated quantization pipeline. Conventional asymmetric W2 substantially improves over the standard level set, indicating that W2A4 failure is not only a bit-width problem but also a reconstruction-level problem. Across all 224 linear modules in each of LLaMA-2-7B and LLaMA-3.1-8B, pretrained weights are already nearly zero-centered, while Hadamard rotation primarily Gaussianizes their standardized shape: excess kurtosis and Q-Q error drop by orders of magnitude. Based on this approximate zero-centered Gaussian-like source model, we propose Qift, a fixed no-zero W2 level set for rotated W2A4/KV4 inference. The main level set is {+/-0.5, +/-1.5}, equivalently {+/-1, +/-3} under a half-scale reparameterization; a power-of-two variant uses {+/-1, +/-4} for sign-and-shift decoded weight application. Qift redesigns the fixed two-bit code-to-level mapping and is training-free, learned-codebook-free, group-grid-free, and zero-point-free, retaining the standard per-channel scale. A scale-invariant ratio analysis identifies an effective inner/outer centroid ratio range of 0.25 to 0.33, explaining why mirror no-zero (MNZ), Lloyd, NF2, and PoT-MNZ perform well while {+/-1, +/-2} does not. On both models, the no-zero level sets consistently improve pure W2A4 perplexity, L-layer mixed W2/W4 perplexity, downstream accuracy, and GPTQ residual behavior over the standard W2 level set. At L=16 mixed precision, they substantially narrow the gap to W3A4 while keeping half of the transformer layers at two-bit precision, giving a simple, source-aware, and deployment-friendly alternative to more complex learned W2 codebooks.

Chi-Wei Huang, Chia-Chi Tsai

National Cheng Kung University

LLM Quantization Rotation-Based Quantization Post-Training Quantization Low-Bit Quantization

May 28, 2026cs.LG

HARP: Hadamard-Preconditioned Adaptive Rotation Processor for Extreme LLM Quantization

Post-training quantization (PTQ) is essential for deploying LLMs under memory and bandwidth constraints. However, extreme low-bit quantization remains highly sensitive to activation outliers and anisotropic weight curvature. Existing incoherence-based PTQ methods mitigate this issue with fixed randomized Hadamard transforms (RHTs), which improve quantization robustness but cannot adapt the rotated basis to the layer, calibration distribution, or quantizer. We introduce HARP (Hadamard-preconditioned Adaptive Rotation Processor), a learnable structured two-sided orthogonal processor that replaces fixed Hadamard mixing while preserving exact full-precision equivalence. HARP represents each rotation as a product of sparse butterfly-like block-orthogonal stages, supports non-power-of-two dimensions through Mixed-Radix schedules, and initializes to the RHT processor up to a fixed permutation. Fitted only on calibration data, HARP adapts the quantization basis to each layer and backend. Across 2--4-bit settings on Llama models from 1B to 70B, HARP consistently improves perplexity and yields its clearest zero-shot gains at 2 bits; a 2-bit Qwen3-8B experiment shows the same transfer beyond the Llama family. HARP also preserves deployment efficiency: on Llama 2 7B at 2 bits, it reaches 128 tok/s, retaining 90% of RHT throughput (142 tok/s) and running approximately

2.1\times

faster than FP16 (61 tok/s).

Artur Zagitov, Gleb Molodtsov, Aleksandr Beznosikov

1MIRAI · 2BRAIn Lab · 3Innopolis University

LLM Quantization Rotation-Based Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

May 27, 2026cs.CV

Ω-QVLA: Robust Quantization for Vision-Language-Action Models via Composite Rotation and Per-step Scaling

