{"id":"3164e7a2-2d18-4247-998d-c48fc4bf2d33","arxiv_id":"2412.12968","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Networks routinely forget some test points during training even while overall accuracy improves, and combining mid-training checkpoints selected by a forget-score recovers some of this lost accuracy.","lead":"The paper introduces a 'forget fraction' score that tracks how many validation points a neural network classifies correctly in mid-training but misclassifies at the end, showing this happens even when test accuracy is rising. It also presents Knowledge Fusion, a checkpoint-averaging method that uses this score to recover lost knowledge and improve accuracy at no extra inference cost.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Positive Fe is not yet distinguished from benign boundary movement: without a null model that preserves per-epoch accuracies and final margins, the paper's central 'local overfitting' claim remains a re-description of classifier drift.","rationale":"The paper's strongest and most cited claim is not the method but the diagnostic: Fe > 0 while test accuracy rises means local overfitting exists. Everything downstream—the PCA theory, the Knowledge Fusion method—is presented as a consequence or use of that diagnosis. The weakest link is the mapping from a positive Fe to 'forgotten useful knowledge.' Fe is a count of individual flips; it contains no information about why those flips happened or whether the flipped points form a coherent subregion. Any final classifier that improves globally will have some Fe > 0, because the decision boundary moves; near-boundary points that were barely correct earlier can become barely wrong later. The paper's Figs. 3b–3c show persistence of correct predictions before the final flip, but that is precisely the signature of a late boundary shift, not of 'forgetting' in a knowledge-loss sense. A null model built from final margins can separate these two readings. If the observed Fe is no larger than the null, the central conceptual claim is unsupported, although the method may still be useful. I therefore agree with the reader's CONDITIONAL verdict: the empirical work is real and extensive, but the interpretive core needs an additional control before the headline claim can be accepted.","tokens_in":18460,"tokens_out":11340,"duration_ms":118961,"concrete_test":"Using the saved checkpoints from a representative run (e.g., ResNet-18 on CIFAR-100), construct a null distribution for Fe_e as follows. For each epoch e, fit a logistic regression model predicting P(final error | final margin) from the final model's logits on the test set. Under the null that final errors are pure boundary jitter, sample final error sets independently for each point using these probabilities, holding the final error count fixed, and recompute Fe_e; repeat 1,000 times. If the observed Fe_e lies within the null's 95% interval for all e, then Fe_e is indistinguishable from benign boundary movement and the 'local overfitting' claim fails. If it lies above the interval, the claim survives.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that positive Fe in the absence of global accuracy drop demonstrates 'local overfitting'—rests on interpreting Fe = acc(e, M_E)|M_E|/|T| (Eq. 1) as a loss of useful knowledge. The paper never compares Fe to a null model: for any two classifiers with similar accuracy from the same training run, some test points will flip correct-to-wrong as the decision boundary moves, because a better global boundary can sacrifice previously correct near-boundary points. The persistence statistics in Figs. 3b–3c (many final-wrong points were correct for long stretches) are consistent with exactly this benign late-stage boundary shift; they do not establish spatial concentration in a sub-region, nor that the flipped points encode recoverable knowledge. The Knowledge Fusion gains do not settle the issue either, since any diverse ensemble of checkpoints can improve accuracy even if no 'forgetting' occurred. Thus the paper's novelty claim—overfitting can occur locally without global overfitting—is currently underdetermined by the evidence.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces the forget fraction F_e, defined as the fraction of validation/test points correctly classified at an intermediate training epoch but misclassified by the final model. It argues that positive F_e with non-decreasing test accuracy indicates 'local overfitting'—a loss of accuracy on sub-regions of the data space that is invisible to aggregate accuracy. The paper documents this phenomenon on CIFAR-100, TinyImageNet, and ImageNet across convnets and transformers, analyzes a deep linear model for a theoretical characterization, and tests the corresponding PCA-based prediction by correlating sets S(k) and M(n). It then proposes Knowledge Fusion (KF), which ensembles the final model with selected mid-training checkpoints using the F_e metric, and reports consistent