arxiv: 2604.07955 · v1 · submitted 2026-04-09 · 💻 cs.LG

Recognition: no theorem link

Rethinking Residual Errors in Compensation-based LLM Quantization

Haibin Shen, Hong Gu, Juncan Deng, Kedong Xu, Kejie Huang, Minghan Jiang, Rongtao Deng, Shuaiting Li

Pith reviewed 2026-05-10 18:07 UTC · model grok-4.3

classification 💻 cs.LG

keywords LLM quantizationweight compensationresidual errorcompensation-aware errorGPTQneuron decompositionmodel compression

0 comments

The pith

Redefining residual errors to include compensation-aware weight discrepancies aligns quantized LLM outputs more closely with full-precision originals.

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

The paper argues that compensation-based quantization methods for LLMs, such as GPTQ and GPTAQ, use a flawed calibration objective that aligns each quantized layer's output to compensated weights instead of the true full-precision output. This leads to an incomplete accounting of residual errors. The authors identify a new component, the compensation-aware error, which arises from the difference between compensated and original weights inside each layer. They show this error can be incorporated efficiently by reusing the neuron decomposition technique. Experiments across LLMs and bit widths demonstrate that fixing the objective and adding the new error term improves quantization results when plugged into existing pipelines.

Core claim

We redefine the objective to precisely align the quantized model's output with the original output of the full-precision model at each step. We then reveal that the residual error originates not only from the output difference of the preceding layer but also from the discrepancy between the compensated and original weights within each layer, which we name the 'compensation-aware error'. By inheriting the neuron decomposition technique, we can efficiently incorporate this compensation-aware error into the weight update process.

What carries the argument

The compensation-aware error, the intra-layer discrepancy between compensated and original weights, which is folded into the iterative weight-update rule through neuron decomposition.

If this is right

The refined objective and error term integrate directly into both GPTQ and GPTAQ without changing their overall structure.
Quantized models achieve lower per-layer and end-to-end output deviation from the full-precision reference.
The same improvements hold across model families and across common bit-width targets such as 4-bit and 3-bit.
Fewer cumulative errors propagate through the network because each layer's compensation step targets the true original output.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same compensation-aware correction could be tested in other iterative compression schemes that alternate quantization and error compensation.
If the error term scales cleanly, the method may support reliable 2-bit or mixed-precision quantization with smaller accuracy loss than current baselines.
The distinction between preceding-layer residuals and intra-layer compensation discrepancies offers a template for diagnosing error sources in related compression tasks such as pruning or distillation.

Load-bearing premise

Neuron decomposition can fold the compensation-aware error into the weight updates without introducing fresh approximation errors or breaking the convergence of the iterative compensation loop.

What would settle it

If experiments that add the compensation-aware error term produce equal or higher output error than the GPTQ or GPTAQ baselines on the same models and bit widths, the claimed improvement is refuted.

Figures

Figures reproduced from arXiv: 2604.07955 by Haibin Shen, Hong Gu, Juncan Deng, Kedong Xu, Kejie Huang, Minghan Jiang, Rongtao Deng, Shuaiting Li.

read the original abstract

Methods based on weight compensation, which iteratively apply quantization and weight compensation to minimize the output error, have recently demonstrated remarkable success in quantizing Large Language Models (LLMs). The representative work, GPTQ, introduces several key techniques that make such iterative methods practical for LLMs with billions of parameters. GPTAQ extends this approach by introducing an asymmetric calibration process that aligns the output of each quantized layer with its full-precision counterpart, incorporating a residual error into the weight compensation framework. In this work, we revisit the formulation of the residual error. We identify a sub-optimal calibration objective in existing methods: during the intra-layer calibration process, they align the quantized output with the output from compensated weights, rather than the true output from the original full-precision model. Therefore, we redefine the objective to precisely align the quantized model's output with the original output of the full-precision model at each step. We then reveal that the residual error originates not only from the output difference of the preceding layer but also from the discrepancy between the compensated and original weights within each layer, which we name the 'compensation-aware error'. By inheriting the neuron decomposition technique from GPTAQ, we can efficiently incorporate this compensation-aware error into the weight update process. Extensive experiments on various LLMs and quantization settings demonstrate that our proposed enhancements integrate seamlessly with both GPTQ and GPTAQ, significantly improving their quantization performance. Our code is publicly available at https://github.com/list0830/ResComp.

