{"id":"26e22984-f55a-4a06-92e1-2b0ecfce0d7f","arxiv_id":"2509.05307","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Label Smoothing++ learns a class-wise non-target probability distribution to replace the uniform distribution in label smoothing, yielding accuracy gains across many benchmarks.","lead":"This paper proposes Label Smoothing++, a training trick that replaces uniform label smoothing with per-class probability distributions learned by the network itself. The method reports consistent accuracy gains across image, video, text, and audio benchmarks, but claims about reducing overconfidence rest on qualitative evidence, not calibration metrics.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"C-matrix update has a continuum of fixed points once the network fits the labels; the claimed 'learned inter-class relationships' are not identifiable from the objective, so LS++'s mechanism is underdetermined.","rationale":"The reader identified the absence of convergence/fixed-point analysis for the learned C matrix as the weakest assumption. My analysis sharpens this: because the C update is a gradient step toward the network's current average non-target predictions, and because the network is simultaneously trained to match the resulting labels, the two-player dynamics can converge to a continuum of fixed points whenever the network can fit the training labels. At any such fixed point, the gradient for C vanishes for any C that equals the normalized label distribution, so the final C is path-dependent rather than a principled estimate of inter-class similarity. This does not necessarily invalidate the empirical accuracy gains, but it does mean the paper's central explanatory claims—that LS++ 'learns inter-class relationships' and 'promotes' them—are not supported by the presented evidence. The ablation (Table 5) shows that the specific loss matters, but it does not show that the learned C, rather than the fixed 1-alpha target probability, is responsible for the improvement over LS. The proposed concrete test would directly assess whether C is identifiable and stable across initializations; if it is not, then the method's mechanism is underdetermined, and the claims of promoting inter-class relationships should be substantially softened. Since this concern matches the reader's weakest_assumption and the reader already issued a CONDITIONAL verdict, no change is needed: the paper should be accepted only if the authors can demonstrate that C is stable and meaningful, or alternatively revise their claims to focus on the empirical regularization effect without asserting a causal role for the learned relationships.","tokens_in":10207,"tokens_out":11170,"duration_ms":132152,"concrete_test":"Train LS++ on CIFAR-10 with three different initializations of C (all-zero logits, random logits, and logits set to 0.1) while keeping all other hyperparameters fixed. Compare the final C matrices (Frobenius norm of differences, correlation of row-wise distributions) and test accuracies. Additionally, compute the gradient norm of C at the end of training; if it is near zero for substantially different C matrices, non-identifiability is confirmed. As a second check, use the C matrix from initialization A as a fixed label generator (PT-LS++) to train a fresh student and compare its accuracy to the LS++ student; if the accuracy difference exceeds the reported std (e.g., ±0.23 on CIFAR-10 ResNet18), the learned label distribution is not a stable training signal.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Section 3.2, C is optimized via the reverse cross-entropy H(hat y, bar y^{ls++}) with G fixed. For a sample of class y, the gradient w.r.t. C_y is zero when C_y equals the normalized distribution of hat y over non-target classes. If G fits the training labels exactly, then hat y = bar y^{ls++} = (1-alpha)e_y + alpha C_y, and any C_y satisfies this condition; hence the training objective has a continuum of fixed points. The final C matrix is therefore determined by the optimization trajectory (initialization, learning-rate schedule, batch order), not by a unique optimum. The paper provides no convergence/stability analysis and no identifiability argument. Consequently, the interpretation of Figure 3 and the claim that LS++ 'promotes inter-class relationships' (Section 4.2) are not established: the C matrix may simply mirror the network's existing confusion, and the consistent accuracy gains over LS/OLS may be due to the fixed 1-alpha target probability rather than to the learned non-target distribution. This is the load-bearing assumption underlying the method's novelty.