accuracy improvements over single networks and several snapshot/SWA/FGE baselines, with larger gains under label noise.","tokens_in":18611,"tokens_out":10437,"duration_ms":96106,"significance":"If the interpretation of F_e as local overfitting is accepted, the paper would fill a real gap in the literature: accuracy curves alone would understate the degree of overfitting in deep learning, and checkpoint ensembles could be targeted at forgotten sub-regions. The empirical contribution is strong in breadth: multiple datasets, architectures, optimizers, label-noise regimes, ablations, and fairness checks, with standard errors. The main theoretical and algorithmic pieces are clearly presented. However, the central conceptual claim currently rests on an interpretation of F_e that has not been separated from ordinary boundary movement, and the theory-experiment correlation in Sec. 4.2 relies on a fitted index mapping with modest overlap. These issues are addressable with additional analyses, so the work is promising but not yet conclusive.","major_comments":[{"comment":"The central claim that a positive forget fraction F_e with monotonically non-decreasing test accuracy constitutes 'local overfitting' is underdetermined by the reported evidence. F_e as defined in Eq. (1) counts validation points that are correct at an intermediate epoch and incorrect at the final epoch; any two classifiers of comparable accuracy from the same training run will exhibit some such flips merely because the decision boundary has moved, so positive F_e is also the null expectation for benign boundary drift. The persistence statistics in Figs. 3b–3c show that flipped points were often correct for many epochs, but this is equally consistent with a single late boundary shift; it does not establish that the flips are concentrated in a sub-region of the data space, which is the paper's own definition of local overfitting in the abstract. I recommend adding a null model that preserves per-epoch accuracies and final margins (or a random-subset baseline of the same cardinality), and a spatial- or feature-space clustering analysis of the flipped points.","section":"Section 3, Eq. (1), Figs. 3b–3c"},{"comment":"The empirical support for the theoretical characterization is weaker than the text suggests. The sets S(k) and M(n) are compared after fitting the linear map n = alpha k + beta between the index ranges, so the correspondence is not a parameter-free prediction. No significance test or confidence interval is reported for the overlap shown in Fig. 4, and the early value of |S(k) ∩ M(n)|/|M(n)| is roughly 1/6, which is modest without a null baseline based on random sets of the same sizes. I recommend reporting a permutation or bootstrap test for the overlap, and stating the number of fitted parameters involved.","section":"Section 4.2, Fig. 4"},{"comment":"The conclusion that Knowledge Fusion's accuracy gains demonstrate recovery of forgotten knowledge is an interpretation rather than a supported mechanism. The comparisons to fixed-jump and horizontal baselines in Table 1 use the same number of checkpoints, and KF often improves on them (e.g., TinyImageNet 66.98 vs 66.54 in the limited regime), but any diverse set of checkpoints can improve accuracy even if no point-specific 'forgetting' occurred. To substantiate the recovery claim, the authors should report accuracy of the KF predictor on the set of final-epoch errors M_E (or on the F_e points) versus the rest of the test set, and compare the recovery rate with that of equally spaced checkpoints. Without per-point evidence, the sentence in Section 7 that KF's success 'shows that indeed models forget useful knowledge' overstates what is demonstrated.","section":"Section 5 and Section 7, Tables 1–3"}],"minor_comments":[{"comment":"The claim that self-distillation post-processing 'will enhance the performance of any trained model without adding inference costs' is not empirically evaluated anywhere in the paper; only the algorithm is described. The authors should either add the corresponding experiment or soften the claim.","section":"Abstract and Section 5"},{"comment":"The Input line repeats 'w and validation data V' twice, and the line 'best epsilon = combined prob' appears to be a typo; it should store the epsilon value that maximized validation accuracy.","section":"Appendix C, Algorithm 2"},{"comment":"The citation of (Annavarapu 2021) for the double-descent phenomenon is odd, since that work is about snapshot ensembles; the standard references (Belkin et al. 2019; Nakkiran et al. 2021) appear later in the related work and should be cited here.","section":"Section 1"},{"comment":"The subscripts 'e' and 'E' (epoch and final epoch) are visually similar; please use a more distinct notation, for example e and E with different fonts, and state explicitly that M_E is the set misclassified by the final model.","section":"Equation (1) and surrounding text"},{"comment":"The notation F^L_e and F^D_e is