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REVIEW 5 major objections 6 minor 56 references

Data-Free Group-Wise Fully Quantized Winograd Convolution via Learnable Scales

T0 review · 5 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Tuning Winograd scale matrices on random noise makes fully quantized 8-bit Winograd convolution near-lossless for diffusion models.

desk verdict Tuning only the Winograd scale factors on random noise largely fixes fully quantized Winograd on diffusion models, but the 'safely guaranteed' generalization claim overreaches and key implementation details are missing. read the letter →

arxiv 2412.19867 v2 pith:2YQFIOP4 submitted 2024-12-27 cs.CV cs.AIcs.LG

Shuokai Pan , Gerti Tuzi , Sudarshan Sreeram , Dibakar Gope This is my paper · ORCID
classification cs.CVcs.AIcs.LG
keywords post-trainingquantizationWinogradconvolutiongroup-wisediffusionmodelslearnablescalesdata-free8-bitinferenceCPUkernels
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

This paper tries to establish that fully quantized 8-bit Winograd convolution—a fast-convolution method normally too lossy to use in quantized neural networks—can be made near-lossless by retuning only the diagonal scale factors of the Winograd transform, with no real training or calibration data. The scales are learned on random Gaussian or uniform noise, and the same learned scales are shared across all convolution layers of a model. If the claim holds, large text-to-image diffusion models could use 8-bit weights and activations together with Winograd $F(6,3)$ speedups while keeping FID and CLIP scores close to the full-precision model. The paper demonstrates this on InstaFlow-0.9B and Stable Diffusion v1.5, and shows ImageNet top-1 accuracy gains over prior Winograd post-training quantization methods, along with CPU kernel runtime improvements.

What carries the argument

The load-bearing object is the Vandermonde factorization of Winograd transforms, $B^T = S_B V^{-T}$, $G = S_G V$, $A^T = V^T S_A$, with diagonal scale matrices constrained by $S_A S_B S_G = I$. The method learns only $S_B$ and $S_G$ ($S_A$ follows from the constraint) by minimizing the SQNR loss between the quantized Winograd output and the full-precision convolution output on random noise inputs. This reweights the row norms of the transform matrices, compressing the cross-shaped dynamic-range spread in the Winograd-domain output $Y$ that group-wise quantization cannot absorb, and it does so without altering the algorithmic structure or requiring calibration data.

What would settle it

Take a model and learn the Winograd scales on random noise, then evaluate on inputs whose activations have extreme dynamic range, such as early diffusion timesteps, very high-resolution images, or a dataset with heavy-tailed outliers; if FID or top-1 accuracy drops substantially compared with scales learned on a small real calibration set, the data-free proxy is falsified. A more direct check is to compare the $8\times8$ Winograd-domain output range ratios for noise versus real activations and see whether the learned scales compress both.

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Extended reading notes

Core claim

The central discovery is that the severe accuracy drop in fully quantized Winograd convolution comes from the dynamic-range imbalance of the Winograd-domain output tile $Y$, not from quantization of the input transform or the Hadamard product. Group-wise quantization handles those stages well, but the output transform sees a cross-shaped pattern of very different magnitudes across the tile's taps, and a single or per-row scale cannot represent it. The paper shows this imbalance can be largely removed by learning only the diagonal scaling matrices $S_B$ and $S_G$ of the Vandermonde-based Winograd transforms, with $S_A$ determined by the identity $S_A S_B S_G = I$; the full transformation matrices themselves are never finetuned. Because the objective is minimized on random noise inputs, the learned scales transfer across datasets, and the result is 8-bit fully quantized Winograd $F(4,3)$/$F(6,3)$ that nearly matches full-precision image generation and classification quality.

Load-bearing premise

The method assumes that random Gaussian or uniform noise captures the dynamic-range structure of real activations well enough that scales learned on noise transfer to actual images, so if real activation distributions differ in ways noise cannot mimic, the quality recovery would not generalize.

