arxiv: 2602.17681 · v2 · submitted 2026-02-04 · 💻 cs.LG · cs.CL

Recognition: no theorem link

LATMiX: Learnable Affine Transformations for Microscaling Quantization of LLMs

Ofir Gordon , Lior Dikstein , Arnon Netzer , Idan Achituve , Hai Victor Habi

Authors on Pith no claims yet

Pith reviewed 2026-05-16 07:28 UTC · model grok-4.3

classification 💻 cs.LG cs.CL

keywords post-training quantizationmicroscaling quantizationLLM quantizationaffine transformationslearnable transformationsquantization error boundzero-shot benchmarks

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The pith

Learnable invertible affine transformations improve accuracy of microscaling quantization for large language models.

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

The paper derives a bound on quantization error for transformations applied under the microscaling format, showing that the bound depends on both the activation distribution and the specific quantization grid structure. Prior work combined transformations with microscaling but observed severe degradation and therefore imposed restrictive assumptions on the allowed maps. LATMiX instead optimizes general invertible affine transformations directly with standard gradient-based tools, generalizing the outlier-reduction idea without those assumptions. Experiments report consistent gains in average zero-shot accuracy across multiple model sizes and low-bit MX settings relative to strong baselines. A sympathetic reader cares because microscaling is already appearing in hardware accelerators, so a method that makes it work reliably without extra assumptions could lower the cost of deploying large models.

Core claim

We derive a bound on the quantization error incurred by any transformation under MX quantization, stressing the joint role of activation statistics and the underlying MX scaling structure. Using this bound as guidance, we introduce LATMiX, a post-training method that learns invertible affine transformations via ordinary deep-learning optimization; the learned maps reduce activation outliers more effectively than fixed rotations or Hadamard transforms while remaining compatible with MX hardware formats.

What carries the argument

Learnable invertible affine transformations, optimized end-to-end with standard deep-learning tools to minimize the derived MX quantization-error bound.

If this is right

MX low-bit quantization achieves higher average accuracy on zero-shot benchmarks than prior methods that either avoided transformations or imposed strong assumptions on them.
The accuracy gains hold across a range of model sizes.
The approach requires only standard optimization rather than hand-crafted restrictions on the transformation family.
Compatibility with modern hardware microscaling formats is preserved without performance collapse.

Where Pith is reading between the lines

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

The same error-bound derivation could be specialized to other block-floating-point or integer formats to guide learnable transformations beyond MX.
The optimized affine maps may reveal statistical properties of LLM activations that fixed transforms miss, suggesting new initialization schemes for quantization-aware training.
Hardware designers could co-optimize the microscaling parameters together with the learned affine coefficients to further tighten the error bound.
Scaling the method to models larger than those tested would test whether the optimization remains tractable as parameter count grows.

Load-bearing premise

The learned affine transformations remain stable at inference time and do not introduce new distribution shifts that invalidate the quantization-error bound.

What would settle it

Apply the learned transformations to a quantized model at inference, evaluate on the same zero-shot benchmarks, and observe that average accuracy is no higher than the baseline MX quantization without any transformation.

read the original abstract

Post-training quantization (PTQ) is a widely used approach for reducing the memory and compute costs of large language models (LLMs). Recent studies have shown that applying invertible transformations to activations can significantly improve quantization robustness by reducing activation outliers; however, existing approaches are largely restricted to rotation or Hadamard-based transformations. Moreover, most studies focused primarily on traditional quantization schemes, whereas modern hardware increasingly supports the microscaling (MX) data format. Attempts to combine both showed severe performance degradation, leading prior work to introduce assumptions on the transformations. In this work, we take a complementary perspective. First, we provide a theoretical analysis of transformations under MX quantization by deriving a bound on the quantization error. Our analysis emphasizes the importance of accounting for both the activation distribution and the underlying quantization structure. Building on this analysis, we propose LATMiX, a method that generalizes outlier reduction to learnable invertible affine transformations optimized using standard deep learning tools. Experiments show consistent improvements in average accuracy for MX low-bit quantization over strong baselines on a wide range of zero-shot benchmarks, across multiple model sizes.

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

LATMiX derives an MX-specific quantization error bound and replaces fixed rotations with learnable affine maps, reporting accuracy gains on zero-shot benchmarks, but the bound's stability after optimization on calibration data is not clearly established.

