{"id":"3288fc65-2fab-4e6f-977e-b46ca28026a7","arxiv_id":"2504.16763","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"The paper introduces noise-tolerant gradient-coreset replay for class-incremental learning and reports large accuracy gains on five datasets under label and instance noise.","lead":"The paper proposes two continual-learning methods, Continual CRUST and Continual CosineCRUST, that build replay buffers by selecting gradient coresets, and claims a new theoretical bound for robustness to uncorrelated instance noise. A generalist might read it because noisy, continuously arriving data is common in deployed vision systems, and most replay-based lifelong learners are not designed for it.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 4 collapses because Eq. (7) assumes the Jacobian decomposes additively under input perturbation, which only holds for affine networks; the nonlinear architectures in the experiments violate it.","rationale":"Not every weakness needs equal weight; the one that sinks the paper is the false additive-Jacobian identity. The reader identified this as the weakest assumption, and I agree. The theorem's statement also has a vacuous epsilon bound due to log(delta), but that could be a typo; Eq. (7) is not a typo—it is a structural assumption that fails for every nonlinear network, including the ResNet18 and EfficientNetV2s models used in the experiments. The proof's later Lemmas inherit this error: Lemma 10's approximate residual recursion, Lemma 11's bound on the average Jacobian, and Lemma 14's contraction factor all rely on separating J(W,EX) and Jbar(W,EX) as additive contributions. Without a valid perturbation expansion, the claimed number of iterations in Theorem 4 is unsupported. Empirical results are extensive and the proposed methods appear to outperform baselines, which gives the paper value as an empirical study, but the central theoretical claim—the headline contribution—does not hold as stated. Hence I would not change the reject verdict.","tokens_in":32291,"tokens_out":5532,"duration_ms":48855,"concrete_test":"Use autodiff on a two-layer ReLU MLP with fixed random weights and inputs X and EX (e.g., 10-dim, 100 samples). Compute J1 = J(W,X+EX)^T, J2 = J(W,X)^T, and J3 = J(W,EX)^T, and evaluate the relative Frobenius error ||J1 - J2 - J3||_F / ||J2||_F. If the error is not near machine precision, Eq. (7) fails. Then simulate the claimed residual recursion r_{t+1} = (I - eta(C + EJ2 J^T + Jbar EJ1)) r_t with EJ1 and EJ2 defined as in the paper, and compare to the true gradient-descent update on X+EX; if the one-step residual prediction error exceeds 10%, Lemma 10's approximation is invalid for the tested architecture.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central theoretical result, Theorem 4, depends on Eq. (7): J(W,X+EX)^T = J(W,X)^T + J(W,EX)^T, with EJ1 = J(W,EX)^T, and Eq. (9) makes the same additive assumption for the average Jacobian. For any nonlinear network, the Jacobian of the output with respect to the weights is not an affine function of the input, so J(W,X+EX) != J(W,X) + J(W,EX) in general. For example, a two-layer ReLU network f(W1,W2,x) = W2 ReLU(W1 x) has Jacobian with respect to W2 equal to ReLU(W1 x)^T, which is piecewise linear but not additive in x; the cross term from the change in activation pattern is absent from Eq. (7). Lemmas 10 and 11 and Lemma 14 propagate this false identity into the residual recursion, and the proof of Theorem 4 therefore does not establish the claimed iteration bound. The error is load-bearing: without Eq. (7) there is no mechanism to separate the perturbed and clean Jacobian contributions, and the convergence factor in Eq. (47) has no derivation. Additionally, the statement of Theorem 4 contains epsilon <= O(delta alpha^2/(k beta log(delta))); for delta<1, log(delta) is negative, making the RHS negative and the hypothesis unsatisfiable, likely a sign error (log(1/delta)), but as written the theorem is vacuous.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses class-incremental continual learning (CIL) under label noise and uncorrelated instance noise. It proposes two replay-buffer construction methods, Continual CRUST and Continual CosineCRUST, built on the CRUST coreset selection algorithm. The central theoretical claim is Theorem 4, which asserts an iteration bound and correct-classification guarantee for gradient descent with MSE loss on a dataset with a delta fraction of perturbed instances, under a stated condition on the Jacobian approximation error epsilon. The empirical section compares the proposed methods against memory-based baselines (Random Replay, Random Replay with EWC, Dark ER, iCaRL) on MNIST, FashionMNIST, CIFAR10, MSTAR, and PathMNIST+ under label-flipping and salt-and-pepper instance noise, reporting accuracy, forgetting, and coreset purity. The supplementary material contains the proof of Theorem 4 as Lemmas 7-15 and Theorem 16.","tokens_in":32689,"tokens_out":4012,"duration_ms":41147,"significance":"If