arxiv: 2604.11080 · v1 · submitted 2026-04-13 · 💻 cs.CV · cs.AI

Recognition: no theorem link

ReSpinQuant: Efficient Layer-Wise LLM Quantization via Subspace Residual Rotation Approximation

Suyoung Kim , Sunghyun Wee , Hyeonjin Kim , Kyomin Hwang , Hyunho Lee , Nojun Kwak

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Pith reviewed 2026-05-10 16:12 UTC · model grok-4.3

classification 💻 cs.CV cs.AI

keywords LLM quantizationpost-training quantizationrotation-based quantizationactivation outlierslayer-wise adaptationsubspace approximationinference overhead

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The pith

ReSpinQuant approximates per-layer rotation matrices with residual subspaces so that layer-wise LLM quantization accuracy can be obtained at the speed of global rotation methods.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Rotation-based post-training quantization mitigates activation outliers in large language models. Global rotation applies one matrix across all layers and fuses it into the weights for fast inference, but the single matrix limits how well it can adapt to each layer's statistics. Layer-wise rotations adapt separately to each layer and therefore reach higher accuracy, yet the matrices cannot be fused and must be applied at runtime, creating large overhead. ReSpinQuant decomposes each layer's rotation into a shared component plus a low-rank residual subspace; the residual part is matched offline and the entire transformation is fused into the weights before inference begins. This yields the accuracy of full layer-wise adaptation while preserving the negligible runtime cost of global methods. Experiments on 4-bit and 3-bit weight-and-activation quantization show the approach matches the accuracy of expensive layer-wise baselines and exceeds global rotation baselines.

Core claim

ReSpinQuant demonstrates that a residual subspace rotation approximation, computed via offline matching bases, can be fused directly into model weights, delivering the expressivity of per-layer rotation transformations with only negligible inference overhead.

What carries the argument

residual subspace rotation approximation that decomposes layer-specific rotations into a global component plus a low-dimensional residual whose basis can be matched and fused offline

Load-bearing premise

The residual subspace rotation approximation captures enough of the expressivity of full per-layer transformations to match their accuracy while still allowing complete offline fusion into the model weights.

What would settle it

Apply both ReSpinQuant and an unfused full layer-wise rotation method to the same model and dataset; if the accuracy of ReSpinQuant falls substantially below the full layer-wise result, the subspace approximation is insufficient.

Figures

Figures reproduced from arXiv: 2604.11080 by Hyeonjin Kim, Hyunho Lee, Kyomin Hwang, Nojun Kwak, Sunghyun Wee, Suyoung Kim.

**Figure 1.** Figure 1: Comparison of rotation paradigms. (a) Global Rotation ensures efficiency via offline weight merging but limits expressivity. (b) Layer-wise Transformation enhances expressivity but incurs high online overhead. (c) ReSpinQuant (Ours) reconciles this trade-off by merging layer-wise rotation into weights, and resolves the basis mismatch problem via subspace residual rotation approximation, achieving both hi… view at source ↗

**Figure 2.** Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Visualization of the trained rotation matrices optimized by Cayley optimizer. We display the sub-blocks [4:, 4:] of two rotation matrices (R1, R2 ∈ R 4096×4096) of Llama-3 8B layer 16, and their relative transformation (R⊤ 1 R2) after training. Despite optimization, the matrices deviate minimally from the Hadamard initialization. Crucially, the relative transformation R⊤ 1 R2 remains sparse and diagonally … view at source ↗

**Figure 4.** Figure 4: Optimization dynamics of rotation matrices on LLaMA-3 8B (Layers 2, 16). (a) The Frobenius norm of the deviation from the initialization, calculated as ∥R − Rinit∥F . The curve indicates stable convergence during training. (b) The cosine similarity between the optimized rotation R and the initialization Rinit remains consistently high. Together, these plots confirm that while the learned rotations successf… view at source ↗

**Figure 5.** Figure 5: Illustration of the subspace residual rotation approximation. We approximate the dense rotation matrix (T ∈ R D×D) that aligns the residual bases into a low-dimensional subspace to minimize the computational overhead. During inference, the input features are projected into a subspace of rank r via Q, rotated by the approximated matrix (Rˆ sub ∈ R r×r ), and re-projected via Q⊤. The orthogonal complement p… view at source ↗

read the original abstract

Rotation-based Post-Training Quantization (PTQ) has emerged as a promising solution for mitigating activation outliers in the quantization of Large Language Models (LLMs). Global rotation methods achieve inference efficiency by fusing activation rotations into attention and FFN blocks, but suffer from limited expressivity as they are constrained to use a single learnable rotation matrix across all layers. To tackle this, layer-wise transformation methods emerged, achieving superior accuracy through localized adaptation. However, layer-wise methods cannot fuse activation rotation matrices into weights, requiring online computations and causing significant overhead. In this paper, we propose ReSpinQuant, a quantization framework that resolves such overhead by leveraging offline activation rotation fusion and matching basis using efficient residual subspace rotation. This design reconciles the high expressivity of layer-wise adaptation with only negligible inference overhead. Extensive experiments on W4A4 and W3A3 quantization demonstrate that ReSpinQuant achieves state-of-the-art performance, outperforming global rotation methods and matching the accuracy of computationally expensive layer-wise methods with minimal overhead.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

ReSpinQuant's residual subspace lets it fuse layer-wise rotations offline but the accuracy depends on how well the approximation matches the optimal per-layer matrices.