Editorial extensions

If this is right

  • 8-bit fully quantized Winograd $F(4,3)$ and $F(6,3)$ on InstaFlow-0.9B and Stable Diffusion v1.5 keep FID and CLIP scores near the FP16 baseline, whereas standard group-wise Winograd collapses FID from about 22 to above 300.
  • On ImageNet, learned scales beat the PAW+FSQ baseline by 1.62% top-1 accuracy on ResNet-18 and 2.56% on ResNet-34 for Winograd $F(6,3)$, restoring most of the full-precision accuracy.
  • The same learned scales transfer across datasets without retraining: ImageNet-learned scales recover CIFAR-10 accuracy, and COCO-learned scales work on the MJHQ prompt set.
  • Highly optimized group-wise quantized Winograd kernels add a 31.3% runtime reduction on convolution layers and a 12.8% end-to-end speedup for InstaFlow-0.9B on CPU hardware.
  • Because only scales are tuned, the method avoids the cost of finetuning whole Winograd transformation matrices, which prior work found necessary for full quantization.

Reading between the lines

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

  • The same mechanism could apply to other fast transforms whose intermediate domains have uneven magnitude spreads, such as FFT-based convolution or Strassen-like matrix multiplication, since the analysis identifies Vandermonde row-norm structure rather than Winograd specifically as the culprit.
  • Using a single set of scales shared by all layers implies a much smaller parameter search than per-layer calibration; a natural test is whether layer-specific scales further close the small remaining $F(6,3)$ gap without hurting transfer.
  • The data-free claim is only as strong as the noise proxy; a stress test on distributions with heavy-tailed outliers, such as very early denoising steps or high-resolution inputs, would show whether random noise is truly sufficient or merely adequate on the tested models.
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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

5 major / 6 minor

Summary. The paper proposes a data-free method for fully quantized Winograd convolution. The key ideas are (i) group-wise quantization applied to all stages of the Winograd pipeline (input transform, Hadamard product, output transform) and (ii) learning only the diagonal scale matrices S_B and S_G of the Winograd transform matrices, using random Gaussian or uniform noise inputs and a per-layer SQNR objective, with a single shared scale set across layers. The method is evaluated on InstaFlow-0.9B and Stable Diffusion v1.5 for text-to-image generation and on ResNet-18/34/50 for ImageNet classification. The authors report near-lossless W8A8 generation quality with fully quantized Winograd F(4,3) and F(6,3), top-1 accuracies close to full precision, and CPU kernel optimizations that yield a 31.3% convolution-layer speedup.

Significance. If the empirical results hold, the paper makes a useful practical contribution: a simple, calibration-free recipe for recovering quality in fully quantized Winograd convolution, which is relevant for on-device deployment of diffusion models. The strengths include evaluation across generation and classification tasks, transfer experiments to CIFAR-10 and MJHQ, release of code and kernels, and a method that is easy to describe and potentially easy to adopt. The main caveat is that the paper frames the data-free property as a theoretical generalization guarantee, which is not established by the presented analysis. The missing optimization details also need to be addressed before the method can be independently reproduced.

