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REVIEW 5 major objections 5 minor 54 references

The paper argues that label noise corrupts Sharpness-Aware Minimization's perturbation and that subtracting a simulated noise-gradient term restores flat-minimum-seeking, yielding large accuracy gains on noisy-label benchmarks.

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2026-08-03 08:17 UTC pith:VN5F56PD

load-bearing objection A novel SAM-based heuristic for noisy labels with large synthetic gains, but the central compensation step is unsupported and the manuscript is not in reviewable shape. the 5 major comments →

arxiv 2601.19947 v3 pith:VN5F56PD submitted 2026-01-24 cs.LG cs.AIcs.CV

NCSAM Noise-Compensated Sharpness-Aware Minimization for Noisy Label Learning

Jiayu Xu , Junbiao Pang This is my paper
classification cs.LG cs.AIcs.CV
keywords noisy labelssharpness-aware minimizationflat minimanoise compensationperturbation distortionPAC-Bayeslabel-flip simulationoptimization-based noisy-label learning
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper claims that the failure of Sharpness-Aware Minimization under label noise is not a weakness of flat-minima-seeking itself but a distortion of the perturbation by noisy gradients. It proposes NCSAM, which estimates the noise-induced gradient by temporarily flipping low-confidence labels to their second-most-likely class, then subtracts a scaled version of that gradient from the SAM perturbation. The result is a perturbation aligned with the clean-gradient direction, so SAM can again find flat minima instead of amplifying noise. If this is right, noisy-label training can be improved by an optimizer-level fix without sample selection, label correction, or robust-loss redesign. Experiments on CIFAR, Tiny-ImageNet, and real-world noise benchmarks report consistent gains over SAM and competitive results against specialized noisy-label methods.

Core claim

The paper claims that label noise does not merely degrade training; it systematically corrupts the perturbation step of sharpness-aware minimization. Under clean labels, SAM's perturbation epsilon = rho * g / ||g|| follows the steepest-ascent direction of the loss, encouraging flat minima. Under noisy labels, the gradient is g_clean + g_noise, so the perturbation both rotates away from the clean direction (the expected inner product <g_clean, g_noise> is negative) and changes in magnitude, causing over- or under-perturbation. Through a PAC-Bayes bound, the paper shows the noise-induced parameter deviation Delta W and the SAM perturbation epsilon combine additively, meaning the biased perturb

What carries the argument

The central object is the noise-compensated perturbation epsilon' = (Delta W + epsilon) - Delta W_c, with epsilon = rho * (g_clean + g_noise) / ||g_clean + g_noise|| and Delta W_c = -s(t) g*_n. The simulation step (Eqs. 21–23) selects samples with small top-2 logit gaps, flips their labels to the second-highest logit class, and computes the gradient g*_n of those flipped samples; the time-dependent scale s(t) starts near zero and rises after a warm-up. The correction term is subtracted from the SAM perturbation to cancel the dominant noise-induced deviation, keeping the perturbation aligned with the clean-gradient direction while preserving the SAM radius rho.

Load-bearing premise

The paper's load-bearing premise is that the simulated noise gradient g*_n—obtained by flipping low-confidence samples to the second-highest logit class and scaled by s(t)—closely matches the true noise-induced parameter deviation Delta W, so that subtracting it from the SAM perturbation cancels the distortion; this is asserted, not proved, and the paper's own cross-reference for the scaling schedule is left blank.

What would settle it

On a synthetic-noise benchmark with a known noise transition matrix, compute the cosine similarity between the true per-batch noise gradient and NCSAM's simulated gradient g*_n. If the average similarity is not positive—or if the accuracy gain disappears when flipping targets are chosen at random instead of by second-highest logit—the compensation is not tracking the actual noise, and the proposed mechanism is not the source of the gain.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • On CIFAR-10 with 20–60% symmetric label noise, the paper reports NCSAM reaches 94.53/92.65/89.00, against 90.44/79.71/67.22 for plain SAM, so the correction pays off most where noise is severe.
  • Because the compensation is built into the optimizer, it can be layered on top of label-correction frameworks; the paper states the two mechanisms are orthogonal and reports gains when combined.
  • The PAC-Bayes analysis identifies an additive interaction between noise-induced deviation and the SAM perturbation; if correct, any flat-minima method that uses a gradient-based perturbation should account for that bias under noisy labels, not just SAM.
  • The progressive scaling schedule avoids injecting unreliable corrections early; this suggests the method's behavior depends on warm-up duration and the maturity of the model's confidence estimates.