Vision-Language-Action (VLA) models unify perception, reasoning, and control within a single policy, yet their multi-billion-parameter backbones and diffusion-based action heads make on-device deployment prohibitively expensive. Prior quantization efforts offer only partial solutions, compressing the LLM backbone while leaving the DiT action head at full precision, or resorting to mixed-precision schemes, driven by the belief that uniformly quantizing the action head is inherently unstable. We challenge this assumption with Omega-QVLA, the first training-free post-training quantization framework that compresses both the language backbone and the entire diffusion action head of a VLA model to a uniform W4A4 precision, eliminating the need for mixed-precision allocation. Omega-QVLA combines a composite SVD-Hadamard rotation that equalizes per-channel weight energy while diffusing residual activation outliers with per-step DiT activation scaling quantization that absorbs dynamic-range drift across denoising steps. On LIBERO, Omega-QVLA compresses Pi 0.5 and GR00T N1.5 to W4A4 with 98.0% and 87.8% task success rates, matching or exceeding their FP16 references of 97.1% and 87.0%, while reducing the static memory footprint by 71.3%. Real-world manipulation experiments further confirm smooth, accurate manipulation where prior methods fail. Code is available at https://github.com/UCMP13753/Omega-QVLA.

Xinyu Wang, Mingze Li, Sicheng Lyu +6

McGill University · Université de Montréal · Mila – Quebec AI Institute +2

VLM Quantization Efficient VLA Model Inference Rotation-Based Quantization Efficient VLA Models Activation Quantization Vision-Language-Action Models+1

May 25, 2026cs.LG

QAM-W: Joint 2D Codebook Quantization for LLM Weights via Hadamard Rotation and Activation-Aware Scaling

Scalar post-training quantizers discard pairwise coordinate structure within weight rows. We introduce QAM-W (Quadrature Amplitude Modulation for Weights), a codec that recovers this structure: each row is L2-normalized, block-Hadamard rotated, paired into 2D coordinates, and quantized against a single Lloyd-Max codebook trained on the unit circular Gaussian, with activation-aware per-channel scaling. In a cross-model study spanning five LLMs from four families (1.1B--13B parameters) and eight quantized configurations, the activation-aware variant at

\approx 5.5

bpw stays within

\pm 0.4\%

of BF16 WikiText-2 perplexity on every model, matching the SmoothQuant W8A8 quality envelope at

32\%

fewer weight bits. Joint 2D coding outperforms polar (amplitude

\times

phase) coding by 2--15pp $Δ$ PPL at equal bitrate, and paired KL against BF16 tracks $Δ$ PPL% at Spearman $ρ= 0.99$ across 37 (method, model) rows, consistent with a monotone composite bound from codec distortion to KL divergence. A 3.5bpw variant is competitive on quantization-tolerant architectures. At strict 4~~bpw, the rotated-codebook frontier method QTIP outperforms QAM-W; the contribution is the quality-preserving 5--6~~bpw band.

Preetam Sharma, Kacper Dobek

Independent Research · Institute of Computing Science Poznan University of Technology, Poznan, Poland

LLM Quantization Rotation-Based Quantization Vector Quantization Weight-Only Quantization Post-Training Quantization

May 24, 2026cs.LG

Influence-Inspired Spectral Rotations for Extreme Low-Bit LLM Quantization

We apply the influence-adaptive Walsh geometry of a companion theory paper (arXiv:2605.01637) to extreme low-bit weight-only LLM quantization. The recipe is one math-invariant transformation: WHT-rotate each linear layer's weight matrix and rescale its columns by per-coordinate Walsh-basis activation energy before handing off to a reconstruction-error quantizer (Intel auto-round). This biases per-group integer rounding toward high-spectral-energy channels. On four pretrained decoder-only models from 135M to 1.5B parameters, BBT-spectral reduces wikitext-2 perplexity by 15-58% relative to vanilla auto-round at W2A16; we also report a TinyLlama-1.1B auxiliary data point. Three extensions transfer the recipe to families it failed on: a per-head PCA matrix-Gamma replacement of q_norm/k_norm for Qwen3 attention (PPL 136.76 -> 88.99 on Qwen3-0.6B); an SO(2) per-pair rotation that commutes with RoPE (PPL 36.93 -> 21.84 on Qwen2.5-1.5B); and an MoE-aware input-side absorption fix identified by architectural fuzzing of Laguna-style fused-expert layouts. A W2-vs-W4 ablation gives a deliberate negative control: the redistribution payoff falls within the +/-0.5 PPL noise floor at W4, consistent with the Schur-convexity intuition that the cost of unconcentrated influence vanishes as the noise budget shrinks. All quantized weights export to OpenVINO IR and run on Intel NPU + Arc dGPU + CPU with PPL invariant to device within +/-0.1. We do not claim a formal Boolean-to-real-valued transfer of the theory paper's majorization argument: the WHT activation energy used here is not the Boolean influence of the theory paper, the link is intuitive, and the contribution is engineering value rather than a transferred theorem. Head-to-head benchmarks against SpinQuant, QuaRot, QuIP-sharp, AQLM, OmniQuant, and ButterflyQuant at matched calibration are the main future-work item.

