{"id":"df05be9a-2d45-472d-9a12-be5087832c43","arxiv_id":"2601.19947","paper_version":3,"verdict":"REJECT","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"NCSAM adds a logit-gap-selected, label-flipped noise-gradient correction to SAM perturbations, claiming improved noisy-label training, but the derivation is heuristic and the empirical support is incomplete.","lead":"This paper proposes NCSAM, a variant of Sharpness-Aware Minimization that simulates label noise from model logits and subtracts the simulated noise gradient from the SAM perturbation to reduce the effect of real noisy labels. It matters because a simple optimization-only fix for noisy-label training would be broadly useful, but this version does not yet provide a sound derivation or complete evidence.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central compensation step is not a well-defined cancellation: ΔW_c in Eq. 24 is a gradient (with no learning-rate factor) added to the parameter-space perturbation ϵ in Eq. 27, and no argument shows the simulated-flip gradient g*_n approximates the true noise gradient.","rationale":"The paper's central promise is that NCSAM restores flat-minimum-seeking by removing the noise-induced component of the SAM perturbation. For that promise to hold, the term subtracted in Eq. 27 must be (a) in the same space as the perturbation and (b) an estimate of the noise-induced deviation rather than of the model's own confusion. Neither condition is established. The units issue is concrete and easily checked: Eq. 4 gives ΔW_hat = −η g_noise, so a gradient-only correction is off by a factor of the learning rate unless absorbed into s(t). The approximation issue is deeper: the simulated noise is generated from current-model logits (low margin, second-highest class), whereas the actual noise is generated by the dataset corruption process. In the synthetic symmetric case these distributions are very different (uniform flips vs. top-2 flips), and for real-world noise there is no known ground truth to justify the choice. Without a correlation/ablation check, the empirical gains are consistent with the correction acting as a regularizer that has nothing to do with noise compensation. This is the load-bearing soft spot in an otherwise clearly presented optimization recipe, and it supports the reader's REJECT verdict.","tokens_in":15796,"tokens_out":5516,"duration_ms":56314,"concrete_test":"Use CIFAR-10 with 40% symmetric noise, where the true noise mask is known. During NCSAM training after warm-up, compute the true batch-level noise deviation ΔW_true = −η ∇_W L(W; x_j, ŷ_j) for the actual mislabeled samples, and the proposed correction ΔW_c = −s(t)∇_W L(W; x_i, ŷ*_i) for the simulated flips. Record the cosine similarity between ΔW_true and ΔW_c over epochs. If the median cosine similarity is not consistently positive (say >0.5), the correction does not cancel the noise it targets. As a second arm, replace g*_n with a same-norm random vector; if accuracy is unchanged, the specific simulated-noise direction is not doing causal compensation work.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.3.2 is where the central claim must be made true, and it is not. Eq. (4) defines the noise-induced weight disturbance as ΔW_hat = −η g_noise — a parameter-space displacement with an explicit learning rate. Eq. (24) defines ΔW_c = −s(t)g*_n, where g*_n is the gradient from the model's own label-flipped samples. Eq. (27) then sets ϵ′ = (ΔW + ϵ) − ΔW_c and the NCSAM objective (28) is min_W max_{|ϵ′|≤ρ} L(W+ϵ′). For ϵ′ to be a perturbation of W, every term must be in parameter-space units. ΔW_c has gradient units unless η is absorbed into s(t); the paper never states this. More importantly, the intended cancellation ΔW − ΔW_c ≈ 0 requires g*_n ≈ g_noise (up to scale). This is asserted, not derived. The simulation procedure (Eqs. 21–23) selects low-margin samples and flips them to the second-highest logit class. For symmetric noise the actual noisy labels are uniform over all classes, and for real-world noise the corruption process is unknown; there is no reason the model's top-2 confusion direction should equal the empirical noise gradient. The reported gains could come from a confidence-weighted regularizer rather than from noise compensation. This is the load-bearing premise, and it is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":16319,"tokens_out":5514,"duration_ms":61658,"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":[{"comment":"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.","section":"3.1, Eq. (2)"},{"comment":"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.","section":"3.2.1, Eq. (12)"},{"comment":"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.","section":"3.3.2, Eqs. (24)-(27)"},{"comment":"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.","section":"3.3.1, Eqs. (21)-(23)"},{"comment":"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.","section":"4.3, Tables 5-7"}],"minor_comments":[{"comment":"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.","section":"Eq. (25)"},{"comment":"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.","section":"Abstract and Section 3.2.1"},{"comment":"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]).","section":"General presentation"},{"comment":"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.","section":"Table 2"},{"comment":"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.","section":"Table 1 caption"}],"recommendation":"reject","confidential_remarks":"I agree with the reader's assessment. The central mechanism is both theoretically unsupported and dimensionally inconsistent; the proposed g*_n approximation is self-referential, and no verification of the key equivalence is provided. These are not local issues that a revision could easily patch without fundamentally reworking the method and its justification. The empirical results may be of interest, but as presented the manuscript does not meet the standard for publication. A resubmission would need a rigorous derivation of the correction, a unit-consistent formulation, and controlled experiments that separate the effect of the proposed compensation from generic confidence-based regularization."