Where Pith is reading between the lines

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

  • Because g*_n is generated from the model's own logits, the correction may double-count the model's errors rather than the dataset's noise; a clean test is to evaluate NCSAM under synthetic noise with a known transition matrix and compare the cosine similarity between g*_n and the true noise gradient.
  • An implicit corollary is that the top-2 logit gap is used as a proxy for 'likely mislabeled'; a testable extension is to replace it with an external confidence score or an ensemble disagreement to make the selection less self-referential.
  • The reported gains at high noise rates (e.g., 60% symmetric) suggest NCSAM behaves like a regularizer that suppresses memorization; one could test whether the same perturbation correction transfers to other perturbation-based robust optimizers such as GSAM or BSAM.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The paper proposes Noise-Compensated Sharpness-Aware Minimization (NCSAM), a modification of SAM for learning with noisy labels. The authors argue via a PAC-Bayesian-style analysis that label noise induces a parameter-space deviation ΔW that enters additively with the SAM perturbation ε, distorting SAM's flat-minima seeking behavior. They propose to compensate this distortion by replacing the SAM perturbation with ε′ = (ΔW + ε) − ΔW_c, where ΔW_c = −s(t)g*_n is built from a simulated noise gradient obtained by flipping low-margin samples to their second-highest logit class. Experiments on CIFAR-10/100, Tiny-ImageNet, and real-world noisy datasets (Food-101N, Animal-10N, Clothing1M) report consistent improvements over SAM and BSAM baselines.

Significance. If the central claim were established, optimization-only noise compensation would be a valuable alternative to sample selection and label correction. The paper deserves credit for identifying a plausible failure mode of SAM under noisy labels and for benchmarking against SAM/BSAM and several LNL methods on multiple datasets. However, the core theoretical and algorithmic claims are not supported as stated: the label-noise model is invalid for discrete labels, the PAC-Bayes bound is informal, the correction term is dimensionally inconsistent with the perturbation, and the key approximation g*_n ≈ true noise gradient is asserted rather than derived or verified. These are load-bearing issues, not presentational ones. The paper also does not provide machine-checked proofs or a working code link, so the empirical results cannot be independently reproduced from the manuscript.