Gorgi Pavlov

Lehigh University

LLM Quantization Rotation-Based Quantization Weight-Only Quantization Low-Bit Quantization Neural Network Quantization

May 20, 2026cs.LG

OCTOPUS: Optimized KV Cache for Transformers via Octahedral Parametrization Under optimal Squared error quantization

The key-value (KV) cache dominates memory bandwidth and footprint in long-context autoregressive inference. Recent rotation-preconditioned codecs (TurboQuant, PolarQuant) show that a structured random rotation followed by a per-coordinate scalar quantizer matched to an analytically tractable marginal is a near-optimal recipe for KV compression. OCTOPUS advances this paradigm through joint quantization of rotated coordinate triplets. Each triplet's direction is mapped to a square via an octahedral parameterization, and the two resulting coordinates and the triplet norm are Lloyd-Max quantized against implementation-matched marginals. Optimizing the per-triplet squared error gives a strictly non-uniform bit allocation depending only on the total dimensionality of the keys. We find the finite-dimensional quality optimum with sweeps to be constant on every real decoder we test. The codec is data-oblivious, online, and deterministic given a seed. Across text, video, and audio, OCTOPUS matches or beats every prior rotation codec at every reported bit width and metric, with a lead that grows as bits drop for extreme compression. Furthermore, a fused Triton implementation reconstructs keys on the fly without materializing the uncompressed key, so the codec adds no decode-time bandwidth or latency over the existing dequantization. Project Page: https://octopus-quant.github.io/

Mark Boss, Vikram Voleti, Simon Donné +1

Stability AI

KV Caching Memory-Efficient Optimization Rotation-Based Quantization Vector Quantization KV-Cache Compression KV-Cache Quantization

May 19, 2026cs.LG

Block-Sphere Vector Quantization

Vector quantization is a fundamental primitive for scalable machine learning systems, enabling memory-efficient storage, fast retrieval, and compressed inference. Recent rotation-based quantizers such as EDEN, RabitQ, and TurboQuant have introduced strong guarantees and empirical performance, but the surrounding comparisons have been difficult to interpret because they rely on different distortion criteria, probability regimes, and implementation assumptions. As our first contribution, we provide a unified theoretical comparison of these methods and show that their relative advantages are criterion-dependent rather than absolute: EDEN and TurboQuant are favorable for MSE distortion, EDEN is also effective for expected inner-product distortion, and RabitQ provides strong high-probability control. This comparison further clarifies that EDEN provides particularly strong guarantees for expected distortion measures. As our second contribution, we introduce Block-Sphere Quantization (BlockQuant), a new rotation-based block quantization algorithm designed around the spherical geometry of randomly rotated vectors. Unlike coordinate-wise quantizers, BlockQuant quantizes blocks on the sphere, preserving the geometry of rotated embeddings more faithfully. We prove that this block-spherical design theoretically improves over the baselines considered in this paper for both reconstruction MSE and expected inner-product distortion. Our experiments on real embedding datasets and long-context LLM inference tasks show practical gains that are consistent with our theoretical improvements.

