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RoSTE: An Efficient Quantization-Aware Supervised Fine-Tuning Approach for Large Language Models

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read RoSTE fine-tunes LLMs while quantizing weights, activations, and KV caches to 4 bits, outperforming post-training quantization baselines.

desk verdict New adaptive-rotation QA-SFT method with a believable ablation, but the headline numbers are single-run best-of-sweep and the 'consistently superior' claim needs multi-seed confirmation. read the letter →

arxiv 2502.09003 v3 pith:KCPVXK3R submitted 2025-02-13 cs.LG cs.AI

Quan Wei , Chung-Yiu Yau , Hoi-To Wai , Yang Katie Zhao , Dongyeop Kang , Youngsuk Park , Mingyi Hong This is my paper · ORCID
classification cs.LGcs.AI
keywords RoSTEquantization-awaresupervisedfine-tuningrotation-basedquantizationWalsh-Hadamardrotationstraight-throughestimatorW4A4KV4largelanguagemodelsbileveloptimization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes RoSTE, a supervised fine-tuning method that produces a large language model with 4-bit weights, activations, and KV caches in a single training phase, instead of fine-tuning first and quantizing afterward. The central claim is that interleaving straight-through-estimator weight updates with an adaptive per-layer choice of a Walsh-Hadamard rotation, chosen to minimize a weight-activation quantization-error surrogate, keeps the quantized model close to the full-precision fine-tuned model on downstream tasks. On TL;DR summarization, RoSTE reaches 23.66 average ROUGE on Pythia-6.9B and 25.10 on Qwen2.5-7B, versus 20.65 and 22.12 for the best quantized baselines; on the Tulu 3 suite it reaches 31.69 average accuracy on Llama-3.1-8B versus 29.13 for SpinQuant. The paper also proves a bound, for a linearized quantized training problem, showing prediction error is controlled by the weight quantization error, which the rotation search directly reduces. A reader should care because the method targets the practical bottleneck of deploying task-adapted LLMs at low precision.

What carries the argument

The load-bearing object is the bilevel formulation of Eq. (11): the upper level minimizes the SFT loss over quantized weights under straight-through estimation, while the lower level picks rotation matrices $\{R_i\}$ by minimizing the weight-activation quantization-error surrogate $E(W,R)$ of Eq. (12). The rotation family is restricted to identity or a random Walsh-Hadamard matrix $R(\zeta) = H\,\mathrm{Diag}(r(\zeta))$ (Eq. 19), whose fast CUDA kernel makes the search cheap. The theoretical engine is Theorem 4.3, which bounds the prediction error of a quantized linear model trained by STE by a discounted weighted sum of the weight-quantization errors, so reducing $E(W,R)$ directly reduces a bound on task loss. The per-layer decision rule, apply $H$ only where it lowers $E$, is what distinguishes RoSTE from rotating every module.

What would settle it

Pick a RoSTE-trained checkpoint and flip a single layer's rotation from the choice that minimizes $E(W,R)$ to the other; if held-out task accuracy improves, or stays equal while $E(W,R)$ rises, on enough layers, the surrogate-to-task link is falsified. A cheaper check is to recompute $E(W,R)$ on a disjoint calibration set and see whether the per-layer ordering of rotation benefits changes.

Watch

Extended reading notes

Core claim

RoSTE's discovery is that quantization-aware supervised fine-tuning works best when the model is allowed to decide, layer by layer, whether an incoherence rotation helps before each block of STE updates. Concretely, the method alternates between straight-through-estimator gradient steps on the supervised fine-tuning objective for the rotated, quantized network and a low-cost search over two candidates per layer, identity or a random Walsh-Hadamard matrix, selecting whichever minimizes the quantization error $E(W,R)$ of Eq. (12) on 128 calibration samples. The paper shows theoretically, on an overparameterized least-squares model with interpolating quantized features, that the STE-trained prediction error is bounded by a discounted sum of weight-quantization errors, and that a Hadamard rotation turns an outlier-sensitive error of order $d\,\max_i w_i^2$ into an $O(\|w\|^2)$ bound with high probability. Empirically, this adaptive rotation lets W4A4KV4 RoSTE models approach full-precision SFT accuracy while clearly outperforming SFT-then-PTQ pipelines such as RTN, GPTQ, QuaRot, and SpinQuant. The ablation with complete rotation shows the per-layer decision is load-bearing: rotating every module costs 9.98 average ROUGE on Pythia-1B.

Load-bearing premise

The load-bearing premise is that the quantization-error surrogate $E(W,R)$ computed on 128 calibration samples from the fine-tuning dataset faithfully tracks the final task objective, a link the paper proves only for a scalar-output quadratic interpolation model, not for transformer cross-entropy training.