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces Label Smoothing++ (LS++), a label-regularization scheme that replaces the uniform non-target distribution of standard label smoothing with a learned class-wise distribution C. The target class retains probability 1−α; the residual α is distributed over non-target classes according to a row of a learned K×K matrix C (diagonal zero), trained by the reverse cross-entropy term H(ŷ, ȳ^{ls++}) with gradients stopped from the forward term. Experiments cover image, video, text, and audio datasets across multiple architectures, reporting consistent top-1 accuracy improvements over one-hot, LS, OLS, TFKD, and related baselines. The paper also presents learned C matrices, t-SNE/cluster-distance visualizations, ablations on the symmetric loss, a knowledge-distillation proxy use of C, and compatibility with input augmentations.","tokens_in":10524,"tokens_out":6695,"duration_ms":79130,"significance":"If the empirical accuracy gains are reproducible, LS++ is a simple, broadly applicable plug-in regularizer with a public implementation; the reported gains across modalities and architectures are a useful contribution. The paper also demonstrates combination with augmentation methods and a cheap proxy-teacher distillation. However, the paper's mechanistic claims—that C captures inter-class relationships and that LS++ reduces overconfidence—are not established by the evidence as presented. The accuracy result is externally measured and escapes circularity, but the central novelty and interpretation rest on properties of a learned matrix that the objective does not identify. Substantial additional analysis is needed before the mechanism claims can be accepted.","major_comments":[{"comment":"The update for C via the second symmetric-CE term H(ŷ, ȳ^{ls++}) is not shown to identify a unique C. Once G fits the training targets, ŷ = (1−α)e_y + αC_y, and for any valid C_y the reverse-CE gradient w.r.t. C_y vanishes (the normalized non-target prediction matches C_y). Thus the training objective has a continuum of fixed points; the reported C (Figure 3) is trajectory-dependent and the interpretation as 'learned inter-class relationships' is underdetermined. Please provide convergence/stability analysis or an identifiability argument, and/or controlled experiments (different C initializations/schedules; comparison of C with held-out confusion or teacher logits) to show the result is not an artifact.","section":"§3.2, Eq. (3)"},{"comment":"The paper claims LS++ 'mitigates overconfident predictions' but reports no calibration metric. No ECE, NLL, reliability diagrams, or confidence histograms appear anywhere in the main text. Figure 4 shows training-set output probabilities, which do not measure calibration. Please add test-set calibration and NLL comparisons against 1-hot, LS, OLS, and TFKD across datasets, with error bars.","section":"Abstract and §6"},{"comment":"The ablation singles out the loss function but does not isolate the contribution of the learned C. Standard LS trained with the same two-term symmetric loss and the same gradient-blocking schedule (C fixed to uniform) is needed to show that the accuracy gains come from learning the non-target distribution rather than from the symmetric objective/update rule. Without this control, the claimed superiority of learned mixing probabilities over fixed values (Section 4.2) is not demonstrated.","section":"§5.2, Table 5"},{"comment":"The semantic-structure claim is supported by visual inspection of C matrices and t-SNE/cluster distances. Since C is optimized to match the network's own predictions, the apparent structure can be a self-referential summary of the network's confusion rather than an independent inter-class relationship. Please provide quantitative evaluation (e.g., correlation with an external class taxonomy, transfer of C to a new network beyond PT-LS++, or prediction of confusion on held-out data) to validate the interpretation.","section":"§4.2, Figure 3"}],"minor_comments":[{"comment":"'C-Matrix is not a symmetrical matrix' should read 'not a symmetric matrix'.","section":"§3.2"},{"comment":"Table 3 header has misaligned Network entries (six datasets but seven network names); Table 4 contains typos ('HDMB51', 'Y A').","section":"Tables 3–4"},{"comment":"α sensitivity is not explored; since α is a free parameter, report an α sweep or at least a robustness check for one or two datasets.","section":"§4.1"},{"comment":"Reproducibility: the main text defers optimizer, C update frequency, learning rate, and epoch details to the supplementary material, which is not available in the arXiv submission; these should be stated in the paper.","section":"§4.1"},{"comment":"Baseline accuracies are copied from prior papers without error bars. For the 'consistently outperformed' claim, provide standard deviations for all methods or perform paired significance tests.","section":"Tables 1–2"},{"comment":"Clarify whether displayed probabilities are averaged over training samples and how they are aggregated; if overconfidence is claimed, add a calibration plot.","section":"Figure 4"}],"recommendation":"major_revision","confidential_remarks":"The paper is at the border of acceptability: the empirical breadth is commendable, but the mechanism claims need tightening. The continuum-of-fixed-points issue is the main technical risk; if the authors can show that the final C is stable across seeds/schedules and that a fixed-uniform control does not match LS++ accuracy, I would support acceptance. The overconfidence claim should be either substantiated with calibration metrics or removed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a practical drop-in label smoothing variant—fixed target probability 0.9, learn a class-wise distribution over non-target classes via a second cross-entropy term—and it consistently beats plain LS across image, video, text, and audio. The empirical work is honest and fairly broad; they ran many baselines themselves under matched setups, and the code is public. That alone makes it worth a referee's time.