{"id":"0eb24abc-d68f-4c1f-b0e2-aceca6c7f875","arxiv_id":"2607.21999","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Sharpness-Guided Equilibrium Sampling reweights long-tailed training batches using cumulative class counts and SAM perturbation-loss gaps, improving tail accuracy by up to 10.8 points.","lead":"This paper introduces SGS, a sampling method that uses how much each class's loss changes under SAM's perturbation to decide which classes to sample next, combining exposure and sharpness signals. On long-tailed benchmarks it substantially raises tail-class accuracy (e.g., CIFAR-100-LT tail accuracy nearly doubles) at claimed 2% extra training cost.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 3's key conditions (Eq. 14 and the sharp-risk trade-off) are assumed, not derived; the theory does not establish SGS's geometry-aware benefit, leaving frequency rebalancing as a possible full explanation.","rationale":"The reader's weakest assumption correctly identifies Theorem 3 as circular: it assumes the balancedness and favorable trade-off that SGS is supposed to achieve. This is indeed the most load-bearing concern because the paper's abstract and contribution list explicitly claim a theoretical explanation of how frequency-sharpness feedback moves training toward balanced flat minima. If Theorem 3's conditions are merely assumed, the theory provides no mechanistic backing, and the empirical gains could stem solely from frequency rebalancing. The proposed test directly checks whether the theorem's assumptions hold in the actual trained dynamics and whether the sharpness term has any measurable effect. I maintain the CONDITIONAL verdict because the empirical results are plausible and the requested checks could resolve the concern; there is no evidence of fraud or internal inconsistency in the algorithm itself. The paper should be accepted only after the theory is either derived non-circularly or demoted to heuristic status, and after a κ=0 ablation is provided.","tokens_in":13196,"tokens_out":7827,"duration_ms":73906,"concrete_test":"Run Algorithm 1 on CIFAR-100 LT IR100 with the paper's setting (κ=0.6, r_w=0.7, α_max=1, etc.), and after each epoch record the actual sampling distribution q(t) and the EMA sharpness h_c(t). At the end (and at the 180-epoch mark before deferred LA), compute ∥q−u∥_1 and ∥π−u∥_1, the SAM sharp empirical risks under q and π, and the PAC penalty B(q) from Eq. (13). Check whether inequality (14) and the trade-off condition stated in Theorem 3 hold. Additionally, run the same experiment with κ=0 (sharpness term set to a constant) to isolate the frequency-only contribution; compare tail/overall accuracy to the κ=0.6 result. If Eq. (14) is false or the trade-off is unfavorable, Theorem 3 is vacuous; if κ=0 matches κ=0.6 accuracy, the geometry-aware claim collapses.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that SGS improves long-tailed generalization by jointly controlling data exposure and optimization geometry, with the PAC-Bayes analysis providing the theoretical justification. Theorem 3, however, is conditional on assumptions that are essentially the desired conclusion: it assumes Eq. (14), that the stationary SGS distribution q* is closer to the balanced prior than the empirical prior π, and that any increase in sharp empirical risk is smaller than the reduction in the PAC penalty B(q). These conditions are never derived from the SGS update rule (Eqs. 1–9) or from the SDE analysis in Theorems 1–2. The SDE theorems are heuristic—they posit a Stratonovich limit and a stationary density on a compact support with no derivation from the discrete process. Thus the theory does not explain why SGS should produce balanced flat minima; it merely states that if it did, the bound would improve. In the absence of this derivation, the empirical gains could be fully explained by the frequency-feedback term alone (which drives cumulative exposure toward balance), with the sharpness term being ineffective or even harmful. The paper does not include an ablation that disables the sharpness term (κ=0), and its comparison baselines (CE, CE+SAM, ImbSAM, CC-SAM, Focal-SAM) are all SAM/loss-side methods, not sampling-side frequency-only rebalancing. Hence the load-bearing premise of the novelty—that sharpness-guided sampling, not just frequency rebalancing, drives the improvement—is unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes Sharpness-Guided