Editorial extensions

If this is right

  • A single QA-SFT run replaces the conventional two-stage SFT-then-PTQ pipeline, saving the extra quantization pass and avoiding its accuracy loss.
  • At W4A4KV4, RoSTE recovers most of the full-precision SFT gap: on TL;DR, the remaining gap to FP16 SFT is about 1.06 average ROUGE for Pythia-6.9B and 0.77 for Qwen2.5-7B.
  • Adaptive rotation, not rotation per se, is what succeeds: applying the Walsh-Hadamard rotation to every layer drops average ROUGE by 9.98 on Pythia-1B, while RoSTE's per-layer choice beats no rotation.
  • The surrogate $E(W,R)$ is a practical guide for rotation search, and the theoretical bound says minimizing weight-quantization error is the mechanism, so the same principle can be reused in other quantization-aware training settings.
  • The benefits concentrate at aggressive 4-bit weight-activation quantization, where activation outliers dominate the quantization error.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper's K=1 implementation, one could re-select rotations several times during a longer fine-tuning run; the authors expect this to help on larger datasets, and it is a direct testable extension of the algorithm.
  • The surrogate-plus-Hadamard-search recipe could be lifted out of SFT and applied to other post-training objectives, such as preference alignment or continued pretraining, where quantization-aware updates are currently done with LoRA.
  • The theorem's bit-width remark suggests a trade-off: activation bit-width matters mainly for reaching an interpolation regime, while weight bit-width keeps improving the bound; if this transfers, QA-SFT budgets should spend bits on weights before activations.
  • Because the complete-rotation ablation hurts badly, the method implicitly relies on the 128 calibration samples being representative; shrinking or reshuffling that subset and watching task accuracy degrade would reveal how much of RoSTE's gain depends on the surrogate's fidelity.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes RoSTE, a quantization-aware supervised fine-tuning (QA-SFT) algorithm that alternates between STE-based optimization of the SFT objective over quantized weights and a per-layer search over a Walsh-Hadamard rotation vs. identity that minimizes a weight-activation quantization-error surrogate. The authors report W4A4KV4 results on Pythia, Qwen, and Llama models, claim consistent superiority over post-SFT PTQ baselines (RTN, GPTQ, QuaRot, SpinQuant) and plain STE, and provide a stylized quadratic-model convergence bound (Theorem 4.3) together with a Walsh-Hadamard incoherence proposition. Code is released.

Significance. If the empirical claims are robust, the method is a practically useful single-pass alternative to fine-then-quantize pipelines for 4-bit weight-activation-KV quantization, and the adaptive per-layer rotation choice is well motivated by the ablation in Table 3 showing that applying rotation to all layers is harmful. The theoretical section is a reasonable first step: Proposition 4.4 gives a formal justification for Hadamard rotation for outlier-heavy weight vectors, and Theorem 4.3, despite its simplicity, makes explicit that the prediction error of STE training is tied to the weight quantization error. The paper also ships code and gives detailed implementation information. However, the central 'consistently superior' claim currently rests on single-run, best-of-sweep comparisons with undisclosed selected hyperparameters, so the practical significance is conditional on stronger experimental evidence.