major comments (5)
  1. [Section 4.2, Eq. (17) and Algorithm 1] The paper does not specify how gradients are computed through the non-differentiable quantization function Q used in Eqs. (14)-(16). Because the objective in Eq. (17) depends on quantized outputs, backpropagation requires an approximation such as a straight-through estimator or a similar relaxation. Without this detail, the optimization procedure is underspecified, and the reported results cannot be reproduced or independently evaluated for correctness.
  2. [Abstract and Section 1] The statement that generalization is 'safely guaranteed' because the method uses no training data is not justified. The method optimizes scales against random Gaussian/uniform noise inputs, which is itself a specific distribution; if the per-tap variance profile of the Winograd-domain output Y under real activations differs from that under noise, the learned scales may not minimize the actual quantization error. The 'theoretically grounded analysis' in Section 1 is a heuristic about row norms of B and G, not a generalization bound. The transfer results in Section 11 are empirical and suggestive, but they do not constitute the invoked guarantee. Please temper the claim or provide a principled analysis of when noise is a sufficient proxy.
  3. [Section 4.2, Eq. (17)] The optimization target is per-layer SQNR on synthetic noise, whereas the reported metrics are FID, CLIP, and top-1 accuracy. No evidence is given that minimizing this proxy on noise translates to reduced quantization error under real activation distributions, especially for diffusion models where activations change across sampling steps. The assertion in Section 2 that group-wise quantization is 'inherently more robust to distribution changes' does not cover the learned-scale optimization. An ablation comparing the per-tap dynamic range of Y under noise versus real inputs (using a small calibration set for analysis only) would strengthen the argument.
  4. [Section 5.1 and Algorithm 1] Key optimization hyperparameters are missing: learning rate, number of epochs, batch size, noise type and magnitude, the number of layers K selected per iteration, and how the shared scale set is updated when different layers are sampled across iterations. The paper also does not state the range or variance of the random noise used. These details are essential for reproducibility and for assessing the sensitivity of the method to optimization choices.
  5. [Section 9, Table 8] The comparison between learning with noise and learning with calibration data is confounded because the calibration-data runs use end-to-end training while the noise runs use layer-wise training. The F(6,3) FID gap (36.18 vs 26.58) therefore cannot be attributed to the input distribution alone. A matched comparison (layer-wise training with calibration inputs) is needed, or the confound should be acknowledged explicitly.
minor comments (6)
  1. [Section 4 heading] The heading contains a typo: 'qantized' should be 'quantized'.
  2. [Tables 1-4] The alignment of row labels ('Standard scales', 'Learned scales') with the tile sizes is unclear; please reformat the tables so that each row's condition is explicit.
  3. [Section 4.2] The paper leaves open whether Gaussian or uniform noise was used for the reported results; specify the distribution and its magnitude for reproducibility.
  4. [Eqs. (14)-(16)] The notation 'sqB sqB sqx' is terse and ambiguous; define the individual scale factors (e.g., left and right transform scales and input scale) more explicitly.
  5. [Section 7.1] The polynomial points are attributed to [2], but the standard points are conventionally taken from [15] and [41]; please adjust the citation to point to the original sources.
  6. [Table 5] The standard Winograd F(6,3) accuracy for ResNet-18 is 0.08%, which is near chance; a brief explanation of why the baseline collapses would help readers appreciate the challenge being addressed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: learned scales are optimized on a per-layer SQNR proxy with random noise, while FID/CLIP/top-1 accuracy are independent external evaluations.

full rationale

The paper's core procedure (Eq. 17, Algorithm 1) optimizes SB and SG by minimizing the SQNR between a full-precision convolution yi and its group-wise quantized Winograd counterpart yi~ on random Gaussian or uniform noise inputs, with each layer treated independently and one shared set of scales per network. The reported evaluation metrics (FID, CLIP, top-1 ImageNet/CIFAR-10 accuracy, MJHQ FID) are computed from the full model on real data and do not appear in the optimization objective or in the scale-update loop. The claim that generalization is 'safely guaranteed' because no training data is used is an overstrong logical assertion, but it is a robustness/correctness concern, not a circular reduction: the transfer results in Tables 11-12 and the calibration-vs-noise comparison in Table 8 are external evidence, and the paper does not rename its optimization target as its prediction. No load-bearing self-citations or author-imported uniqueness theorems are used; the Winograd construction is attributed to external prior work [41]. Hence no step reduces by construction to its own input.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim relies on optimizing a small set of scale parameters on random noise and assuming this transfers to real data. No new physical entities are introduced; the method is an optimization-based approach using standard Winograd algebra.

free parameters (2)
  • Winograd scale vectors S_B and S_G = Optimized values; F(6,3) example in Supplementary Table 6
    Diagonal scale matrices in the Vandermonde decomposition of Winograd transforms, tuned via SGD to minimize SQNR on random noise inputs.
  • Quantization group size = Not reported (described as groups of 32, 64, or 256 in Section 1)
    Hand-chosen group size for group-wise quantization, affecting the trade-off between quality and vectorization; the exact value used in experiments is not stated.
assumptions (4)
  • standard math Winograd transformation matrices constructed from Vandermonde matrices satisfy S_A S_B S_G = I, and scaling rows of B^T and G controls dynamic range.
    Standard result from the Winograd convolution literature [41], used in Sections 3.1 and 4.1.
  • ad hoc to paper Random Gaussian or uniform noise inputs are a sufficient proxy for real activation distributions when tuning quantization scales.
    This is the load-bearing assumption of the data-free approach; Section 4.2 and Section 11 provide empirical transfer evidence but no theoretical guarantee.
  • ad hoc to paper Gradient descent can optimize through the quantization function, implicitly using a straight-through estimator or similar approximation.
    The paper does not state how gradients of the round-to-nearest quantization are computed; Section 4.2 says 'use gradient descent (SGD)' without detailing the gradient approximation.
  • domain assumption Group-wise quantization with dynamic min-max activation scaling is effective for fully quantized Winograd when dynamic range is controlled.
    Based on prior LLM quantization work [7] and the paper's own experiments; the paper relies on this assumption when applying group-wise quantization to all Winograd stages.