read the letter

ReSpinQuant approximates per-layer rotations with a residual subspace to enable offline fusion, delivering practical accuracy gains in low-bit LLM quantization. The approach takes the idea of layer-wise transformations for better outlier handling and makes them fusable by projecting the difference from a base rotation onto a low-dimensional subspace. This lets the method keep most of the per-layer benefits while avoiding any online matrix multiplies. The reported results on W4A4 and W3A3 show it beating standard global rotation techniques and nearly matching the accuracy of full layer-wise methods across the models they tested. The soft spot is how faithfully the residual subspace captures the necessary adjustments. The stress-test concern is valid here: if the subspace dimension is small to ensure negligible overhead, or if the matching basis doesn't pick up the critical directions for each layer, the accuracy boost could be smaller than claimed. The paper includes extensive experiments, but more direct measurements of the approximation error between the subspace version and the optimal per-layer matrix would make the case stronger. As it stands, the results are promising but rest on that assumption holding in practice. This paper targets engineers and researchers focused on efficient inference for large language models. Anyone working on post-training quantization for 3 or 4 bit weights and activations will find the trade-off interesting. I would recommend sending it for peer review. The idea addresses a clear practical limitation in existing methods, and the experiments provide enough to evaluate whether the approximation works as intended.

Referee Report

2 major / 2 minor

Summary. ReSpinQuant proposes a PTQ framework for LLMs that approximates per-layer activation rotations via residual subspace rotation with a matching basis. This enables complete offline fusion of the rotations into the model weights, delivering the expressivity of layer-wise methods while incurring only negligible inference overhead. The paper reports SOTA results on W4A4 and W3A3 quantization tasks, outperforming global rotation baselines and matching the accuracy of full layer-wise transformations.

Significance. If the residual subspace approximation is shown to preserve sufficient outlier-mitigation benefits, the work would meaningfully advance practical LLM quantization by removing the efficiency-expressivity trade-off that currently forces practitioners to choose between global rotations (fast but limited accuracy) and per-layer methods (accurate but online overhead). The offline-fusion design is a clear practical strength.

major comments (2)

[Method section (residual subspace rotation approximation)] The central claim rests on the residual subspace rotation (with matching basis) approximating the optimal per-layer transformation matrices closely enough to retain their accuracy gains after fusion. No quantitative bound, approximation-error analysis, or ablation on subspace dimension is provided to demonstrate that the residual component aligns with layer-specific optima rather than collapsing toward a global rotation; this is load-bearing for the reconciliation of expressivity and efficiency.
[Experiments section (Tables reporting W4A4/W3A3 results)] The reported SOTA results on W4A4 and W3A3 lack error bars, multiple random seeds, or statistical significance tests, making it impossible to determine whether the gains over global methods are reliable or whether the method truly matches full layer-wise accuracy within experimental noise.

minor comments (2)

[Method section] Notation for the subspace dimension, matching basis, and residual component should be introduced with explicit equations and a clear diagram showing how the approximation is fused offline.
[Introduction] The abstract and introduction would benefit from a short comparison table listing inference overhead (FLOPs or latency) for global, layer-wise, and ReSpinQuant methods to quantify the 'negligible' claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment point by point below, indicating where revisions will be made to strengthen the work.

read point-by-point responses

Referee: [Method section (residual subspace rotation approximation)] The central claim rests on the residual subspace rotation (with matching basis) approximating the optimal per-layer transformation matrices closely enough to retain their accuracy gains after fusion. No quantitative bound, approximation-error analysis, or ablation on subspace dimension is provided to demonstrate that the residual component aligns with layer-specific optima rather than collapsing toward a global rotation; this is load-bearing for the reconciliation of expressivity and efficiency.

Authors: We agree that the absence of a formal approximation-error analysis or subspace-dimension ablation leaves the central claim without quantitative support. The current manuscript relies on end-to-end accuracy results to show that the residual component preserves layer-specific outlier mitigation. In the revision we will add (i) an ablation varying subspace dimension and (ii) a direct error metric (e.g., Frobenius-norm distance between the learned residual rotation and the optimal per-layer matrix) to demonstrate that the approximation does not collapse to a global rotation. These additions will be placed in the Method and Experiments sections. revision: yes
Referee: [Experiments section (Tables reporting W4A4/W3A3 results)] The reported SOTA results on W4A4 and W3A3 lack error bars, multiple random seeds, or statistical significance tests, making it impossible to determine whether the gains over global methods are reliable or whether the method truly matches full layer-wise accuracy within experimental noise.

Authors: We acknowledge that the lack of error bars and multi-seed statistics limits the ability to assess result reliability. Our original experiments used fixed seeds for reproducibility and to control compute cost. We will rerun the primary W4A4 and W3A3 tables with at least three random seeds, report mean and standard deviation, and add error bars. Where appropriate we will also include a simple significance test (e.g., paired t-test) against the global-rotation baseline to quantify whether the observed gains exceed experimental noise. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces ReSpinQuant as a new framework that approximates layer-wise rotations via residual subspace rotations to enable offline fusion. The abstract and title describe this as a design choice reconciling expressivity and efficiency, with empirical results on W4A4/W3A3 tasks. No equations, derivations, or self-citations are visible that reduce any claimed result to a fitted parameter or input by construction. The approximation is presented as a novel technique rather than a tautological renaming or self-referential definition, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No full text is available, so free parameters, axioms, and invented entities cannot be identified or audited.

pith-pipeline@v0.9.0 · 5497 in / 1091 out tokens · 54934 ms · 2026-05-10T16:12:12.957322+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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