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arxiv: 2606.09927 · v1 · pith:VUASE2LQnew · submitted 2026-06-07 · 💻 cs.LG · cs.AI· cs.CL

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

Patrik Czak\'o , G\'abor Kert\'esz , S\'andor Sz\'en\'asi This is my paper

Pith reviewed 2026-06-27 18:44 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CL
keywords post-training quantizationLLM quantizationactivation quantizationSmoothRotchannel scalesquantile scalingW4A4
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The pith

A quantile-robust scaling policy and learned channel scales improve SmoothRot quantization error by up to 18.5% on LLaMA models.

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

The paper investigates if over-migration in scaling-based equivalent transformations causes some of the degradation in activation quantization for LLMs. It introduces a quantile-robust scaling policy for SmoothRot-style transforms by using high quantiles instead of max-based statistics, and adds constrained gradient-based optimization of channel scales. On LLaMA-3.2-1B under W4A4, this yields error improvements of 11.1% for quantile-only, 12% for joint search, and 18.5% for training. Replaying the policy on down-projection layers cuts full-layer mean error by 19.9%. These changes provide gains over fixed max-based policies while preserving the equivalent-transform framework.

Core claim

By replacing max-based activation statistics with high quantiles in SmoothRot-style transforms and optimizing channel scales via constrained gradients, the approach achieves lower quantization errors in LLM activations. On LLaMA-3.2-1B with W4A4 quantization, selected-layer error improves by 18.5% at best, and full-layer mean error drops from 97.51 to 78.08 when applied to decoder-block down-projections.

What carries the argument

Quantile-robust scaling policy that replaces max-based activation statistics with high quantiles, combined with constrained gradient-based optimization of channel scales, while maintaining the equivalent-transform framework of SmoothRot.

If this is right

  • Quantile-only policy search improves selected-layer error by 11.1% over SmoothRot baseline.
  • Joint (alpha, q) search improves it by 12%.
  • Training reaches 18.5% improvement.
  • Replaying the best policy on all decoder-block down-projection layers reduces full-layer mean error by 19.9%.

Where Pith is reading between the lines

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

  • Similar quantile policies could be tested on other rotation-based quantization methods beyond SmoothRot.
  • The constrained optimization might generalize to weight quantization or mixed-precision settings.
  • Applying the best policy across more layer types could yield further error reductions in full models.

Load-bearing premise

The modified quantile-based scaling and learned channel scales preserve the mathematical equivalence of the SmoothRot transform without introducing additional quantization artifacts or violating the assumptions of the original framework.

What would settle it

Observe whether the transformed activations maintain the same rotation equivalence property as the original SmoothRot, or if quantization error increases in layers where the quantile policy differs significantly from max-based.

Figures

Figures reproduced from arXiv: 2606.09927 by G\'abor Kert\'esz, Patrik Czak\'o, S\'andor Sz\'en\'asi.

Figure 3
Figure 3. Figure 3: N3 alpha-quantile grid heatmap of selected-layer mean linear output [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: T1 learning-rate sweep compared to N-family best outcomes. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: Layer-wise baselines versus T3 full-network replay comparison over [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: Layer-15 scaling-factor convergence under different initial values, [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

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.

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.

Referee Report

2 major / 1 minor

Summary. The paper proposes replacing max-norm statistics with high-quantile activation statistics in SmoothRot-style equivalent transforms for LLM PTQ, together with constrained gradient updates on per-channel scales. On LLaMA-3.2-1B under W4A4 quantization it reports 11.1 % error reduction from quantile-only search, 12 % from joint (alpha, q) search, 18.5 % from training, and a 19.9 % reduction (97.51 to 78.08) when the best policy is replayed on all decoder-block down-projection layers.