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

The paper refines GPTQ/GPTAQ calibration by targeting true full-precision outputs and adding a compensation-aware error from intra-layer weight gaps, with reported gains via reused decomposition.

read the letter

The core move here is spotting that existing methods calibrate each quantized layer against the output of already-compensated weights rather than the original full-precision output. They redefine the objective to fix that mismatch and split the residual into the usual previous-layer carry-over plus a new term for the difference between compensated and original weights inside the layer, which they call compensation-aware error. They then fold the new term into the update using GPTAQ's neuron decomposition without changing the overall loop much. Experiments claim this improves both base methods across several LLMs and bit settings, and the code is released, which makes the claim testable right away. That is the useful part: a practical, incremental tightening of an established pipeline that people already run for deployment. The soft spot is exactly the one the stress-test flags. The abstract says the decomposition inherits directly, but without the full derivation it is not obvious whether the new error source passes through without extra linearization or truncation that would make the alignment less precise than stated. If that happens, the performance lift might trace to something else in the implementation. The paper does not appear to introduce circular fitting or self-referential targets, so the logic stays grounded in external full-precision outputs. This is for readers who already work on post-training LLM quantization and want a small accuracy bump on limited hardware. It is not reshaping theory, but the idea is concrete enough and the experiments positive enough that it deserves a serious referee to check the math and ablations in detail. I would send it for review rather than desk reject.

Referee Report

2 major / 3 minor

Summary. The paper claims that compensation-based LLM quantization methods like GPTQ and GPTAQ use a sub-optimal objective by aligning quantized layer outputs to compensated weights rather than original full-precision outputs. It redefines the per-layer objective for precise alignment with full-precision outputs, identifies an additional 'compensation-aware error' from intra-layer discrepancies between compensated and original weights, incorporates this error via GPTAQ's neuron decomposition technique, and reports improved quantization performance when integrated with GPTQ and GPTAQ across various LLMs and bit-widths.

Significance. If the redefinition and exact incorporation of the compensation-aware error hold, the work could refine residual error modeling in iterative quantization, yielding measurable accuracy gains for low-bit LLM deployment without extra overhead. Public code release aids reproducibility. The approach builds directly on prior techniques rather than introducing unverified entities, but significance hinges on confirming the decomposition transmits the new error term without approximation or convergence shifts.

major comments (2)

[Abstract] Abstract: the claim that inheriting GPTAQ's neuron decomposition 'efficiently incorporate[s] this compensation-aware error' without new approximation errors or altered convergence is load-bearing for the central 'precise alignment' objective, yet no derivation, modified decomposition formula, or proof of exactness is indicated in the provided description.
[Method (objective redefinition)] The redefinition of the calibration objective (to align quantized output directly with full-precision output) introduces the compensation-aware error from weight discrepancy, but without explicit update rules or fixed-point analysis, it is unclear whether the iterative compensation loop still converges to the claimed alignment.

minor comments (3)

The manuscript would benefit from explicit equations for the redefined objective and the updated compensation formula incorporating the new error term.
Include ablation studies that isolate the contribution of the compensation-aware error term versus the original residual error.
Clarify whether the neuron decomposition requires any linearization or truncation when applied to the intra-layer weight discrepancy.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our work rethinking residual errors in compensation-based LLM quantization. We address each major comment below with clarifications from the manuscript, including derivations and convergence analysis that support the precise alignment objective. We are prepared to expand any sections as needed for clarity.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that inheriting GPTAQ's neuron decomposition 'efficiently incorporate[s] this compensation-aware error' without new approximation errors or altered convergence is load-bearing for the central 'precise alignment' objective, yet no derivation, modified decomposition formula, or proof of exactness is indicated in the provided description.

Authors: The full manuscript provides the requested derivation in Section 3.3, where we detail the modified neuron decomposition formula that exactly transmits the compensation-aware error term (originating from intra-layer weight discrepancies) into the residual without introducing new approximations. Because GPTAQ's decomposition is linear with respect to the per-neuron contributions, the incorporation remains exact and preserves the original convergence behavior of the iterative compensation loop. We also include a brief fixed-point argument showing the alignment objective is achieved at equilibrium. If the presentation in the main text is deemed insufficient, we will expand this derivation and add the explicit formula to the abstract or a new subsection. revision: partial
Referee: [Method (objective redefinition)] The redefinition of the calibration objective (to align quantized output directly with full-precision output) introduces the compensation-aware error from weight discrepancy, but without explicit update rules or fixed-point analysis, it is unclear whether the iterative compensation loop still converges to the claimed alignment.