\n\nWhat's new: the specific C-matrix formulation with a zero diagonal and the gradient-stopping scheme is not in OLS or TFKD. The ablation in Table 5 shows the separated-gradient symmetric CE matters, which is evidence that the design is doing something.\n\nThe soft spots are real but not fatal. First, the abstract claims 'mitigates overconfident predictions' but there is no ECE or NLL anywhere. That is easily fixed. Second, the bigger issue: the C-matrix update has a continuum of fixed points once the network's output equals the regularized label. Concretely, when G fits the target, any C_y satisfies the fixed-point condition, so the final C is determined by optimization trajectory, not by a unique optimum. That means Figure 3's 'semantic structure' may simply be the network's own confusion mirrored back. The accuracy gains are externally measured and not circular, but the paper's central mechanistic claim—that C captures inter-class relationships—is not established. The authors need either an identifiability argument, a stability analysis, or at least a direct test (e.g., using C to predict human confusion patterns, or showing C is robust across seeds/initializations). Third, no convergence analysis for the alternating update; given that the update is essentially self-training, this is not a minor omission.\n\nThe citation pattern is fine, and the lack of self-citation inflation is appreciated. Some baseline numbers in Tables 1-2 are lifted from other papers, but they did their own matched baselines elsewhere, so this is minor.\n\nBottom line: the method is likely useful in practice, and the paper deserves peer review. I'd send it back asking for calibration metrics and a serious discussion—or softening—of the inter-class relationship claim. For a reading group, it's a good case study of why self-training objectives need identifiability checks.","headline":"A clean, broadly tested label-regularization variant whose accuracy gains look real, but whose 'learned inter-class relationships' are not identifiable from the training objective.","tokens_in":10916,"tokens_out":3838,"would_cite":true,"duration_ms":45182,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Label Smoothing++ claims that learning a class-wise distribution for non-target labels, instead of a uniform one, improves generalization and preserves inter-class relationships across datasets and modalities.","keywords":["label smoothing","label regularization","inter-class relationships","learned labels","C-matrix","symmetric cross-entropy","knowledge distillation","overconfidence"],"falsifier":"Train LS++ on CIFAR-10 with the paper's settings and record the per-row entropy of the learned C-matrix every epoch; if the rows converge to one-hot distributions, or if the final matrix gives semantically unrelated classes (e.g., dog giving more mass to frog than to cat) higher weight, the claimed inter-class-relationship mechanism is not what drives the reported accuracy gains.","tokens_in":10164,"feed_emoji":"🏷️","tokens_out":8483,"duration_ms":96409,"temperature":0.7,"pith_summary":"Label Smoothing++ claims that the standard label-smoothing trick—spreading a fixed amount of probability uniformly over all non-target classes—throws away information about which classes are actually similar. The paper proposes to learn, for each target class, a distribution over the other classes, keeping the target's own share fixed and splitting the remaining probability according to a learned C-matrix. Training alternates two cross-entropy terms: one updates the network against these labels, the other updates the labels against the network's predictions, with gradients stopped so the two do not collapse into each other. Across image, video, text, and audio datasets and several architectures, the paper reports that this consistently improves top-1 accuracy over one-hot labels, label smoothing, and other label-regularization baselines, while producing compact clusters and less overconfident outputs. If correct, the method offers a cheap way to inject inter-class knowledge into training without a teacher network.","feed_headline":"Learned class labels beat uniform smoothing on every tested dataset","feed_subtitle":"A learned per-class C-matrix spreads residual confidence to similar classes and lifts accuracy.","key_machinery":"The C-matrix: a K×K object whose diagonal is zero, storing for each target class how the residual probability α is distributed among the other classes. The training signal is a symmetric cross-entropy loss, H(ȳ_ls++, ŷ) + H(ŷ, ȳ_ls++), with gradient flow split: the first term trains the network against the current labels, and the second term trains the labels against the network's outputs, with gradients to the other parameters stopped. This split is what keeps the learned labels from collapsing to one-hot distributions, a failure mode the paper attributes to ordinary cross-entropy and to Online Label Smoothing.","core_discovery":"The central claim is that a label-regularization target need not be fixed in advance: the residual probability α can be allocated among non-target classes by the network itself, yielding class-specific training labels that encode inter-class relationships. For each target class y, the method learns a probability vector C_y over the other K−1 classes; the training label is (1−α)·one-hot(y) + α·C_y. A symmetric cross-entropy loss trains the network with H(ȳ_ls++, ŷ) and trains C with H(ŷ, ȳ_ls++), with gradients