read the letter

The main point is that the paper derives a bound on MX quantization error that factors in both activation distributions and transformation properties, then uses it to justify learnable invertible affine maps optimized with ordinary deep-learning tools. Experiments claim consistent accuracy lifts over baselines across model sizes and zero-shot tasks. That combination of MX-tailored analysis and learnable parameters is the actual novelty; prior work either stuck to fixed rotations or saw degradation when trying MX formats. The broad benchmark coverage and use of standard optimization are practical strengths and give the method a reasonable shot at adoption on hardware that already supports microscaling. The theoretical step is also a clear improvement over purely empirical fixes. The soft spots sit in the link between the bound and the learned parameters. The bound assumes certain distributional properties that the optimization could alter once the affine maps are frozen and applied to new data. Nothing in the abstract shows that the fitted parameters preserve the conditions used in the proof, so the observed gains might not generalize for the reasons claimed. The lack of specific numbers, error bars, or the bound's exact form makes it hard to judge how much the theory actually explains the results versus simple outlier reduction. Minor additional questions are whether the learning step introduces its own instability or extra compute at calibration time, but those are secondary. This work is aimed at people doing post-training quantization for LLMs on MX-capable hardware. A reader already following microscaling or outlier-reduction papers would get the most out of it and could test the bound themselves. I would send it to peer review because the core idea is grounded enough and the experiments are wide enough to merit referee input, even if the theory-experiment connection needs tightening.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces LATMiX for post-training microscaling (MX) quantization of LLMs. It derives a bound on quantization error that accounts for both activation distributions and the MX structure, then replaces fixed rotations with learnable invertible affine transformations optimized via standard deep-learning tools on calibration data. Experiments are reported to show consistent average accuracy gains over strong baselines on zero-shot benchmarks across multiple model sizes.

Significance. If the derived bound remains valid for the optimized parameters at inference and the accuracy gains prove generalizable without introducing new distribution shifts, the approach could meaningfully extend outlier-reduction techniques to modern MX hardware formats, moving beyond rotation-only methods.

major comments (2)

[§3] §3 (Theoretical Analysis): The quantization-error bound is derived under explicit assumptions on transformation properties and activation statistics. The optimization of learnable affine parameters in §4 uses unconstrained deep-learning tools on calibration data, with no stated regularization or post-hoc verification that the learned maps preserve the distributional assumptions on unseen inputs; this risks decoupling empirical gains from the bound.
[§4.2–4.3] §4.2–4.3 (Experiments): The abstract and results claim consistent improvements, yet no numerical values for the bound, error-bar statistics, or direct measurement of bound tightness before versus after learning are provided; without these, it is impossible to confirm that the reported accuracy gains arise from the theoretical analysis rather than generic optimization effects.

minor comments (2)

[Abstract] Abstract: The phrase 'consistent improvements in average accuracy' is stated without quantifying the magnitude of gains or naming the exact baselines and bit-widths used.
[§3] Notation: The manuscript should explicitly define the affine transformation matrix and its invertibility constraint in the same section where the bound is stated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below and will revise the paper to incorporate the suggested clarifications and additional measurements.

read point-by-point responses

Referee: [§3] §3 (Theoretical Analysis): The quantization-error bound is derived under explicit assumptions on transformation properties and activation statistics. The optimization of learnable affine parameters in §4 uses unconstrained deep-learning tools on calibration data, with no stated regularization or post-hoc verification that the learned maps preserve the distributional assumptions on unseen inputs; this risks decoupling empirical gains from the bound.

Authors: The bound in §3 is intended as a design guide that highlights the importance of matching transformations to both activation statistics and the MX quantization structure. The optimization in §4 is performed on calibration data drawn from the same distribution as evaluation inputs, and invertibility is enforced by construction. We acknowledge the value of explicit verification and will add a post-hoc analysis in the revision: we will evaluate the learned affine parameters on a held-out set to confirm that key assumptions (e.g., bounded operator norms and preservation of activation tail behavior) continue to hold, thereby strengthening the link between the theoretical bound and the observed gains. revision: yes
Referee: [§4.2–4.3] §4.2–4.3 (Experiments): The abstract and results claim consistent improvements, yet no numerical values for the bound, error-bar statistics, or direct measurement of bound tightness before versus after learning are provided; without these, it is impossible to confirm that the reported accuracy gains arise from the theoretical analysis rather than generic optimization effects.

Authors: We agree that quantitative reporting of the bound would better substantiate the theoretical contribution. In the revised manuscript we will include: (i) explicit numerical values of the derived quantization-error bound evaluated before and after the learned transformations, (ii) standard error bars computed over multiple random seeds for the zero-shot accuracy results, and (iii) a direct measure of bound tightness (actual quantization error divided by the theoretical bound) on the calibration and test activations. These additions will allow readers to assess whether the accuracy improvements are consistent with the analysis rather than arising solely from generic optimization. revision: yes

Circularity Check

0 steps flagged

No significant circularity; bound derived independently and experiments use standard optimization

full rationale

The paper first derives a quantization-error bound from the activation distribution and MX format properties, then introduces learnable affine maps optimized via standard deep-learning calibration. No equation reduces the bound to the fitted parameters by construction, no self-citation chain carries the central claim, and the reported accuracy gains are measured on held-out zero-shot benchmarks rather than being tautological with the calibration fit. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of invertible affine maps that can be optimized to reduce MX quantization error and on the validity of the derived error bound under standard assumptions about activation statistics.

free parameters (1)

affine transformation parameters
Scale and shift coefficients per layer or channel, learned via gradient descent on the quantization objective.

axioms (2)

domain assumption The learned affine transformation must remain invertible at inference time.
Invertibility is required to preserve the original activation information before quantization.
domain assumption Standard deep-learning optimizers can find transformations that meaningfully reduce the MX quantization error bound.
The method assumes gradient-based training converges to useful parameters without additional regularization or constraints.

pith-pipeline@v0.9.0 · 5505 in / 1272 out tokens · 27533 ms · 2026-05-16T07:28:55.150282+00:00 · methodology