Heesang Ann, Joongkyu Lee, Min-hwan Oh

Seoul National University

Rotation-Based Quantization Vector Quantization Neural Network Quantization

May 19, 2026cs.LG

OScaR: The Occam's Razor for Extreme KV Cache Quantization in LLMs and Beyond

The rapid advancement toward long-context reasoning and multi-modal intelligence has made the memory footprint of the Key-Value (KV) cache a dominant memory bottleneck for efficient deployment. While the established per-channel quantization effectively accommodates intrinsic channel-wise outliers in Key tensors, its efficacy diminishes under extreme compression. In this work, we revisit the inherent limitations of the per-channel quantization paradigm from both empirical and theoretical perspectives. Our analysis identifies Token Norm Imbalance (TNI) as the primary bottleneck to quantization fidelity. We demonstrate that TNI systematically amplifies errors when shared quantization parameters are required to span token groups exhibiting substantial norm disparities. Instead of relying on intricate quantization pipelines (e.g., TurboQuant), we propose OScaR (Omni-Scaled Canalized Rotation), an accurate and lightweight KV cache compression framework for X-LLMs (i.e., text-only, multi-modal, and omni-modal LLMs). Advancing the per-channel paradigm, OScaR employs Canalized Rotation followed by Omni-Token Scaling to mitigate TNI-induced sequence-dimensional variance both effectively and efficiently, further supported by our optimized system design and CUDA kernels. Extensive evaluations across X-LLMs show that OScaR consistently outperforms existing methods and achieves near-lossless performance under INT2 quantization, establishing it as a robust, low-complexity, and universal framework that defines a new Pareto front. Compared with the BF16 FlashDecoding-v2 baseline, our OScaR implementation achieves a notable up to 3.0x speedup in decoding, reduces memory footprint by 5.3x, and increases throughput by 4.1x. The code for OScaR is publicly available at https://github.com/ZunhaiSu/OScaR-KV-Quant.

Zunhai Su, Rui Yang, Chao Zhang +11

Tsinghua University · Meituan LongCat Team · The University of Hong Kong +3

KV Caching Rotation-Based Quantization Memory-Efficient Inference LLM Inference Acceleration KV-Cache Quantization Low-Bit Quantization+1

May 19, 2026cs.LG

TORQ: Two-Level Orthogonal Rotation for MXFP4 Quantization

As Large Language Models (LLMs) advance toward practical deployment, the Microscaling FP4 (MXFP4) format has emerged as a cornerstone for next-generation low-bit inference, owing to its ability to balance high dynamic range with hardware efficiency. However, directly applying MXFP4 to LLM activation quantization inevitably leads to significant accuracy degradation. In this paper, we theoretically analyze the error structure of MXFP4 activation quantization, revealing that the root cause of this performance drop lies in two structural imbalances between activation distributions and the MXFP4 block floating-point format: (1) extreme inter-block variance imbalance and (2) intra-block codebook utilization imbalance. To address these challenges, we propose TORQ (Two-level Orthogonal Rotation for MXFP4 Quantization), a training-free Post-Training Quantization (PTQ) framework designed to reshape the geometric properties of the activation space through optimal coordinate transformations. At the macroscopic level, TORQ leverages the Schur-Horn theorem to redistribute activation energy via inter-block orthogonal rotation, preventing high-variance blocks from driving up shared scaling factors and thereby preserving the precision of small-magnitude elements. At the microscopic level, TORQ employs maximum-entropy-guided intra-block rotation to alleviate codebook collapse and maximize the MXFP4 codebook's information capacity. Experiments on mainstream LLMs such as LLaMA3 and Qwen3 show that TORQ significantly improves the accuracy of MXFP4 activation quantization compared to existing methods: on Qwen3-32B, the perplexity on WikiText is reduced to 8.43 (vs. 7.61 for BF16), and the average accuracy increases from 38.40% with direct RTN to 73.63% (vs. 74.82% for BF16), substantially narrowing the gap between 4-bit floating-point quantization and full-precision inference.

Zukang Xu, Xing Hu, Dawei Yang

1Houmo AI.