rendered inconsistently in the text; the superscripts/subscripts should be fixed.","section":"Figure 7 caption and Appendix B"},{"comment":"'Universally useful' is too strong; in Table 1, KF (∞) underperforms fixed jumps (∞) on CIFAR-100 (79.13 vs 79.17). Suggest 'generally useful'.","section":"Section 6.1, first paragraph"},{"comment":"The extension from binary deep linear networks to multi-class nonlinear networks is stated as a suggestion ('suggesting similar qualitative outcomes'); this should be explicitly labeled as a conjecture rather than part of the theoretical derivation.","section":"Section 4.1"}],"recommendation":"major_revision","confidential_remarks":"The main risk for the editors is the conceptual claim: F_e > 0 without a null model is indistinguishable from boundary drift. I would make the null-model analysis a condition of acceptance. The paper also advertises self-distillation in the abstract without experiments; ask the authors to align claims with evidence. The manuscript appears to be a conference submission (AAAI-25) with appendices; the length is acceptable but some appendices (e.g., Algorithm 2) have typographical errors."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know about this paper. First, it introduces a simple score, the forget fraction Fe, that measures how much of the test set flips from correct in mid-training to wrong at the end. Second, it builds a checkpoint-ensemble method (Knowledge Fusion) that consistently beats the final model and several baselines, with gains around 0.8–3.5 points on clean datasets and much larger under label noise. Both are real contributions, and the empirical work is solid: standard errors, ablations, multiple architectures, and an honest recognition that the theory is a ``certain characterization,'' not a proof.\n\nThe central claim, though, is that Fe > 0 without a global accuracy drop constitutes ``local overfitting.'' That interpretation is under-supported. The paper shows that many final-wrong points were correct for long stretches, and that Fe grows with model size. But it never compares Fe against a null model of random boundary shifts with the same per-epoch accuracies. A better global classifier can sacrifice previously correct near-boundary points without any sub-region being ``forgotten'' in a meaningful sense. The KF gains don't settle this: diverse checkpoints can improve an ensemble even if the flips are benign jitter. The stress-test note is right on target here.\n\nThe theory section is suggestive but not load-bearing. The authors fit a linear map n = alpha*k + beta before measuring overlap between sets S(k) and M(n), and the overlap is modest early on (about 1/6). That weakens the claim that PCA dynamics govern forgetting in deep networks. Still, the empirical phenomenon stands independent of the theory, so this is a secondary issue.\n\nOther soft spots: no code or data released, and the related-work section omits Toneva et al. on example forgetting and Model Soups-style checkpoint averaging. These are addressable and minor next to the null-model issue.\n\nWho should read this: anyone interested in double descent, training dynamics, or cheap ensembles. The method is practical and the diagnostic is easy to compute. It deserves a serious referee, not a desk reject. I'd send it to review with a request for a null model or a control experiment that rules out boundary jitter, plus the missing citations. If Fe remains significant under that control, the local-overfitting story is solid. Even if it doesn't, the paper still gives the community a useful tool and a clean empirical observation.","headline":"A useful new diagnostic (forget fraction) and a genuinely effective checkpoint-ensemble method, but the 'local overfitting' interpretation needs a null model before it fully lands.","tokens_in":19208,"tokens_out":1801,"would_cite":true,"duration_ms":18109,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T07"],"pacs":[],"model":"deepseek-v4-flash","headline":"Deep networks quietly forget sub-regions of the test population during training even when overall accuracy never falls, and blending mid-training checkpoints with the final model recovers much of the lost knowledge.","keywords":["local overfitting","forgetting","forget fraction","deep linear networks","principal components","checkpoint ensemble","self-distillation","double descent"],"falsifier":"Train a network and record the real forget fraction $F_e$. Then take the final model and perturb its logits randomly, calibrated to flip exactly the same fraction of test predictions while preserving final accuracy; if this null model produces an $F_e$ as large as the real one, the paper's measure does not distinguish forgetting from boundary jitter. A complementary check is to replace the $F_e$-selected checkpoints in Knowledge Fusion with the same number of randomly chosen or evenly spaced checkpoints: if accuracy gains are unchanged, the targeted recovery of forgotten knowledge is not