Equilibrium Sampling (SGS), a class-level adaptive sampling strategy for long-tailed classification. SGS maintains cumulative class counts and per-class EMA estimates of the SAM perturbation loss gap, and uses the inverse product of these quantities to reweight the class sampling distribution after each mini-batch. The authors provide a continuous-time SDE analysis (Theorems 1–2) and a PAC-Bayes argument (Theorem 3) intended to show that SGS moves training toward a balanced flat minimum. They report large gains on CIFAR-10/100-LT, ImageNet-LT, and CLIP fine-tuning, and claim a training time of 1.02× vanilla SAM.","tokens_in":13718,"tokens_out":6946,"duration_ms":71045,"significance":"The core idea is attractive and potentially useful: reusing the SAM perturbation response as a cheap class-level sharpness signal to steer mini-batch construction is novel, and the method is lightweight, requiring no class-wise perturbations or extra backward passes. The reported tail-class improvements are substantial and the extension to foundation-model fine-tuning is a useful stress test. At the same time, the theoretical support is conditional in a way that does not establish the claimed mechanism, and the empirical comparison contains several protocol mismatches. In particular, the paper never isolates the sharpness term from plain frequency rebalancing, and the 1.02× speed figure is not measured. If these issues are fixed, the contribution could be valuable; as it stands, the evidence is suggestive rather than conclusive.","major_comments":[{"comment":"Theorem 3 assumes essentially the desired conclusion. Eq. (14), namely ∥q*−u∥₁ < ∥π−u∥₁, and the condition that any increase in sharp empirical risk is smaller than the reduction in B are imposed as suppositions; they are never derived from the SGS update rule (Eqs. 1–9) or from Theorem 2. The 'equalizing-transfer decomposition' is also introduced without a definition. Thus the theorem does not explain why SGS should yield a tighter PAC-Bayes bound; it merely states that if the bound improves, then the bound improves. Please either derive these conditions from the update rule under explicit, verifiable assumptions, or clearly label the argument as a conjecture/heuristic and soften the corresponding claims in the abstract and introduction.","section":"A Stochastic Dynamics Perspective of SGS, Theorem 3 (Eqs. 13–15)"},{"comment":"Both theorems rest on unproved continuous-time assumptions: 'Assume g_c(t) admits the Stratonovich limit' and 'Assume the remaining class-wise noise can be represented by an effective volatility σ~_c with reflecting boundaries on [q_min, q_max]'. No discrete-to-continuum derivation, scaling argument, or empirical consistency check links the actual mini-batch process to the SDE. As written, the SDE analysis is a formal analogy rather than a theorem about SGS. Please provide a rigorous limit or explicitly state that this is a heuristic analogy and remove the claim that it constitutes a proof of SGS's behavior.","section":"Theorems 1 and 2"},{"comment":"The LA+SGS-SAM results use a deferred LA protocol: the model is first trained with SGS-SAM for 180 epochs, then the backbone is frozen and only the classifier is fine-tuned for 20 epochs with LA+SAM. The LA baselines (LA, LA+SAM, LA+ImbSAM, LA+CC-SAM, LA+Focal-SAM) do not receive this deferred classifier fine-tuning. This protocol mismatch confounds the comparison; the large tail gains under LA could be due to the extra classifier fine-tuning stage rather than to SGS. Please apply the same deferred protocol to all LA baselines, or report SGS without deferred fine-tuning, or use a standard matched protocol for all methods.","section":"Long-Tailed Classification, 'Comparison on CIFAR10/100-LT' (Table 3)"},{"comment":"SGS-SAM25 and LIFT+SGS-SAM25 are trained for 25 epochs, while all compared methods and the default protocol use 20 epochs. The 25-epoch results are therefore not directly comparable to the 20-epoch baselines. The claim that SGS 'continues to improve beyond the default schedule' does not justify comparing a 25-epoch method against 20-epoch results. Please report 20-epoch SGS results under the same protocol, or compare against baselines also trained for 25 epochs.","section":"Large-Scale Long-Tailed Fine-Tuning (Table 5)"},{"comment":"No ablation disables the sharpness term (κ=0) or compares SGS against a frequency-only sampler. Since SGS combines inverse cumulative