Theorem 4 were correct, it would provide a quantitative robustness guarantee for coreset-based replay under instance noise, including a comparison of the hardness of label versus instance noise and a bound on the required number of training iterations. The empirical study is broad: five datasets, two noise types, multiple noise levels, five seeds, and a statistical significance test, and the authors honestly record limitations of their method (e.g., the worst-case two-cluster scenario for CosineCRUST and the lack of adversarial-noise experiments). However, the theoretical contribution is the stated core of the paper, and it is not supported by the supplied proof: the key additive Jacobian identity is false for the nonlinear networks used, the perturbation terms EJ1 and EJ2 are never bounded, and the epsilon hypothesis of Theorem 4 is vacuous as written owing to a sign error. The empirical results, while suggestive, do not validate Theorem 4 because the experiments use cross-entropy loss and Adam rather than the MSE/gradient-descent setting of the theorem. Given that the load-bearing theoretical claims collapse, the paper in its current form cannot be accepted.","major_comments":[{"comment":"Equation (7) asserts J(W,X+EX)^T = J(W,X)^T + J(W,EX)^T and defines EJ1 by this decomposition; Eq. (9) makes the same additive assumption for the average Jacobian and defines EJ2. This identity is false for any nonlinear network: the Jacobian of the network output with respect to the weights is not an affine function of the input, so the Jacobian evaluated at X+EX is not the sum of the Jacobians at X and EX. The experiments use ResNet18 and EfficientNetV2s (Table 4), which are nonlinear. Because Lemmas 10, 11, and 14 of the supplement all inherit this decomposition, the residual recursion leading to Eq. (47) and the final iteration bound in Theorem 4 have no valid derivation.","section":"Section 3, Eq. (7)"},{"comment":"Lemma 10 states that the update takes the form rhat approx (I - eta(C(W) + EJ2 J(W)^T + EJ1 Jbar(What,W)))r and then says 'Numerical analysis suggests we can ignore the second order error term EJ2 EJ1.' Dropping a term without bounding it is not a proof step. The product of the two perturbation terms is of the same formal order as the kept cross terms, and no bound in terms of delta or the noise amplitude is given for any of EJ1 or EJ2. The subsequent Lemma 14 and Eq. (47) therefore rest on an unproved approximation rather than an inequality.","section":"Supplement, Lemma 10"},{"comment":"The theorem states the hypothesis epsilon <= O(delta alpha^2 / (k beta log(delta))). For a fraction delta of perturbed samples with delta < 1, log(delta) is negative, so the right-hand side is negative, making the hypothesis unsatisfiable for any positive epsilon. This appears to be a sign error (log(1/delta) was likely intended), but as written the condition is vacuous and the theorem cannot hold for any instance-noise level delta in (0,1).","section":"Theorem 4, epsilon hypothesis"},{"comment":"The contraction factor in Eq. (47) and in Lemma 15 is written as 1 - eta(alpha/2 + EJ2 alpha + EJ1 alpha - eta EJ2 beta^3/2 - eta EJ1 beta/3), with EJ1 and EJ2 appearing with mixed signs. No bounds for EJ1 and EJ2 in terms of delta, the noise amplitude, or the problem dimensions are ever established; consequently the positivity of the contraction factor, and hence the stated iteration bound, is not guaranteed. Additionally, the proof of Theorem 16 asserts the epsilon bound by saying one can 'follow the steps outlined in [36]' and reinterpret delta as the image-perturbation fraction; the label-noise proof in [36] relies on label margin and coreset purity, for which no instance-noise analogues are provided, so the derivation of the epsilon condition is absent.","section":"Theorem 4 and Supplement Theorem 16, contraction factor"},{"comment":"Theorem 4 assumes MSE loss and vanilla gradient descent, but the experiments use cross-entropy loss with the Adam optimizer (e.g., Supplement Sections 10.2 and 10.6), and the main text states only that labels are treated as ordinal values in the theory. No argument is given to transfer the theorem to the cross-entropy/Adam setting, and no experiment uses MSE loss with gradient descent. The empirical validation therefore does not test Theorem 4's assumptions, and the claim that the algorithms are 'theoretically-sound' in the experimental setting is unsupported.","section":"Section 2.1 and Section 5; Supplement Sections 10.2, 10.6"}],"minor_comments":[{"comment":"The caption says '(top)' and '(bottom)' but the table shown contains only one set of rows; the reference to a bottom half for uniform random noise is confusing and should be corrected to match the actual table content.","section":"Section 5.7, Table 3"},{"comment":"The sentence 'Not that Coreset size refers to...' should read 'Note that Coreset size refers to...'