the active mechanism.","tokens_in":18177,"feed_emoji":"🧠","tokens_out":12741,"duration_ms":103120,"temperature":0.7,"pith_summary":"The paper sets out to show that overfitting in deep neural networks is more common than test-accuracy curves make it look. It proposes a forget fraction $F_e$: the share of test points that the network classified correctly at an intermediate epoch $e$ but misclassifies at the end of training. Across standard image datasets, architectures, optimizers, and learning-rate schedules, the paper finds $F_e>0$ even when test accuracy never decreases, and larger models or smaller training sets produce larger forget fractions. The paper then derives a spectral characterization of forgotten points in deep linear networks, shows it correlates with what deep networks forget, and introduces Knowledge Fusion, a checkpoint-blending method that recovers part of the lost knowledge and improves accuracy without adding inference cost after self-distillation. If correct, the work implies that rising accuracy and simultaneous forgetting can coexist, so conventional accuracy-based monitoring understates how much deep models overfit.","feed_headline":"Networks forget test points even as accuracy climbs","feed_subtitle":"A 'forget fraction' reveals local overfitting, and blending mid-training checkpoints recovers lost accuracy.","key_machinery":"The central object is the forget fraction $F_e=\\mathrm{acc}(e,M_E)|M_E|/|T|$, the share of test points correct at an intermediate epoch but wrong in the final model. The argument is carried by three mechanisms: the identity $\\mathrm{acc}(E,T)=\\mathrm{acc}(e,T)+L_e-F_e$, which lets local forgetting grow while global accuracy improves; the deep-linear evolution formula $w(n)\\approx w(0)\\Lambda^n+w_{\\mathrm{opt}}(I-\\Lambda^n)$, which makes forget time analytically tractable and ties it to the principal-component spectrum of the data; and the Knowledge Fusion algorithm, which averages the final model's probability outputs with checkpoints in a window around the epoch of maximal $F_e$, with weights chosen on validation data and iteration until no further gain appears.","core_discovery":"The central discovery is that learning and forgetting happen at the same time in different sub-regions of the data space. The paper defines $F_e$ and $L_e$ so that $\\mathrm{acc}(E,T)=\\mathrm{acc}(e,T)+L_e-F_e$; when $F_e>0$ even though $L_e\\ge F_e$ for every $e$, global test accuracy rises while a measurable part of the test population is forgotten. Empirically this local overfitting appears with and without label noise, on CIFAR-100, TinyImageNet, and ImageNet, and grows with model capacity and with smaller training sets. In deep linear networks the paper derives a forget time for each point and shows the forgetting rate is governed by the data's singular-value spectrum, with points concentrated on leading principal components forgotten fastest; the set of points forgotten by such a linear model overlaps substantially with the set forgotten by real deep networks. Finally, Knowledge Fusion selects checkpoints near the epoch of maximal $F_e$, averages their probability outputs with the final model using validation-chosen weights, and reports consistent accuracy gains, up to about 3.5 accuracy points on TinyImageNet and roughly 15 percent relative error reduction in a 10 percent asymmetric-noise setting.","pith_inferences":["A consequence the paper leaves implicit: if local overfitting is genuine knowledge loss, then accuracy-based early stopping and model selection can silently pick networks that have forgotten subpopulations; tracking $F_e$ on groups of interest would be a more informative selection signal.","The spectral result suggests a direct test the paper does not run: sort test points by their projection onto leading principal components and check whether the earliest forgotten points are the ones with the largest leading-component mass, as the deep-linear analysis predicts.","The success of forget-weighted checkpoint fusion hints that the training trajectory itself is an underused ensemble resource; comparing $F_e$-weighted checkpoints against uniformly weighted or randomly sampled checkpoints of the same count would isolate how much of the gain comes from targeting forgotten knowledge specifically."],"forward_implications":["Global test accuracy should no longer be treated as a sufficient monitor of overfitting; $F_e$ can rise while accuracy climbs, so a flat or improving curve can hide a shrinking set of correctly classified test points.","Overfitting indicators should grow where classical theory expects them to: the paper reports larger forget fractions for larger networks and for smaller training sets, even when final accuracies are similar.","Mid-training checkpoints carry recoverable knowledge: Knowledge Fusion improves over the single network on clean and noisy data, with the largest gains under label noise where classical overfitting is strongest.","The recovered