LLM Quantization Rotation-Based Quantization Activation Quantization Post-Training Quantization Neural Network Quantization

May 18, 2026cs.LG

OSCAR: Offline Spectral Covariance-Aware Rotation for 2-bit KV Cache Quantization

INT2 KV-cache quantization is attractive for long-context LLM serving, but it remains difficult to make both accurate and deployable. Simple rotations such as Hadamard transforms reduce outliers, but still degrade at INT2 because they are not aligned with downstream attention. We propose OSCAR, an Ultra-low-bit KV Cache quantization method that estimates attention-aware covariance structures offline and uses them to derive fixed rotations and clipping thresholds for quantization. In this way, it aligns KV quantization with the covariance structures that attention actually consumes. More importantly, we not only provide theoretical justification but also develop a fully deployable OSCAR system with a custom INT2 attention kernel that remains compatible with paged KV-cache serving and fused kernel pipelines, enabling seamless integration into modern LLM serving frameworks such as SGLang and vLLM. We evaluate our methods on recent reasoning models with reasoning traces of up to 32k tokens across 5 tasks. On Qwen3-4B-Thinking-2507 and Qwen3-8B, OSCAR reduces the BF16 accuracy gap to 3.78 and 1.42 points, respectively, while naive rotation INT2 collapses to nearly zero. We further scale OSCAR to Qwen3-32B and GLM-4.7 (358B params), where it remains effectively on par with BF16. On long context - RULER-NIAH up to 128K, OSCAR remains robust on both Qwen3 models, while naive rotation INT2 collapses. System-wise, OSCAR reduces KV-cache memory by approximately 8x, improves throughput by up to 7x at large batch sizes under the same memory budget, and accelerates batch-size-1 decoding by up to 3x over BF16 due to reduced memory bandwidth overhead.

Zhongzhu Zhou, Donglin Zhuang, Jisen Li +4

Together AI · University of Sydney · University of Illinois Urbana-Champaign

Rotation-Based Quantization LLM Inference Acceleration KV-Cache Quantization Post-Training Quantization Low-Bit Quantization Neural Network Quantization

May 16, 2026cs.CV

DiRotQ: Rotation-Aware Quantization for 4-bit Diffusion Transformers

Diffusion Transformers (DiTs) achieve state-of-the-art image generation quality but incur substantial memory and computational costs at inference. While aggressive Post-Training Quantization (PTQ) to 4-bit precision offers significant efficiency gains, it typically results in severe quality degradation. Existing approaches, including smoothing-based methods, mixed-precision schemes, rotation techniques, and low-rank residual methods, partially mitigate this issue but still leave a noticeable gap to FP16/BF16 performance. In this work, we introduce DiRotQ, a W4A4 PTQ framework that mitigates this degradation through rotation-aware activation quantization. DiRotQ identifies a low-rank subspace capturing dominant activation variance via Principal Component Analysis (PCA), preserving coefficients in this subspace at higher precision while quantizing the remaining components to 4-bit. Activations are rotated into the PCA basis at inference time using calibration-derived orthogonal transformations, while the inverse rotation is fused into the layer weights offline. Combined with GPTQ-based weight quantization, DiRotQ achieves an FID (lower is better) of 15.9 and PSNR (higher is better) of 19.1 dB on PixArt-Σ over the MJHQ-30K dataset, outperforming the prior state-of-the-art SVDQuant (FID 18.9, PSNR 17.6) under the same INT W4A4 setting. Beyond standard metrics, we introduce a VLM-as-a-Judge evaluation protocol for diffusion model quantization, the first such evaluation in this setting, providing a more holistic assessment of perceptual quality and prompt alignment under aggressive compression. On the systems side, we implement a Triton-based custom kernel to enable efficient end-to-end inference, reducing memory usage of the 12B FLUX.1-dev model by 2.1x and delivering 2.3x speedup over the BF16 baseline, on a 24 GB RTX 4090 GPU.

Sayeh Sharify, Mahsa Salmani, Hesham Mostafa

d-Matrix Santa Clara, CA 95054

Diffusion Transformer Diffusion Model Quantization 4-Bit Quantization Rotation-Based Quantization Activation Quantization Post-Training Quantization+2