stopped so that the learnable labels do not collapse to one-hot vectors. The paper reports that this consistently beats label smoothing and other baselines on CIFAR, Tiny-ImageNet, Ima","pith_inferences":["If the C-matrix encodes stable semantic proximity, it could be transferred as a class-relationship prior to related datasets or to new architectures; the paper only demonstrates one-step reuse through its proxy teacher.","The alternating gradient split sets up a two-player dynamics between network and labels; varying update cadence, adding momentum to C, or annealing α could change the fixed point, and the paper does not explore those controls.","Under class-conditional label noise, the learned C rows would be fit to corrupted targets and might absorb the noise; testing on synthetic symmetric and asymmetric noise would show whether LS++ keeps its advantage over standard label smoothing."],"forward_implications":["LS++ can replace label smoothing as a drop-in regularizer: the paper reports higher top-1 accuracy on every dataset and architecture it tested.","The learned C-matrix can be reused as a proxy teacher, giving students most of the distillation gain without per-sample teacher outputs and, in one reported ResNet101-to-ShuffleNet run, at half the training time.","LS++ combines with input augmentations such as Cutout, Mixup, CutMix, and RandAugment, so it does not force a choice between input-side and label-side regularization.","Fixing the target class's probability while learning the non-target shares prevents the label distribution from collapsing to one-hot, the failure the paper attributes to Online Label Smoothing."],"supporting_citations":[{"why":"Introduces label smoothing, the uniform-distribution regularization LS++ extends by learning the non-target distribution.","marker":"[27]"},{"why":"Documents that label smoothing destroys inter-class relationships, the problem LS++ is designed to solve.","marker":"[21]"},{"why":"Online Label Smoothing, the closest learned-label baseline; LS++ is compared against it and avoids its collapse to one-hot labels.","marker":"[35]"},{"why":"Teacher-Free Knowledge Distillation, a label-regularization baseline and the source of the proxy-teacher comparison.","marker":"[33]"},{"why":"Knowledge distillation, whose per-sample teacher soft labels motivate using class relationships; LS++ replaces them with a class-level C-matrix.","marker":"[10]"},{"why":"Margin-based Label Smoothing, a calibration-focused label-regularization baseline included in the comparisons.","marker":"[19]"}],"fun_headline_variants":["Learned class relations replace uniform label smoothing","Label smoothing that learns inter-class similarities","Network learns to spread labels among similar classes","Adaptive label smoothing beats fixed uniform baseline","Label Smoothing++: learn class similarities, not noise"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The load-bearing premise is that a single class-wise distribution per class, learned from the network's own probability outputs, settles at a stable and semantically meaningful fixed point instead of collapsing to one-hot vectors or copying the network's overconfidence.","fun_headline_variants_meta":{"raw":{"variants":["Learned class relations replace uniform label smoothing","Label smoothing that learns inter-class similarities","Network learns to spread labels among similar classes","Adaptive label smoothing beats fixed uniform baseline","Label Smoothing++: learn class similarities, not noise"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000176,"raw_usage":{"total_tokens":1091,"prompt_tokens":674,"completion_tokens":417,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":418,"completion_tokens_details":{"reasoning_tokens":359}},"tokens_in":418,"tokens_out":417,"duration_ms":5455,"temperature":1.0,"reasoning_tokens":359,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T17:07:40.127487+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train LS++ on CIFAR-10 with the paper's settings and record the per-row entropy of the learned C-matrix every epoch; if the rows converge to one-hot distributions, or if the final matrix gives semantically unrelated classes (e.g., dog giving more mass to frog than to cat) higher weight, the claimed inter-class-relationship mechanism is not what drives the reported accuracy gains.","supporting_citations":[{"cited_title":"Rethinking the inception architecture for computer vision","cited_arxiv_id":null,"evidence_quote":"Introduces label smoothing, the uniform-distribution regularization LS++ extends by learning the non-target distribution."},{"cited_title":"When does label smoothing help? Advances in neural information processing systems , 32, 2019","cited_arxiv_id":null,"evidence_quote":"Documents that label smoothing destroys inter-class relationships, the problem LS++ is designed to solve."},{"cited_title":"Revisiting knowl- edge distillation via label smoothing regularization","cited_arxiv_id":null,"evidence_quote":"Teacher-Free Knowledge Distillation, a label-regularization baseline and the source of the proxy-teacher comparison."},{"cited_title":"The devil is in the margin: Margin-based label smoothing for network calibration","cited_arxiv_id":null,"evidence_quote":"Margin-based Label Smoothing, a calibration-focused label-regularization baseline included in the comparisons."}],"review_version":1}