.","section":"Supplement, Section 9"},{"comment":"The marginal utility Fhat(e|S_t) = F(S_t union {e}) - F(S_t) is written with S_t in the definition but the sup over e in V is over the full dataset; the notation should specify that the union is with the current set S_{t-1} to avoid confusion with the set S_t being defined.","section":"Section 2.2, Eq. (6)"},{"comment":"The phrase 'prior work on CL shows only a small degradations in performance' should be 'small degradation'; also 'the roughly average 0.2 achieved by DER' would be clearer as 'the average forgetting of roughly 0.2 achieved by DER'.","section":"Section 5.6"},{"comment":"The theorem statement uses alpha = sqrt(rmin) sigma_min(J(W,X_S)) - Emin and beta = ||J(W,X)||_2 + epsilon + Emax, but Emin and Emax are defined only later in the supplement proof; a forward reference to Definition 2 or to the supplement would improve readability.","section":"Theorem 4, notation"}],"recommendation":"reject","confidential_remarks":"The empirical study is substantial and the authors are candid about limitations, which I weighed in the assessment. However, the stated theoretical contribution is central to the paper's claims, and the proof of Theorem 4 contains a false additivity assumption for nonlinear networks, an unbounded dropped term, and a vacuous epsilon condition. These are not local presentation issues; they invalidate the main theoretical result as stated. If the authors wish to resubmit, a version that either (a) proves the theorem for a model class where the additive Jacobian property holds and explicitly limits the claims accordingly, or (b) reframes the contribution as empirical, would be a more appropriate submission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Jim,\n\nQuick read on arXiv:2504.16763. The central theorem, Theorem 4, is not proven. Eq. (7) asserts J(W, X+E)^T = J(W, X)^T + J(W, E)^T, which holds only if the network is affine in the input. They train ResNet18 and EfficientNetV2s, which are not affine. The supplement's Lemma 10 drops the EJ2*EJ1 term with \"numerical analysis suggests\" it can be ignored—that is not a proof step. Lemma 14 propagates the false additive decomposition into the residual recursion, and Theorem 4 itself has an epsilon bound with log(delta) in the denominator; for delta < 1 that is negative, so the hypothesis is unsatisfiable. Likely a sign error, but as written the theorem is vacuous. EJ1 and EJ2 are never bounded in terms of delta or noise amplitude, so the convergence factor restates the object it needs to control. The theoretical contribution is a new statement, but it is unproven.\n\nWhat the paper does well: the empirical study is broad. Five datasets, including MSTAR and PathMNIST+, label noise up to 50%, instance noise, five seeds, and a statistical test across datasets. Continual CosineCRUST is a reasonable heuristic (spectral clustering on gradient cosine distance, then CRUST within clusters). The label-noise results are striking: at 50% flipping, MNIST accuracy 0.90 for CosineCRUST vs 0.44 for Dark ER, with much lower forgetting. The coreset purity analysis is a nice touch. The authors are also honest about some limitations (CosineCRUST worst-case behavior, CIFAR10 gap).\n\nSoft spots, in proportion: the missing GCR baseline is a real problem, because GCR is the direct gradient-coreset replay predecessor and it is cited but not compared. No code is released, so the numbers are hard to check. Under instance noise, the advantage is mostly in the forgetting metric; final accuracy on MNIST/FashionMNIST is similar across methods. The theory section needs to be removed or rewritten; it cannot be patched with a footnote.\n\nWho this is for: someone working on noisy continual learning could get value from the CosineCRUST idea and the experimental protocol. I would not cite the theorem. I would send this to peer review rather than desk-reject, but with the expectation of major revision: fix or drop the theory, add GCR, release code. As submitted, the central claim fails.","headline":"The empirical part is worth a look, but the central instance-noise theorem is unproven—Eq. (7) is false for the nonlinear networks they actually train.","tokens_in":33169,"tokens_out":3734,"would_cite":false,"duration_ms":33519,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Coreset-based replay buffers let class-incremental learners keep accuracy and cut forgetting under label and instance noise, with a new training-time guarantee for perturbed inputs.","keywords":["class-incremental learning","continual learning","coresets","CRUST","label noise","instance noise","replay buffer","catastrophic forgetting"],"falsifier":"Take a ResNet18 on CIFAR10, add salt-and-pepper noise to a fraction of inputs, and numerically check equation (7): compute $J(W, X+EX)^T$ and compare it with $J(W, X)^T + J(W, EX)^T$ at the same weights. If the norm of the difference is on the same order as the $E_{J_1}$ and $E_{J_2}$ terms driving the bound, then the residual decay predicted by Lemma 14 does not hold for that network, and the theorem's iteration guarantee would not be observed in