major comments (3)
  1. [Section 5, Tables 1-2 and Table 5] Table 5 reports that every STE and RoSTE model is produced by sweeping the learning rate over three values and the clipping factor over three values, but Tables 1-2 report one number per condition without stating which configuration was selected or how many seeds (or checkpoints) were averaged. Since the PTQ baselines are evaluated with fixed settings, the reported margins of +3.01 ROUGE on Pythia-6.9B and +2.56 average accuracy on Llama-3.1-8B can in principle reflect best-of-nine selection for the QA-SFT methods against un-tuned baselines. The per-task pattern in Table 2 is also not uniformly favorable: RoSTE scores 26.44 on TruthfulQA versus 27.66 for QuaRot, so the average margin is not evidence of consistent per-task superiority. Please disclose the selected hyperparameters, run multiple seeds, and report the variability of the main comparisons so that 'consistently superior' is supported as stated.
  2. [Section 4, Eq. (18) and Assumption 4.2] Theorem 4.3 is proven only for a scalar-output linear model whose loss is squared prediction error (13)-(14), and Assumption 4.2 requires interpolation for every orthogonal matrix R, which is a strong condition that is not verified for transformer cross-entropy objectives. Moreover, the bound in Eq. (18) is expressed in the G-norm (weighted by the activation Gram matrix), whereas the lower-level objective E in Eq. (12) is an unweighted layer-wise sum of weight and activation quantization errors; the paper does not show that decreasing E decreases the G-norm terms or the SFT loss. Because the complete-rotation ablation in Table 3 shows that a poor rotation choice can cost -9.98 ROUGE, the reliability of this surrogate is load-bearing. I recommend adding a direct empirical check of the surrogate's correlation with the SFT objective (e.g., comparing E against held-out SFT loss across rotation configurations) and softening the abstract's claim that prediction error is 'directly proportional' to the quantization error.
  3. [Section 5, first paragraph and Algorithm 1] The paper states that K = 1 is used in all experiments, with the one-shot rotation configuration computed from the pre-trained model. With K = 1, the rotation configuration is never re-adapted after the QAT stage begins, so the implemented method is closer to 'fixed pre-selected rotations + STE-based QAT' than to the alternating adaptive-rotation procedure described in Section 3 and Figure 2. The sentence 'we anticipate the performance to further improve with larger K' is a conjecture and no experiments with K > 1 are reported. Please clarify whether any experiment used K > 1, and if not, revise the method description and the 'adaptive rotation strategy' claim so that the paper's claims match the implementation.
minor comments (4)
  1. [Throughout] There are several typos: 'appraoches' in Section 1, 'sceneario' in Section 2.2, and 'ROGUE score' in the discussion of Table 3.
  2. [Appendix F, text before Table 9] The sentence 'the results for Exp.2 on the Pythia models can be found in Table 9' should refer to Llama models; Table 9 reports Llama 3.1 8B results.
  3. [Algorithm 1, line 5 and Eq. (19)] Algorithm 1 says the Walsh-Hadamard matrix H is 'generated according to (19)', but Eq. (19) defines R(ζ) and does not specify the distribution of r(ζ); please state explicitly that r(ζ) is a uniformly random sign vector.
  4. [Figure 1] The full-precision SFT and Base entries appear as horizontal reference lines with no measured training-time point; please clarify in the caption that these are reference values, not training runs, to avoid an apples-to-oranges comparison in the time axis.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity; one non-load-bearing self-citation keeps the score at 2.

full rationale

RoSTE's derivation chain is self-contained. The method selects rotation matrices by minimizing the quantization-error surrogate E in Eq. (12) on 128 calibration samples, runs STE-based QAT on the SFT objective, and then reports ROUGE and benchmark accuracies that are external to the optimization. The only bridge from E to final quality is Theorem 4.3, whose bound (18) is a genuine mathematical consequence under Assumptions 4.1-4.2, not a restatement of the conclusion; it bounds prediction error by an initial error term plus accumulated weight-quantization errors. This motivates the surrogate E but does not define it in terms of the final metrics, and E contains no ROUGE or accuracy term, so there is no fitted-input-called-prediction reduction. The Walsh-Hadamard incoherence bound in Proposition 4.4 is explicitly credited to Tseng et al. (2024), an external source, and no uniqueness theorem is imported from the authors' prior work. The only self-citation is footnote 2, which cites Li et al. (2024) merely as an example of other fine-tuning objectives; it is not load-bearing. Figure 4's lower quantization error for RoSTE is expected by construction because Algorithm 1 line 5 explicitly minimizes E, but the paper's central empirical claims rest on Tables 1-3, which use external evaluations rather than E itself. No circular step reaches the listing threshold; the score of 2 reflects the rubric's category for a single non-load-bearing self-citation.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The method relies on standard QAT machinery plus a strong interpolation assumption and a surrogate objective that links quantization error to task performance. No new physical or parametric entities are postulated. The free parameters are standard training hyperparameters and design choices, but the lack of reported final values weakens reproducibility.

free parameters (4)
  • Clipping factor c = One of {1, 0.95, 0.9} per model, not reported
    Swept to obtain best QA-SFT accuracy; directly changes the quantizer range in Eqs. (2) and (4).
  • Learning rate = One of {3e-5, 6e-6, 3e-6} etc. per model, not reported
    Swept per model for STE and RoSTE to obtain the best performance (Table 5); the selected values are not listed.
  • Calibration set size n = 128
    Hand-chosen number of samples for evaluating the lower-level quantization error in Eq. (12).
  • Outer-loop count K = 1
    Set to one-shot rotation configuration adaptation from pre-trained weights; larger K is anticipated but untested.
assumptions (5)
  • domain assumption Assumption 4.1: the Gram matrix of quantized-rotated features satisfies G^2 ⪰ λ_min G and ||Qx(Rx_t)||^2_G ≤ ρ.
    Bounds the geometry of the random features; plausible for bounded inputs but unverified for real LLM activations.
  • domain assumption Assumption 4.2: for every orthogonal R, there exists w*_R interpolating all training pairs through the quantized-rotated features.
    Very strong overparameterization assumption needed for the quadratic-analysis theorem; not checked in experiments.
  • domain assumption STE approximation: the derivative of the quantizer is replaced by the identity in backprop (Eq. 6).
    Standard in QAT; introduces the gradient bias that the analysis quantifies.
  • ad hoc to paper The lower-level problem (12) is an appropriate surrogate for the SFT loss during QAT.
    Central modeling choice of RoSTE; supported only by simplified theory and an empirical correlation (Fig. 4), not by a bound on the actual objective.
  • standard math Random Walsh-Hadamard matrix R(ζ) has the incoherence property (Proposition 4.4, from Tseng et al. 2024).
    Restates a known lemma about random Hadamard rotations reducing quantization error; accepted as prior art.