Authors: Section 3.2 derives the explicit update rules under the redefined objective, showing that the compensation-aware error is folded directly into the residual term used for weight updates. The iterative loop converges because each compensation step now minimizes the layer output discrepancy to the true full-precision output rather than an intermediate compensated target; the fixed-point analysis (detailed in Appendix A, Equation 8) confirms that the equilibrium remains stable and the quantization error decreases monotonically without oscillation or shift in convergence rate. This analysis builds on the original GPTQ/GPTAQ convergence properties while accounting for the additional error term. revision: no

Circularity Check

0 steps flagged

Redefinition of residual error follows from external full-precision alignment; no reduction to fitted inputs or self-citation

full rationale

The paper redefines the intra-layer calibration objective to align quantized outputs directly with the original full-precision model outputs (rather than compensated-weight outputs). From this external reference it derives the additional 'compensation-aware error' as the discrepancy between compensated and original weights within the layer. Incorporation of the new term is achieved by applying the neuron decomposition technique inherited from the independent prior work GPTAQ. No equation or step reduces the claimed precise alignment or the new error term to a self-referential fit, a renamed input, or a load-bearing self-citation; the target remains the external full-precision output and the decomposition is treated as an off-the-shelf tool. The derivation is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The approach inherits the neuron decomposition technique and assumes the new error term can be added without side effects; no new free parameters are introduced in the abstract description.

axioms (1)

domain assumption Neuron decomposition from GPTAQ can be directly reused to incorporate the compensation-aware error into weight updates.
The paper states it inherits the technique without providing a new derivation.

invented entities (1)

compensation-aware error no independent evidence
purpose: Captures the discrepancy between compensated weights and original full-precision weights inside each layer as part of the residual error.
Newly defined term based on analysis of the compensation process.

pith-pipeline@v0.9.0 · 5578 in / 1314 out tokens · 48178 ms · 2026-05-10T18:07:02.112447+00:00 · methodology

discussion (0)

Reference graph

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Therefore, our method can be integrated with both GPTQ and GPTAQ

13 Published as a conference paper at ICLR 2026 A APPENDIX A.1 INTEGRATION OF OUR METHOD WITHGPTQ Since our focus is on the residual error introduced by weight compensation—an error present in both GPTQ and GPTAQ—it is still sufficient to incorporate the P2 term into the weight compensation. Therefore, our method can be integrated with both GPTQ and GPTAQ...

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training dataset for calibration data. The compared baselines include recent post-training quantization methods such as APQ-ViT (Ding et al., 2022), RepQ-ViT (Li et al., 2023), GPTQ (Frantar et al., 2022), and GPTAQ (Li et al., 2025). For all compensation-based methods (GPTQ, GPTAQ, and Ours), we utilize theactorderoption to sort weight columns by Hessian...

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On DeiT-Small, our approach reaches 74.0% accuracy, out- performing the strong GPTAQ baseline

Under W4A4 quantization, our method achieves highly com- petitive performance across all models. On DeiT-Small, our approach reaches 74.0% accuracy, out- performing the strong GPTAQ baseline. The advantages of our method become more pronounced in the lower-precision W2A4 setting. For DeiT-Base, our approach improves the accuracy to 62.1%, a notable gain o...

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Table 10: Matrix needed to perform calibration and their sizes.C o andC i denotes the output- channel and input-channel of weights, whilebdenotes the blocksize for lazy-batch update. Matrix GPTQ GPTAQ GPTAQ+Ours Original weight:W (0) - - Co ×C i Compensated weight:W Co ×C i Co ×C i Co ×C i Fake quant weight:Q Co ×C i Co ×C i Co ×C i Cholesky factor:L Ci ×...

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Subsequently, we analyzed the influence of the calibration set Table 12: Performance of 3-bit per-group symmetric weight-only quantization

Our method consistently achieves a stable improvement over GPTAQ, demonstrating its robustness across vary- 17 Published as a conference paper at ICLR 2026 ing numbers of calibration samples. Subsequently, we analyzed the influence of the calibration set Table 12: Performance of 3-bit per-group symmetric weight-only quantization. using different cal- ibra...

2026