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Cite this review

Pith. "Pith review of Data-Free Group-Wise Fully Quantized Winograd Convolution via Learnable Scales." pith.science (2026). https://pith.science/paper/2YQFIOP4

@misc{pith2026241219867,
  author       = {Pith},
  title        = {Pith review of: Data-Free Group-Wise Fully Quantized Winograd Convolution via Learnable Scales},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2YQFIOP4}},
  note         = {Machine review of arXiv:2412.19867}
}
read the original abstract

Despite the revolutionary breakthroughs of large-scale text-to-image diffusion models for complex vision and downstream tasks, their extremely high computational and storage costs limit their usability. Quantization of diffusion models has been explored in recent works to reduce compute costs and memory bandwidth usage. To further improve inference time, fast convolution algorithms such as Winograd can be used for convolution layers, which account for a significant portion of computations in diffusion models. However, the significant quality loss of fully quantized Winograd using existing coarser-grained post-training quantization methods, combined with the complexity and cost of finetuning the Winograd transformation matrices for such large models to recover quality, makes them unsuitable for large-scale foundation models. Motivated by the presence of a large range of values in them, we investigate the impact of finer-grained group-wise quantization in quantizing diffusion models. While group-wise quantization can largely handle the fully quantized Winograd convolution, it struggles to deal with the large distribution imbalance in a sizable portion of the Winograd domain computation. To reduce range differences in the Winograd domain, we propose finetuning only the scale parameters of the Winograd transform matrices without using any domain-specific training data. Because our method does not depend on any training data, the generalization performance of quantized diffusion models is safely guaranteed. For text-to-image generation task, the 8-bit fully-quantized diffusion model with Winograd provides near-lossless quality (FID and CLIP scores) in comparison to the full-precision model. For image classification, our method outperforms the state-of-the-art Winograd PTQ method by 1.62% and 2.56% in top-1 ImageNet accuracy on ResNet18 and ResNet-34, respectively, with Winograd F(6, 3).

Figures

Figures reproduced from arXiv: 2412.19867 by the authors.

Figure 1
Figure 1. Group-wise quantization for convolution layers. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Group-wise fully quantized Winograd convolution. Applying group-wise quantization to Hadamard product and input trans [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Dynamic ranges across different taps or pixels of the Winograd domain output (Y) are very different. (a) Relative standard [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: (a) Image generated from FP16 model with AKL. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 6
Figure 6. Figure 6: Convolution layers runtime improvements by using [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: InstaFlow-0.9B with AKL. Prompt ”A puppy wearing a hat; realistic” [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: InstaFlow-0.9B with AKL. Prompt ”A shiny motorcycle on the field; realistic, high-resolution” 15 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: Stable Diffusion V1.5 with AKL and DPMSolver++ sampler. Prompt [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]
Figure 10
Figure 10. Figure 10: Stable Diffusion V1.5 with AKL and DPMSolver++ sampler. Prompt [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]
Figure 11
Figure 11. Figure 11: Stable Diffusion V1.4 with AKL and DPMSolver++ sampler. Prompt [PITH_FULL_IMAGE:figures/full_fig_p017_11.png]
Figure 12
Figure 12. Figure 12: Stable Diffusion V1.4 with AKL and DPMSolver++ sampler. Comparison with Q-Diffusion. Prompt [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

Discussion (0). Continue with ORCID to comment.

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.