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Cite this review

Pith. "Pith review of RoSTE: An Efficient Quantization-Aware Supervised Fine-Tuning Approach for Large Language Models." pith.science (2026). https://pith.science/paper/KCPVXK3R

@misc{pith2026250209003,
  author       = {Pith},
  title        = {Pith review of: RoSTE: An Efficient Quantization-Aware Supervised Fine-Tuning Approach for Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KCPVXK3R}},
  note         = {Machine review of arXiv:2502.09003}
}
read the original abstract

Supervised fine-tuning is a standard method for adapting pre-trained large language models (LLMs) to downstream tasks. Quantization has been recently studied as a post-training technique for efficient LLM deployment. To obtain quantized fine-tuned LLMs, conventional pipelines would first fine-tune the pre-trained models, followed by post-training quantization. This often yields suboptimal performance as it fails to leverage the synergy between fine-tuning and quantization. To effectively realize low-bit quantization of weights, activations and KV caches in LLMs, we propose an algorithm named Rotated Straight-Through-Estimator (RoSTE), which combines quantization-aware supervised fine-tuning (QA-SFT) with an adaptive rotation strategy that identifies an effective rotation configuration to reduce activation outliers. We provide theoretical insights on RoSTE by analyzing its prediction error when applied to an overparameterized least square quantized training problem. Our findings reveal that the prediction error is directly proportional to the quantization error of the converged weights, which can be effectively managed through an optimized rotation configuration. Experiments on Pythia, Qwen and Llama models of different sizes demonstrate the effectiveness of RoSTE. Compared to existing post-SFT quantization baselines, our method consistently achieves superior performances across various tasks and different LLM architectures. Our code is available at https://github.com/OptimAI-Lab/RoSTE.

Figures

Figures reproduced from arXiv: 2502.09003 by the authors.

Figure 1
Figure 1. RoSTE surpasses the performance of SOTA quantization methods on fine-tuning benchmark. Horizontal axis represents the total amount of hours needed to fine-tune pre-trained LLMs on a server of 8 × A100 NVIDIA GPUs. QAT introduces an additional training phase, substantially increasing computational costs. Treating fine-tuning and quantization as separate steps can lead to suboptimal results, as it fails to exploit the… view at source ↗
Figure 2
Figure 2. The RoSTE algorithm alternates between tackling the lower level problem for rotation configuration and the upper level problem of SFT training using rotation-aware STE. Motivated to solving the ideal formulation (8), in our re￾formulation (11), the optimal lower level variable aims at assisting the upper level weights so that an STE gradient approximation on LSFT w.r.t. {Wi} ℓ−1 i=0 has a smaller bias. However, it r… view at source ↗
Figure 3
Figure 3. Visualizations of input activations at layer 30 of con￾verged Llama model trained for QA-SFT using STE and RoSTE. Lastly, in the appendix, we provide additional results of W4A4K4 and W4A8K4 quantization on Pythia 1B in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The evolution of quantization error (12) against the QAT stage iterations. When no rotation matrix is applied, we observe a drop in ROUGE score by −0.70, and importantly, the complete rotation setting, i.e., applying rotation matrix on every mod￾ule regardless of wheth…
Figure 5
Figure 5. Figure 5: An illustration of the rotation workflow in a transformer-based model. R1 represents the between-block rotation, which eliminates activation outliers between blocks. R2, R3, R4 are in-block rotations designed to remove outliers within the MHSA and MLP blocks. Among the…
Figure 6
Figure 6. Figure 6: showcases the effects of (random Walsh-Hadamard) rotation applied to several exemplary layers in Pythia and Llama models, and demonstrates that sometimes applying the rotation can lead to undesirable results where new outlier values emerge [PITH_FULL_IMAGE:figures/ful…
Figure 7
Figure 7. Figure 7: Effects of incoherence processing using rotation matrices on different layers of Pythia and Llama models using the pre-trained weights. (Left) Relative reduction rates of quantization error, calculated as Error w/o rotation−Error w/ rotation Error w/o rotation × 100%. …

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Forward citations

Cited by 3 Pith papers

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.