frequency and inverse EMA sharpness, the empirical gains could be entirely due to frequency rebalancing. Add a frequency-only baseline (e.g., sampling proportionally to 1/p_c(t) without h_c) and a κ=0 ablation on at least CIFAR-100-LT IR100. This is necessary to support the 'sharpness-guided' claim and to distinguish the contribution from existing re-sampling approaches.","section":"Method and Experiments (Eq. (5), Table 3)"},{"comment":"The text states that the comparison ratios in Table 6 'are taken from the Focal-SAM (Li et al. 2025)' paper, not measured here. This means the 1.02× figure for SGS-SAM is not an empirical measurement from this work, and the abstract's speed claim is unsupported. Please measure wall-clock time on the same hardware with the same implementation, or remove/reword the speed claim and clearly state that the figure is an estimate from prior work.","section":"Training Speed (Table 6)"}],"minor_comments":[{"comment":"The paper alternates between 'SGS' and 'SGES' (e.g., in Related Works and the Conclusion). Please use one consistent acronym.","section":"Throughout"},{"comment":"The manuscript repeatedly references an appendix ('More details about datasets, networks, and training settings are presented in Appendix' and 'the reasons why SGS needs more epochs for better results is discussed in Appendix'), but no appendix is included in the provided text. Please include the appendix or remove the references.","section":"References to Appendix"},{"comment":"The objects u, π, and q* are not formalized. Define the balanced prior u, specify the PAC complexity terms Φ(q_c), and state the assumed loss bounds explicitly.","section":"Theorem 3, Eq. (13)"},{"comment":"Table 1 reports the best IR100 result at r_w=0.7 as 47.06 overall and 20.76 tail, while Table 3 reports CE+SGS-SAM as 47.56 overall and 19.75 tail. Clarify whether these are different runs/configurations or whether the tables are inconsistent.","section":"Tables 1 and 3"},{"comment":"The text states that SGS-SAM25's total training time is 1.26× vanilla SAM, but this figure is not included in Table 6. If speed is claimed, report it consistently in the speed table.","section":"Table 5 and Table 6"}],"recommendation":"major_revision","confidential_remarks":"The paper proposes a genuinely interesting and efficient sampling mechanism, and the empirical tail-class gains are large. However, the theoretical narrative is overclaimed: Theorem 3 assumes the very conditions needed for the conclusion, and Theorems 1–2 are formal analogies without a derivation from the discrete process. The empirical comparisons also need matched protocols (deferred LA, epoch count) and, crucially, an ablation that isolates the sharpness term. These are fixable within the scope of a revision, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"What you should know: SGS is a simple, cheap sampling trick — reuse the loss gap from standard SAM as a class-level sharpness signal, combine it with cumulative class counts, and use that to steer the next mini-batches. That is new relative to ImbSAM, CC-SAM, and Focal-SAM, which all intervene after sampling. The reported gains are large: +10.85 tail points on CIFAR-100-LT over Focal-SAM, +6.59 tail points on ImageNet-LT over ImbSAM, and +10.5 tail points in FFT fine-tuning. If those hold under matched protocols, this is a solid within-subfield contribution.\n\nThe core algorithm is well-defined and genuinely plug-and-play: no extra backward passes, just C-dimensional statistics and a modified sampler. The warm-up and mixing schedule is reasonable. I buy the motivation.\n\nBut the soft spots are real. Theorem 3 assumes exactly what it needs to prove: Eq. (14) and the sharp-risk trade-off are stated as suppositions, never derived from the SGS update rule. So the theory doesn't establish that SGS moves training toward balanced flat minima — it says that if it did, the PAC bound would tighten. The SDE theorems are heuristic, with a posited Stratonovich limit and a stationary density on an assumed compact support. That's fine as intuition, but it is not a derivation.\n\nThe evaluation also has asymmetries. LA+SGS uses a deferred classifier fine-tuning stage that the baselines don't have; SGS-SAM25 on iNaturalist uses 25 epochs versus 20 for Focal-SAM; and the 1.02× speed figure is taken from Focal-SAM's paper, not measured here. The appendix is referenced but missing, so we can't check the α(e) schedule or the claimed LVIS results. Most importantly, there is no ablation that disables the sharpness term (κ=0). Without that, the gains could be entirely due to frequency rebalancing — the cumulative-count term essentially implements class-balanced sampling. That's the single missing experiment, and it's load-bearing for the novelty claim.