knowledge can be folded into one model through self-distillation, so the inference-time cost stays the same as the original network.","Epoch-wise double descent with label noise can be reinterpreted as simultaneous memorization of noisy labels and slow learning of clean hard patterns, and a weaker version of the same forgetting occurs without label noise."],"supporting_citations":[{"why":"Supplies the convergence formula and principal-components bias that make forget time analytically tractable in deep linear networks.","marker":"Hacohen and Weinshall (2022)"},{"why":"Provides exact solutions to deep linear network dynamics, the framework the paper uses to model forgetting.","marker":"Saxe, McClelland, and Ganguli (2014)"},{"why":"Supports the use of over-parameterized deep linear networks as a faithful model of practical deep learning phenomena.","marker":"Arora, Cohen, and Hazan (2018)"},{"why":"Establishes that networks first learn simple patterns and later memorize noisy labels, which the paper extends to explain validation-point forgetting and double descent.","marker":"Arpit et al. (2017)"},{"why":"Documents double descent, the empirical phenomenon the paper reinterprets through local overfitting and forgetting.","marker":"Belkin et al. (2019)"},{"why":"Provides the rapidly decaying singular-value statistics of natural images that drive the prediction about which points are forgotten first.","marker":"Hyvärinen, Hurri, and Hoyer (2009)"},{"why":"Defines the horizontal-ensemble baseline that averages late checkpoints and is one of the comparisons Knowledge Fusion must beat.","marker":"Xie, Xu, and Chuang (2013)"},{"why":"Defines stochastic weight averaging, a training-protocol baseline whose performance Knowledge Fusion matches or exceeds.","marker":"Izmailov et al. (2018)"},{"why":"Defines snapshot ensembles, a cost-matched training-protocol baseline that the paper compares against.","marker":"Huang et al. (2017)"},{"why":"Supports the self-distillation step that converts the checkpoint ensemble into a single network with unchanged inference cost.","marker":"Allen-Zhu and Li (2023)"}],"fun_headline_variants":["Local overfitting persists even as global accuracy rises","Forgetting rate exposes hidden overfitting in deep nets","Recover forgotten test points from training history","Checkpoint blending lifts accuracy without extra inference"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that a test point flipping from correct to incorrect during training reflects genuine loss of useful knowledge rather than harmless movement of the decision boundary while the model improves overall.","fun_headline_variants_meta":{"raw":{"variants":["Local overfitting persists even as global accuracy rises","Forgetting rate exposes hidden overfitting in deep nets","Recover forgotten test points from training history","Checkpoint blending lifts accuracy without extra inference"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000304,"raw_usage":{"total_tokens":1767,"prompt_tokens":983,"completion_tokens":784,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":599,"completion_tokens_details":{"reasoning_tokens":726}},"tokens_in":599,"tokens_out":784,"duration_ms":7825,"temperature":1.0,"reasoning_tokens":726,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T13:33:10.935350+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train a network and record the real forget fraction $F_e$. Then take the final model and perturb its logits randomly, calibrated to flip exactly the same fraction of test predictions while preserving final accuracy; if this null model produces an $F_e$ as large as the real one, the paper's measure does not distinguish forgetting from boundary jitter. A complementary check is to replace the $F_e$-selected checkpoints in Knowledge Fusion with the same number of randomly chosen or evenly spaced checkpoints: if accuracy gains are unchanged, the targeted recovery of forgotten knowledge is not the active mechanism.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the convergence formula and principal-components bias that make forget time analytically tractable in deep linear networks."},{"cited_title":"M.; McClelland, J","cited_arxiv_id":null,"evidence_quote":"Provides exact solutions to deep linear network dynamics, the framework the paper uses to model forgetting."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supports the use of over-parameterized deep linear networks as a faithful model of practical deep learning phenomena."},{"cited_title":"S.; Maharaj, T.; Fischer, A.; Courville, A.; Bengio, Y.; et al","cited_arxiv_id":null,"evidence_quote":"Establishes that networks first learn simple patterns and later memorize noisy labels, which the paper extends to explain validation-point forgetting and double descent."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents double descent, the empirical phenomenon the paper reinterprets through local overfitting and forgetting."}],"review_version":1}