major comments (5)
  1. [3.1, Eq. (2)] Equation (2) is not a valid label-noise model for the stated problem. The label space is Y = {1,...,C}, but the corrupted label is written as (1−α)y_i + αu with u ~ Beta(β,γ). This expression is an arithmetic interpolation of class indices and is generally not an element of Y. It is undefined as a label, and it does not correspond to any standard label-corruption process (symmetric, asymmetric, or instance-dependent). The subsequent additive decomposition of the gradient into g_clear + g_noise in Eq. (3) and the derived 'noise-induced weight disturbance' in Eq. (4) therefore do not follow from a well-posed noise mechanism. Since this model underlies the theoretical motivation, the analysis does not apply to the discrete-label problem the paper actually studies.
  2. [3.2.1, Eq. (12)] Eq. (12) is not a derived bound. The right-hand side uses ≲ and O with unquantified constants, and the text explicitly acknowledges it is 'not tight' and calls it an 'upper-bound structure' rather than a theorem. Assumption 1 simply postulates that the posterior is Q = N(w + Δw, σ_q²I); Δw is not derived from any noise model. Consequently the claimed 'additive interaction' between Δw and ε is imposed by assumption, not established. The paper later relies on this structure to justify the correction term, but the structure is an informal motivational story rather than a rigorous foundation.
  3. [3.3.2, Eqs. (24)-(27)] The construction of ε′ is dimensionally inconsistent as stated. Eq. (24) defines ΔW_c = −s(t)g*_n, where g*_n is a gradient. Eq. (26) writes ε̃ = ΔW + ε, where ΔW is a parameter-space deviation and ε is a SAM perturbation. Eq. (27) then subtracts ΔW_c from ε̃. For ε′ to be a perturbation of W, every term must be in parameter-space units; a gradient can be converted to a parameter displacement only with a learning-rate factor η (as in Eq. (4), where ΔŴ = −η g_noise). The paper never states that η is absorbed into s(t), and it never defines how the abstract ΔW is computed. Thus Eq. (27) is not a well-defined operation on parameters, and the 'cancellation' ΔW − ΔW_c ≈ 0 is not established.
  4. [3.3.1, Eqs. (21)-(23)] The load-bearing approximation g*_n ≈ true noise gradient is unsupported. For symmetric noise, the true corruption flips labels uniformly over all classes, whereas Eq. (23) always flips to the second-highest logit class; for real-world noise, the corruption process is unknown and need not align with top-2 confusion. Moreover, the samples selected by Eq. (22) are precisely those the current model is least confident about, so g*_n is generated from the model's own logit-gap choices. The assertion 'By construction, ΔW_c approximates the expected contribution of noisy gradients' assumes the very equivalence that must be proved. No theorem, synthetic diagnostic, or oracle experiment is provided to show that subtracting s(t)g*_n cancels the noise-induced deviation rather than amplifying model error. This is the central premise of the method, and it is not established.
  5. [4.3, Tables 5-7] The ablation study shows that performance is highly sensitive to the choice of r_flip and κ, with optimal values varying across datasets and noise levels and several NULL entries in Table 5. The manuscript provides no principled selection criterion for these hyperparameters and, in the main experiments, does not specify the exact flip-ratio schedule used (Algorithm 1 lists γ but the text uses r_flip and never defines the schedule). This leaves open the possibility that the reported gains come from tuning the simulated-flip strength or the confidence-weighted regularizer, rather than from the claimed noise compensation. At minimum, a fixed, reproducible protocol for setting r_flip and κ is required to support the empirical claims.
minor comments (5)
  1. [Eq. (25)] The definition of s(t) is unclear: 's= (3−2t)t²*2' appears to be missing parentheses and a normalization by the training horizon. The intended schedule should be written explicitly.
  2. [Abstract and Section 3.2.1] The phrase 'theoretically demonstrate' overstates what is provided. The PAC-Bayes discussion is explicitly informal and should be described as a motivating analysis, not a proof.
  3. [General presentation] There are unresolved placeholders such as 'Fig.??' and 'Section??'; the code link in the abstract is empty; and several references are malformed or duplicated (e.g., [Cheng et al., 2020] and [Cheng et al., 2021]).
  4. [Table 2] The CIFAR-10 80% symmetric noise row reports SAM accuracy 76.94, which is higher than the SAM accuracy at 60% (67.22); this is unusual and needs verification or explanation.
  5. [Table 1 caption] Table 1 is captioned 'with IDN' but Section 4.1 discusses symmetric and asymmetric noise; clarify which noise type is used in each experimental setting.

Circularity Check

0 steps flagged

No derivation is circular; the noise-compensation step is an unproven heuristic and the only self-citation is minor and not load-bearing.

full rationale

Walked the claimed chain. Eq. (4) introduces the noise-induced offset ΔŴ = −ηg_noise. Eqs. (21)–(23) define a heuristic simulated-noise gradient g*_n from the model's own logits; Eq. (24) sets ΔW_c = −s(t)g*_n; Eq. (27) subtracts it from the SAM perturbation. There is no equation forcing g*_n to equal g_noise or ΔW_c to equal ΔW, so the cancellation is an asserted design choice, not a definitional identity. The method is therefore not equivalent to its inputs by construction; it rests on an unverified modeling assumption, which is a correctness risk rather than circularity. The PAC-Bayes part (Eqs. 5–12) is explicitly presented as a motivating interpretation, and its additive conclusion follows from the stated modeling assumptions rather than being imported as an external theorem. The flip ratio and κ are tuned per dataset (Tables 5 and 7), but the reported accuracies are empirical results, not a mathematical image of those fitted values. The only self-citation is [Deng et al., 2024] for the empirical claim that SAM-family optimizers degrade under label noise and for baseline numbers in Table 2; this is prior work by one of the authors, but the central comparison does not reduce to it and the paper also provides its own SAM comparisons. Accordingly, no significant circularity is present; a minor non-load-bearing self-citation is noted.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 2 invented entities