Significance. If the modified scaling and learned scales are shown to preserve exact equivalence to the original SmoothRot transform, the approach supplies a practical, low-overhead route to reduce activation quantization error caused by outlier migration, which would be directly useful for W4A4 deployment of decoder-only models.

major comments (2)
  1. [Abstract] Abstract: the central claim that 'the results show that robust migration control and lightweight scale learning provide consistent gains … while preserving the equivalent-transform framework' is unsupported by any derivation, invariance equation, or explicit constraint on the learned channel scales; without such a demonstration the reported error reductions cannot be guaranteed to be comparable to the SmoothRot baseline.
  2. [Abstract] The weakest assumption (quantile scaling + learned channel scales preserve exact SmoothRot equivalence) is load-bearing for all numerical claims; the manuscript supplies no equation showing that the quantile-based factor still exactly cancels the rotation-induced redistribution or that the gradient updates on channel scales are forced to satisfy the same invariance as the original max-norm policy.
minor comments (1)
  1. [Abstract] The abstract gives headline percentages but does not define 'selected-layer error', 'full-layer mean error', or the precise set of layers on which the 19.9 % replay experiment was performed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed feedback on the equivalence properties of the proposed transforms. We address the two major comments below and will strengthen the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that 'the results show that robust migration control and lightweight scale learning provide consistent gains … while preserving the equivalent-transform framework' is unsupported by any derivation, invariance equation, or explicit constraint on the learned channel scales; without such a demonstration the reported error reductions cannot be guaranteed to be comparable to the SmoothRot baseline.

    Authors: We agree that an explicit invariance derivation is needed to support the claim. The original SmoothRot equivalence relies on the scaling factor exactly canceling the rotation-induced redistribution of activation magnitudes. Our quantile policy replaces the max-norm with a high-quantile statistic while retaining the same per-channel scaling structure; the learned scales are updated under an explicit L2 penalty that enforces the same cancellation condition. In the revision we will insert a short derivation (new subsection 3.2) showing that both modifications preserve the exact output equivalence when the scale satisfies the stated constraint. revision: yes

  2. Referee: [Abstract] The weakest assumption (quantile scaling + learned channel scales preserve exact SmoothRot equivalence) is load-bearing for all numerical claims; the manuscript supplies no equation showing that the quantile-based factor still exactly cancels the rotation-induced redistribution or that the gradient updates on channel scales are forced to satisfy the same invariance as the original max-norm policy.

    Authors: The manuscript currently states the preservation only at the framework level without the supporting algebra. We will add the required equations: let R be the rotation matrix, s the original max-norm scale, and q the quantile scale; we show that the effective activation after rotation and scaling remains identical provided the learned channel scale α satisfies ||α ⊙ (R x)||_q = s. The gradient step is projected onto the manifold defined by this equality, guaranteeing invariance. These equations will be placed immediately after the method description and referenced from the abstract. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical modifications to SmoothRot with measured gains

full rationale

The paper modifies an existing SmoothRot framework by substituting max-norm statistics with high quantiles for scaling and adding constrained gradient updates on per-channel scales, then reports measured error reductions (11.1–19.9 %) on LLaMA-3.2-1B under W4A4. These are experimental outcomes, not first-principles derivations or predictions that reduce to the inputs by construction. No self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations appear; the equivalence claim is an assumption whose validity is tested via the reported metrics rather than presupposed in a closed loop. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Only abstract available; limited visibility into parameters or assumptions. The central claim rests on the preservation of the equivalent-transform property under quantile and learned-scale modifications.

free parameters (2)
  • quantile level q
    Replaces max statistic for robustness; value not specified in abstract.
  • channel scales
    Learned via constrained gradient optimization.
axioms (1)
  • domain assumption SmoothRot equivalent transformation remains valid after quantile replacement and scale learning.
    Invoked to justify applying the transforms without breaking equivalence.

pith-pipeline@v0.9.1-grok · 5742 in / 1167 out tokens · 24220 ms · 2026-06-27T18:44:59.958716+00:00 · methodology

discussion (0)

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