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper's specific trick is new: it selects low-confidence samples by logit gap, flips them to the second-highest class, computes a 'simulated noise gradient,' and subtracts a scaled version of it from the SAM perturbation. I have not seen that combination before, and the high-level intuition—that label noise biases SAM's perturbation and you might compensate for that bias—is worth taking seriously.\n\nIt also reports very large gains on synthetic noise. On CIFAR-10 at 40% symmetric noise, NCSAM gets 92.65 versus 79.71 for SAM and 85.58 for BSAM. If those numbers hold under the same training protocol, that is a real effect. The ablation shows the progressive scaling coefficient matters, which suggests the mechanism is not just a constant shift.\n\nBut the paper does not support its central claim. The 'noise model' in Eq (2) is not a valid generative model for discrete labels—it mixes a label, a probability, and a distribution in a way that has no formal meaning. The PAC-Bayes argument in Eq (12) is not a derived bound; it is an informal structural statement with ≲ and O. That would be fine as motivation, but the paper calls it a theoretical connection.\n\nThe load-bearing step is the cancellation between the noise-induced parameter deviation ΔW and the correction ΔW_c = -s(t)g*_n. The paper asserts that the simulated-flip gradient approximates the true noise gradient, but never justifies it. For symmetric noise the true corruption is uniform; the simulation flips to the second-highest logit, which is structured and model-dependent. So the correction may be encoding the model's own uncertainty rather than the dataset's noise. The reported gains could simply come from a confidence-weighted regularizer that down-weights uncertain samples—a plausible and useful heuristic, but not the noise compensation claimed.\n\nThere are also presentation and consistency problems. Eq (4) defines a parameter deviation with an explicit learning rate; Eq (24) defines a correction without one, and the paper never states how the scale is handled. Table 1 shows NCSAM losing to the CC baseline on CIFAR-10 at 40% and 60% instance-dependent noise, which contradicts the text's claim of 'exceptional performance' at high noise rates. The code link is empty, 'Fig.??' and 'Section??' remain, and there are obvious placeholder sentences.\n\nIn short: the idea is suggestive and the synthetic results are interesting, but the theory is not a derivation, the central compensation is unmotivated, and the manuscript is not in a reviewable state. I would desk reject this version and encourage the authors to come back with a coherent noise model, a proper baseline that tests the confidence-weighted-regularization interpretation, and the actual code.\n\nNo reading group, no citation from me.","headline":"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.","tokens_in":16703,"tokens_out":6694,"would_cite":false,"duration_ms":70881,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["noisy labels","sharpness-aware minimization","flat minima","noise compensation","perturbation distortion","PAC-Bayes","label-flip simulation","optimization-based noisy-label learning"],"falsifier":"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.","tokens_in":15688,"feed_emoji":"⚙️","tokens_out":6090,"duration_ms":61615,"temperature":0.7,"pith_summary":"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.","feed_headline":"A corrected perturbation lifts noisy-label accuracy from 79.7 to 92.7","feed_subtitle":"Sharpness-aware minimization can misread noisy gradients; subtracting a simulated noise term restores its flat-minima search.","key_machinery":"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.","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Fix SAM's perturbation to learn from noisy labels","NCSAM: SAM that resists label noise","Noise bends SAM's perturbation; NCSAM straightens it","A noise-corrected SAM for noisy-label learning","SAM misreads noisy gradients; NCSAM corrects them"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Fix SAM's perturbation to learn from noisy labels","NCSAM: SAM that resists label noise","Noise bends SAM's perturbation; NCSAM straightens it","A noise-corrected SAM for noisy-label learning","SAM misreads noisy gradients; NCSAM corrects them"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000202,"raw_usage":{"total_tokens":1192,"prompt_tokens":689,"completion_tokens":503,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":433,"completion_tokens_details":{"reasoning_tokens":423}},"tokens_in":433,"tokens_out":503,"duration_ms":5730,"temperature":1.0,"reasoning_tokens":423,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T08:17:35.499011+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}