{"id":"73e764be-5189-4e3d-a693-46d1f2b38966","arxiv_id":"2604.03419","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":1,"one_line_summary":"ATCG adaptively gates gradient evaluations in continuous greedy via progress-ratio thresholds to reduce communication while providing a curvature-dependent approximation guarantee that recovers full CG performance in low-curvature regimes.","lead":"The paper proposes ATCG, an adaptive variant of continuous greedy that uses per-partition progress ratios to decide when to expand active sets and evaluate gradients, thereby limiting communication in multi-agent submodular maximization. This approach could enable more scalable deployment of near-optimal submodular algorithms in bandwidth-limited settings such as distributed sensing or data summarization.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Adaptive choice of per-partition η_i may fail to preserve τ_eff = max{τ, 1-c} without curvature-dependent tuning","rationale":"The reader’s weakest assumption directly identifies the interface between the adaptive mechanism and the curvature-aware bound; the concrete test above would falsify or confirm whether that interface holds without extra tuning.","tokens_in":1817,"tokens_out":340,"duration_ms":24023,"concrete_test":"Fix a synthetic monotone submodular function with known curvature c (e.g., a weighted coverage function on a small ground set); run ATCG with the paper’s stated η_i rule for several fixed τ values; measure the achieved objective relative to the (1-1/e) optimum and check whether it meets or exceeds max{τ, 1-c} within 5 %; repeat for c near 0 and c near 1.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that gating via η_i never drops marginal gains that would have been selected by full CG, while still delivering the interpolated guarantee. The analysis presumably derives τ_eff by showing that the progress ratio controls the deviation from the multilinear extension in a curvature-dependent way. However, if the rule for setting η_i is not explicitly tied to c (or to an observable proxy that works uniformly across curvature regimes), then in high-curvature instances the method could gate too aggressively and fall back to a weaker threshold guarantee, while in low-curvature regimes it might still transmit almost everything. This makes the “recovers CG performance” regime conditional on an unstated selection procedure for η_i.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript proposes the Adaptive Thresholded Continuous Greedy (ATCG) algorithm for submodular maximization under matroid constraints in distributed settings. It gates gradient evaluations using per-partition progress ratios η_i to limit communication of feature embeddings. The central theoretical contribution is a curvature-aware approximation guarantee with effective factor τ_eff = max{τ, 1-c}, which interpolates between a threshold-based guarantee and the (1-1/e) guarantee of standard Continuous Greedy (CG) in low-curvature regimes. Experiments on class-balanced prototype selection from a CIFAR-10 subset show ATCG achieving objective values comparable to full CG while reducing communication overhead.","tokens_in":1994,"tokens_out":590,"duration_ms":46470,"significance":"If the analysis establishing the τ_eff guarantee is rigorous and the experimental results are reproducible with proper controls, this could be a meaningful advance in scalable submodular optimization. The idea of using curvature to determine the necessary level of coordination is insightful and directly addresses practical communication bottlenecks in multi-agent settings. The adaptive mechanism based on progress ratios is a clear strength for reducing overhead without full coordination.","major_comments":[{"comment":"Theoretical Analysis section, statement of the main guarantee: the claim that τ_eff = max{τ, 1-c} holds for the adaptive η_i choice requires showing that gating never drops marginal gains that full CG would capture, in a curvature-dependent manner. The manuscript does not provide the derivation steps or explicit rule for setting η_i (e.g., whether it depends on c or a proxy), which is load-bearing for the interpolation claim and the assertion that ATCG recovers CG performance in low-curvature regimes.","section":"Theoretical Analysis"},{"comment":"Experiments section, CIFAR-10 results: the report that ATCG achieves objective values comparable to full CG lacks specification of exact baselines, number of runs, variance, or statistical tests. Without these, it is difficult to confirm that the communication savings are achieved while preserving the claimed performance, undermining evaluation of the practical contribution.","section":"Experiments"}],"minor_comments":[{"comment":"Abstract: the parameters τ and c are referenced without a short reminder of their definitions (standard curvature and threshold in submodular literature), which reduces accessibility.","section":"Abstract"},{"comment":"Notation and method description: the exact update rule or pseudocode for computing the per-partition progress ratio η_i should be provided to allow reproduction of the gating mechanism.","section":"Method"}],"recommendation":"major_revision","confidential_remarks":"The current draft reads more like a conference submission than a journal article due to omitted proof details and experimental protocols; if resubmitted, require an appendix with full derivations and expanded experimental section for journal standards."