The paper's central mechanism depends on the assumptions listed. The only standard ingredient is the PAC-Bayes inequality; the rest are ad hoc modeling choices. The free parameters r_flip, κ, T_w, ρ, and the ambiguous schedule are chosen per dataset and not derived from the theory.

free parameters (5)
  • r_flip (simulated label-flip ratio) = 40% (CIFAR-10, matched to noise); 20% reduction for CIFAR-100 at 60-80% noise; ablation optimum 40% for CIFAR-100 40%/60
    Controls how many low-confidence samples are flipped to build g*_n; optimal value changes with noise level and dataset (Section 4.3.1, Table 5).
  • κ (upper bound of s(t)) = 0.1 (CIFAR-10 20%); 0.3 (CIFAR-100 20%); 0.05 (Animal-10N); 0.1 (Food-101N) (Table 7)
    Maximum noise-compensation strength; chosen per dataset by grid search in Table 7; values for main experiments are not all declared.
  • warm-up epoch T_w = 50
    Stage switch from SGD/SAM to NCSAM after 50 epochs (Section 4.1); hand-chosen schedule.
  • SAM radius ρ = not stated
    Needed for SAM perturbation; main text gives no value, so the perturbation scale is unspecified.
  • s(t) schedule = s=(3-2t)t^2*2 is ambiguous; intended smooth rise; exact settings deferred
    The schedule shape is an ad hoc design and is not a well-defined function of training epoch as printed (Eq 25).
axioms (6)
  • standard math PAC-Bayes bound (Seeger 2002)
    Used as starting point in Eq (5); not the source of the NCSAM update.
  • ad hoc to paper Assumption 1: posterior Q=N(w+Δw, σ_q²I)
    Assumes noisy training only shifts the Gaussian posterior mean; this is load-bearing for Eq (12) and is not derived or validated.
  • ad hoc to paper SAM perturbation modeled as ε~N(0,β²I)
    Replaces SAM's deterministic normalized gradient step with a Gaussian; no argument that this preserves the SAM objective (Eq 10).
  • ad hoc to paper Label-noise model Eq (2) with continuous u and (1−α)y_i+αu
    Not a valid generative model for discrete label swaps; also unused by the method.
  • domain assumption E⟨g_clean,g_noise⟩<0 for mislabeled samples
    Assumed to justify directional and magnitude distortion (Eq 19); not generally guaranteed.
  • ad hoc to paper g*_n from top-2 flips approximates true noise gradient
    The correction assumes simulated noise gradient estimates the actual ΔW; no bound or experiment validates this.
invented entities (2)
  • Δw/ΔW (noise-induced parameter deviation) no independent evidence
    purpose: Latent shift in learned weights caused by noisy gradients; target that NCSAM compensates
    Introduced in Assumption 1 (Eq 6); never measured; no falsifiable prediction tied to it.
  • g*_n (simulated noise gradient) no independent evidence
    purpose: Proxy for the true noise gradient, computed by flipping labels of low-confidence samples to the second-best class
    Generated from the model's own logits (Eqs 21-23); no external handle establishes it corresponds to the real noise gradient.

pith-pipeline@v1.3.0-alltime-deepseek · 15476 in / 16688 out tokens · 160464 ms · 2026-08-03T08:17:35.499011+00:00 · methodology

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read the original abstract

Learning from Noisy Labels (LNL) remains a fundamental challenge in deep learning because real-world datasets often contain corrupted annotations. Most existing methods rely on label correction or sample selection mechanisms. In contrast, we study LNL from an optimization perspective by establishing a theoretical connection between label noise and the flatness-seeking behavior of Sharpness-Aware Minimization (SAM). Based on this analysis, we propose Noise-Compensated Sharpness-Aware Minimization (NCSAM), which uses a noise-compensated perturbation to counteract the optimization bias induced by noisy labels. By correcting distorted SAM perturbations, NCSAM mitigates the memorization of noisy labels during training while preserving the simplicity of optimization-based learning. Experiments on synthetic and real-world noisy-label benchmarks show that NCSAM consistently improves over SAM-based optimization baselines and remains competitive with representative noisy-label learning methods.

Figures

Figures reproduced from arXiv: 2601.19947 by Jiayu Xu, Junbiao Pang.

Figure 1
Figure 1. Figure 1: The accuracy curves of ResNet-18 trained on CIFAR [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Reference graph

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