\n\nMinor: the text alternates between SGS and SGES, and the conclusion mentions LVIS results that don't appear in the experiments.\n\nMy take: the empirical claim is plausible but not yet proven. The method deserves serious refereeing, not a desk reject. A good referee should demand matched baselines, a measured speed comparison, a κ=0 ablation, and either a non-circular theoretical derivation or a demotion of the theory to heuristic status. If those checks come back clean, the paper could be a useful contribution to long-tailed learning. Worth sending out.","headline":"A genuinely new sampling-side idea with large reported tail-accuracy gains, but the theory is conditional to the point of circularity and the evaluation has protocol asymmetries that need fixing before the numbers can be trusted.","tokens_in":843,"tokens_out":1415,"would_cite":false,"duration_ms":34680,"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":"This paper claims that actively controlling the mini-batch sampling distribution with frequency and sharpness feedback—not post-hoc perturbation correction—moves long-tailed training toward balanced flat minima, and it backs that claim with","keywords":["long-tailed learning","sharpness-aware minimization","geometry-aware sampling","flat minima","class imbalance","sampling distribution control","PAC-Bayes generalization bound","CIFAR-LT / ImageNet-LT"],"falsifier":"Train SGS with the sharpness feedback inverted (weight w_c ∝ w_freq · h_c^κ, so sharp classes are up-sampled) on CIFAR-100 LT IR100 under identical hyperparameters; if tail accuracy remains near 19.75, the sharpness term is not the cause of the gains. A second check: record the actual final class sampling shares p_c(T) under SGS and test whether ∥q* − u∥₁ < ∥π − u∥₁; if this inequality fails, the premise of Theorem 3 is violated.","tokens_in":13080,"feed_emoji":"🎯","tokens_out":5101,"duration_ms":47965,"temperature":0.7,"pith_summary":"The paper tries to establish that in long-tailed learning, the sampling distribution should be treated as an active control variable for optimization geometry rather than a fixed prior that later methods compensate for. It introduces Sharpness-Guided Equilibrium Sampling (SGS), which raises the sampling probability of classes that have been sampled less often while lowering it for classes whose SAM-induced loss changes are large, using only cumulative class counts and EMA sharpness estimates already produced by the standard SAM update. The paper characterizes this process with a stochastic differential equation whose stationary density concentrates on low frequency-curvature classes, and with a sampling-dependent PAC-Bayes bound claimed to be tighter than ordinary long-tailed SAM. Empirically, SGS-SAM improves tail accuracy by 10.85 points over Focal-SAM on CIFAR-100 LT (IR100) and by 6.59 points over ImbSAM on ImageNet-LT, at 1.02× vanilla SAM's training cost. A sympathetic reader would care because it suggests a sampling-side, nearly free route to controlling loss-landscape geometry, complementing perturbation- and loss-side methods.","feed_headline":"Sharpness-guided sampling lifts tail accuracy 10.85 points","feed_subtitle":"A closed-loop sampler reuses SAM's loss gaps to give rare, low-curvature classes more training turns—at just 1.02× the cost.","key_machinery":"The load-bearing object is the class-level sampling weight w_c = w_freq_c · w_sharp_c = 1/(p_c+ξ) · 1/(h_c^κ+ξ), where p_c(t) is the cumulative sampling share of class c and h_c(t) is the EMA of its SAM-induced loss gaps. This product couples frequency and geometry: the first factor pulls back under-sampled classes, the second pushes away classes in sharp regions. The SAM loss gap ΔL_x = |ℓ_x(w+ε) − ℓ_x(w)| acts as a zero-cost sharpness proxy because the quadratic term in its Taylor expansion captures directional curvature. Theorems 1 and 2 convert this discrete rule into an SDE whose stationary density φ(q) ∝ q^{−γ}, γ = 1 + 2(μ_c − μ̄)/σ̃², providing the 'equilibrium' for which the method","core_discovery":"The central claim is that the mini-batch sampler itself can be the