practice.","tokens_in":32082,"feed_emoji":"🧠","tokens_out":8423,"duration_ms":76351,"temperature":0.7,"pith_summary":"This paper claims that memory-based class-incremental learners, which replay old examples from a stored buffer, can be made noise-tolerant by building the buffer with gradient-selected Coresets. It derives a new convergence bound showing that a Coreset-trained network still reaches correct classification when a fraction of the training inputs are additively perturbed, and that degradation is gradual in the noise fraction rather than abrupt. On that basis it introduces Continual CRUST and Continual CosineCRUST, two replay-buffer methods for class-incremental learning, and reports that they hold accuracy and reduce forgetting compared with existing memory-based learners under label flipping and salt-and-pepper instance noise across five datasets. If correct, continual learning systems could tolerate failing sensors and imperfect labeling without a separate denoising stage.","feed_headline":"Coreset replay keeps continual learners accurate under noise","feed_subtitle":"Gradient-selected replay buffers hold up through 50 percent label flips and heavy pixel noise, with less forgetting.","key_machinery":"The load-bearing object is the Jacobian of the network's loss with respect to its parameters, evaluated on the selected Coreset. CRUST is a greedy submodular Coreset-selection procedure that picks replay samples whose gradients best approximate the full gradient matrix, exploiting the fact that clean samples cluster in the Jacobian spectrum. The new theory extends the standard gradient-descent residual recursion to perturbed inputs by decomposing the Jacobian at $X+EX$ additively into its value at $X$ and its value at $EX$ (equations 7-10), producing error terms $E_{J_1}$ and $E_{J_2}$ that enter the final iteration bound. The proposed algorithms operationalize this by keeping one Coreset per class, refining each Coreset after every experience with CRUST, and optionally adding a spectral-clustering step on cosine distance before submodular selection in Continual CosineCRUST.","core_discovery":"The paper's central claim is that Coreset replay, originally designed for label-noise robustness in static training, extends to class-incremental learning under both label noise and additive input noise. The theoretical engine is a new bound (Theorem 4): for a fraction $\\delta$ of training inputs perturbed as $\\tilde{X} = X + E X$, gradient descent with MSE loss classifies all Coreset samples correctly after $T \\geq O\\big((1/\\eta)\\big(\\alpha/2 + E_{J_2}\\alpha + E_{J_1}\\alpha - \\eta E_{J_2}\\beta^{3/2} - \\eta E_{J_1}\\beta/3\\big)^{-1}\\log(\\|r_0\\|^2/\\nu)\\big)$ iterations, assuming the Coreset approximates the Jacobian within $\\epsilon \\leq O(\\delta\\alpha^2/(k\\beta\\log\\delta))$. The qualitative message is that instance noise degrades accuracy gradually with $\\delta$, at a slower rate than label noise, and requires more training iterations as clean data become scarcer. Building on this, the paper maintains per-class Coresets across experiences, refining each by CRUST's greedy submodular selection, and adds a variant that first clusters gradients by cosine distance and filters out small clusters (Continual CosineCRUST). Across MNIST, FashionMNIST, CIFAR10, MSTAR, and PathMNIST+, the proposed methods report higher final accuracy and lower forgetting than iCaRL, Dark ER, and replay-based baselines under label flipping up to 0.5 and salt-and-pepper instance noise up to 0.8.","pith_inferences":["A direct test the authors do not run: since the additive Jacobian decomposition is exact only for affine networks, the theorem's quantitative iteration count should first be checked on a linear model, where the assumption holds, before being expected to transfer to deep networks.","The CosineCRUST clustering step is essentially outlier detection in gradient space; the same mechanism could transfer to other settings where per-class or per-client gradient clusters need cleaning, such as noisy federated learning, though the paper offers no evidence for that extension.","The authors' own caveat that clustering can split data into two dense clusters, one clean and one noisy, suggests a concrete mitigation: restrict the submodular Coreset selection to the clean cluster or weight samples by cluster purity; this variant is not tested in the paper.","Because the bound expresses robustness in terms of the Coreset's Jacobian approximation error, it implies that any future replay method that better approximates the Jacobian under perturbation should inherit a stronger instance-noise guarantee, a connection the paper leaves implicit."],"forward_implications":["A continual learner can store only a small per-class Coreset and still maintain accuracy when label flipping probability reaches 0.5, whereas random replay, iCaRL, Dark ER, and Replay+EWC degrade sharply in the reported comparisons.","Under salt-and-pepper instance noise with up to 80 percent of samples