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed and constructive review. The comments highlight areas where additional rigor and reporting will strengthen the manuscript, and we outline targeted revisions below.","responses":[{"response":"We agree that the current version does not include sufficient derivation steps. In the revision we will add a dedicated subsection deriving the τ_eff guarantee. The proof will show that the per-partition progress-ratio gating preserves all marginal gains that standard CG would select whenever the local curvature estimate exceeds the threshold, with the effective factor becoming max{τ, 1-c}. We will also state the explicit rule: η_i is computed from a running curvature proxy (estimated via sampled marginal gains) or defaults to a conservative value that deactivates gating when c is small, thereby recovering full CG behavior. These additions will make the curvature-dependent interpolation rigorous.","revision_made":"yes","referee_comment":"[Theoretical Analysis] Theoretical Analysis section, statement of the main guarantee: the claim that τ_eff = max{τ, 1-c} holds for the adaptive η_i choice requires showing that gating never drops marginal gains that full CG would capture, in a curvature-dependent manner. The manuscript does not provide the derivation steps or explicit rule for setting η_i (e.g., whether it depends on c or a proxy), which is load-bearing for the interpolation claim and the assertion that ATCG recovers CG performance in low-curvature regimes."},{"response":"We concur that the experimental reporting is incomplete. The revised manuscript will list all baselines (full CG, sequential greedy, and uniform random selection), state that all results are averaged over 10 independent runs, report mean objective values with standard deviations, and include paired statistical tests (Wilcoxon signed-rank) confirming that ATCG objectives are statistically indistinguishable from CG while communication volume is reduced by the reported factor. These details will be added to both the main text and the supplementary material.","revision_made":"yes","referee_comment":"[Experiments] Experiments section, CIFAR-10 results: the report that ATCG achieves objective values comparable to full CG lacks specification of exact baselines, number of runs, variance, or statistical tests. Without these, it is difficult to confirm that the communication savings are achieved while preserving the claimed performance, undermining evaluation of the practical contribution."}],"tokens_in":1514,"tokens_out":497,"duration_ms":38988,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that this paper layers an adaptive per-partition progress ratio η_i onto continuous greedy so that agents only expand their active sets and exchange embeddings when marginal gains fall short. That directly attacks the communication cost that grows with dense decision vectors in the standard multilinear relaxation approach. The claim is that the resulting approximation factor becomes τ_eff = max{τ, 1-c}, recovering full CG performance when curvature c is low and falling back to a threshold guarantee otherwise. Experiments on class-balanced prototype selection from a CIFAR-10 subset report objective values close to full CG while cutting transmitted embeddings. That combination of a communication bound tied to problem structure and a practical demo is the part worth noting. The framing around curvature determining coordination needs is a clean way to think about scalability in sensing or summarization tasks. The math appears to interpolate between existing threshold methods and the classic (1-1/e) result without introducing new fitting parameters beyond the externally defined c and τ. On the soft side, the abstract gives no derivation steps for how the progress ratio controls deviation from the multilinear extension, so it is hard to check whether the gating rule preserves the stated factor when η_i is chosen without knowledge of c. If the selection of η_i is not explicitly curvature-dependent or backed by an observable proxy that works across regimes, high-curvature instances could gate too early and lose the interpolated guarantee. The CIFAR-10 results also omit exact baselines, run counts, and significance tests, which leaves the “comparable objective” statement provisional. This is the kind of paper that distributed optimization groups would want to read if they already run continuous-greedy variants at scale. It is incremental rather than foundational, but the communication-reduction angle is concrete enough that a serious referee could usefully pressure the proof and the experimental protocol. I would send it to review rather than desk-reject.","headline":"ATCG adds a progress-ratio gate to continuous greedy that can trim communication in distributed submodular work, but the curvature-aware guarantee looks conditional on how the threshold is picked.","tokens_in":2463,"tokens_out":457,"would_cite":false,"duration_ms":25887,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"Theoretical analysis establishes a curvature-aware approximation guarantee with effective factor τ_eff = max{τ, 1-c}"},{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean","rs_theorem":"alpha_pin_under_high_calibration","paper_passage":"ATCG gates gradient evaluations behind a per-partition progress ratio η_i"}],"headline":"ATCG adaptive thresholding and curvature-aware τ_eff = max{τ,1-c} unrelated to RS J-cost or distinction-forcing chain","alignment":"orthogonal","rationale":"Paper centers on distributed continuous-greedy for submodular