mechanism that steers optimization toward balanced flat minima. SGS maintains per-class cumulative counts m_c(t) and EMA sharpness h_c(t), where h_c is an exponential moving average of the per-example loss gap |ℓ_i(w+ε)−ℓ_i(w)| from the standard SAM step. Each class's sampling weight is w_c = [1/(p_c+ξ)] · [1/(h_c^κ+ξ)], so a class receives more samples if it has been under-sampled and fewer if it is currently sharp; this weight is combined with the base prior to form the next mini-batches. The authors prove, under stated conditions, that the continuous-time limit of this closed loop has a stationary density that suppresses o","pith_inferences":["The principle is general: any optimizer that yields a per-example loss gap (e.g., adversarial training, noise injection) could drive a similar sharpness-guided sampler without SAM, so SGS could be lifted to other domains the paper does not explore.","The sharpness EMA h_c acts like an adaptive temperature; annealing κ over training might yield a curriculum that first rebalances exposure and then enforces flatness, a natural extension not studied here.","The class-level weighting assigns equal instance probability within a class; an instance-level variance term could further distinguish easy versus hard tail examples, a testable modification.","If the reported gap between κ=0.6 and small κ is real, the sharpness term is doing substantial work; quantifying the difference between SGS and pure frequency rebalancing under identical compute is the cleanest causal test."],"forward_implications":["SGS changes where optimization happens, not just the loss: sampling probability of under-exposed, low-curvature classes increases automatically over time.","Because it reuses the SAM perturbation output, SGS adds no backward passes or class-wise perturbations; measured cost is about 1.02× vanilla SAM.","It is compatible with deferred logit adjustment: representation learning uses SGS-SAM, then classifier calibration with LA, yielding additional tail-accuracy gains.","The SDE view predicts an automatic 'thermostat': if a tail class becomes sharp, its sampling weight drops, preventing overfitting to unstable regions.","Under severe imbalance (IR100/200, ImageNet-LT) the gains concentrate in medium and tail classes; under mild imbalance (IR10) SGS is comparable to Focal-SAM, so its value scales with skew."],"fun_headline_variants":["Closed-loop sampler reweights batches for flatter minima","Sharpness-aware sampling boosts tail accuracy by 10.85 pts","Sampling itself becomes the optimizer in long-tailed learning","Rare-class boost from geometry-aware mini-batch sampling","SAM's loss gaps drive smarter sampling for long-tail classes"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The PAC-Bayes theorem assumes what it needs to prove: that the stationary SGS distribution q* is closer to the balanced prior than the empirical long-tailed prior (Eq. 14) and that the increase in sharp empirical risk is outweighed by the decrease in the PAC penalty; the paper does not derive these inequalities from the SGS update rule, so the theoretical explanation could fail even if the empirical gains hold.","fun_headline_variants_meta":{"raw":{"variants":["Closed-loop sampler reweights batches for flatter minima","Sharpness-aware sampling boosts tail accuracy by 10.85 pts","Sampling itself becomes the optimizer in long-tailed learning","Rare-class boost from geometry-aware mini-batch sampling","SAM's loss gaps drive smarter sampling for long-tail classes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00021,"raw_usage":{"total_tokens":1304,"prompt_tokens":859,"completion_tokens":445,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":603,"completion_tokens_details":{"reasoning_tokens":364}},"tokens_in":603,"tokens_out":445,"duration_ms":5345,"temperature":1.0,"reasoning_tokens":364,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T06:05:56.600290+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train SGS with the sharpness feedback inverted (weight w_c ∝ w_freq · h_c^κ, so sharp classes are up-sampled) on CIFAR-100 LT IR100 under identical hyperparameters; if tail accuracy remains near 19.75, the sharpness term is not the cause of the gains. A second check: record the actual final class sampling shares p_c(T) under SGS and test whether ∥q* − u∥₁ < ∥π − u∥₁; if this inequality fails, the premise of Theorem 3 is violated.","supporting_citations":[],"review_version":1}