perturbed, the proposed methods keep the forgetting metric below 0.1 on FashionMNIST, about half the forgetting of the strongest replay baseline.","Coreset purity stays above 90 percent up to 30 percent label noise and above 75 percent at 50 percent label noise, which the authors note satisfies the purity condition required by the prior label-noise theorem.","The bound predicts that the number of iterations needed to fit the Coreset decreases as the noise fraction grows, so noisy class-incremental settings may train faster while still fitting the Coreset, though with a less representative buffer."],"supporting_citations":[{"why":"Supplies the CRUST Coreset-selection method and the label-noise robustness theorem (Theorem 1) that this paper extends to instance noise and class-incremental learning.","marker":"[36]"},{"why":"Provides the average-Jacobian residual recursion and the label-noise convergence analysis whose perturbation version (Lemmas 9-15) yields the new instance-noise bound.","marker":"[32]"},{"why":"iCaRL is a principal memory-based CIL baseline against which Continual CRUST and CosineCRUST are compared on all five datasets.","marker":"[40]"},{"why":"Dark Experience Replay is one of the strongest replay baselines used to benchmark the proposed methods in the noisy CIL experiments.","marker":"[7]"},{"why":"Elastic Weight Consolidation, combined with random replay, serves as a regularization-based baseline in the comparisons.","marker":"[27]"},{"why":"Defines the alternating training/evaluation protocol for CIL that all experiments follow.","marker":"[38]"},{"why":"Supplies the forgetting metric formula used to evaluate all methods.","marker":"[35]"}],"fun_headline_variants":["Coreset replay withstands label flips and pixel noise","Noise-tolerant Coresets for class-incremental learning","Gradient-clustered replay improves continual learning under noise","Coreset buffers robust to heavy label and input noise","New bound paves way for noise-tolerant Coreset replay"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The proof assumes that the sensitivity of the network's outputs to its parameters at a noisy input is exactly the sensitivity at the clean input plus the sensitivity at the noise alone, and that the same split holds for the path-averaged sensitivity; this is true only for a network that is a straight-line function of its input, which the experimental networks are not.","fun_headline_variants_meta":{"raw":{"variants":["Coreset replay withstands label flips and pixel noise","Noise-tolerant Coresets for class-incremental learning","Gradient-clustered replay improves continual learning under noise","Coreset buffers robust to heavy label and input noise","New bound paves way for noise-tolerant Coreset replay"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001951,"raw_usage":{"total_tokens":7707,"prompt_tokens":1100,"completion_tokens":6607,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":716,"completion_tokens_details":{"reasoning_tokens":6523}},"tokens_in":716,"tokens_out":6607,"duration_ms":37687,"temperature":1.0,"reasoning_tokens":6523,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:56:46.891661+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a ResNet18 on CIFAR10, add salt-and-pepper noise to a fraction of inputs, and numerically check equation (7): compute $J(W, X+EX)^T$ and compare it with $J(W, X)^T + J(W, EX)^T$ at the same weights. If the norm of the difference is on the same order as the $E_{J_1}$ and $E_{J_2}$ terms driving the bound, then the residual decay predicted by Lemma 14 does not hold for that network, and the theorem's iteration guarantee would not be observed in practice.","supporting_citations":[{"cited_title":"Coresets for robust training of deep neural networks against noisy labels","cited_arxiv_id":null,"evidence_quote":"Supplies the CRUST Coreset-selection method and the label-noise robustness theorem (Theorem 1) that this paper extends to instance noise and class-incremental learning."},{"cited_title":"Gradient descent with early stopping is provably robust to label noise for overparameterized neural networks","cited_arxiv_id":null,"evidence_quote":"Provides the average-Jacobian residual recursion and the label-noise convergence analysis whose perturbation version (Lemmas 9-15) yields the new instance-noise bound."},{"cited_title":"icarl: Incremental classifier and representation learning","cited_arxiv_id":null,"evidence_quote":"iCaRL is a principal memory-based CIL baseline against which Continual CRUST and CosineCRUST are compared on all five datasets."},{"cited_title":"Overcoming catastrophic forgetting in neu- ral networks","cited_arxiv_id":null,"evidence_quote":"Elastic Weight Consolidation, combined with random replay, serves as a regularization-based baseline in the comparisons."},{"cited_title":"Gradient episodic memory for continual learning","cited_arxiv_id":null,"evidence_quote":"Supplies the forgetting metric formula used to evaluate all methods."}],"review_version":1}