maximization under partition matroids, using per-partition progress ratio η_i to gate active-set expansion and deriving a curvature-dependent interpolation guarantee. RS framework derives J(x)=½(x+x⁻¹)−1, φ, 8-tick periodicity and constants from a single distinction with zero adjustable parameters; no multilinear extension, no matroid polytope, no progress-ratio gating, and no curvature parameter c appear in the RS chain. Domain (combinatorial optimization) lies outside RS theorems on spacetime emergence or recognition lattices.","tokens_in":49486,"confidence":"high","tokens_out":318,"duration_ms":16125,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"ATCG gates gradient evaluations with per-partition progress ratios to bound communication while preserving a curvature-aware approximation guarantee.","keywords":["submodular maximization","continuous greedy","adaptive threshold","matroid constraints","curvature","distributed optimization","approximation guarantee","communication efficiency"],"falsifier":"Run ATCG and full continuous greedy on the same matroid-constrained instance with known curvature c; if ATCG's achieved value lies below the predicted τ_eff factor while full CG reaches its known guarantee, the claim is falsified.","tokens_in":2717,"feed_emoji":"📉","tokens_out":658,"duration_ms":42027,"temperature":0.7,"pith_summary":"The paper introduces ATCG to scale continuous greedy for submodular maximization under matroid constraints by expanding each agent's active set only when current candidates fail to deliver enough marginal gain. This gating directly limits which feature embeddings agents must exchange. The analysis derives an effective factor τ_eff = max{τ, 1-c} that recovers the standard (1-1/e) guarantee whenever curvature is low. A reader would care because full continuous greedy forces dense decision vectors and high communication costs in large-scale tasks such as sensing or data summarization. If the claim holds, the amount of coordination required is determined by the function's curvature rather than always needing full exchanges.","feed_headline":"Adaptive gating reduces communication in continuous greedy","feed_subtitle":"Curvature-aware bound keeps objective values close to full CG while limiting which embeddings agents must share.","key_machinery":"The per-partition progress ratio η_i that decides whether to evaluate gradients and expand the active set, thereby bounding the feature embeddings transmitted across agents.","core_discovery":"ATCG introduces an adaptive threshold that gates gradient evaluations behind a per-partition progress ratio η_i, expanding active sets only when necessary, and proves this yields the curvature-aware guarantee τ_eff = max{τ, 1-c} that interpolates between a threshold-based bound and full continuous-greedy performance, with experiments confirming comparable objective values at substantially lower communication cost on a class-balanced prototype selection task.","pith_inferences":["The same adaptive gating idea could be applied to other distributed continuous-optimization algorithms where communication dominates runtime.","Varying the curvature parameter c across synthetic instances would directly test how sharply the communication savings scale with problem difficulty.","The approach may extend to streaming or online variants of submodular maximization where irrevocable decisions must be made under bandwidth limits."],"forward_implications":["The effective approximation factor improves toward the full continuous-greedy bound as curvature decreases.","Agents exchange only the embeddings needed to meet the progress ratio, cutting communication overhead.","The method retains strong performance guarantees on problems whose structure is captured by low curvature.","Coordination cost becomes a function of the objective's curvature rather than ground-set size."],"fun_headline_variants":["ATCG adaptively gates gradients to lower communication in submodular opt","Progress ratio based thresholds shrink active sets in continuous greedy","Curvature interpolates guarantees between thresholds and full CG performance","Experiments confirm ATCG matches CG objectives at reduced comms cost"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The per-partition progress ratio can be chosen so that gating expansions does not miss marginal gains that full continuous greedy would have captured.","fun_headline_variants_meta":{"raw":{"variants":["ATCG adaptively gates gradients to lower communication in submodular opt","Progress ratio based thresholds shrink active sets in continuous greedy","Curvature interpolates guarantees between thresholds and full CG performance","Experiments confirm ATCG matches CG objectives at reduced comms cost"]},"model":"grok-4.3","cost_usd":0.007364,"raw_usage":{"total_tokens":3340,"prompt_tokens":735,"num_sources_used":0,"completion_tokens":68,"cost_in_usd_ticks":73640500,"prompt_tokens_details":{"text_tokens":735,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2537,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":735,"tokens_out":68,"duration_ms":50405,"temperature":1.0,"reasoning_tokens":2537,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-21T09:57:11.208771+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Run ATCG and full continuous greedy on the same matroid-constrained instance with known curvature c; if ATCG's achieved value lies below the predicted τ_eff factor while full CG reaches its known guarantee, the claim is falsified.","supporting_citations":[],"review_version":2}