{"id":"7b1c54b1-bf15-4ce6-a76e-004f7c635861","arxiv_id":"2607.01726","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Experimental comparison shows solver-dependent performance of polynomial symmetry breakers on bin-packing problems, recommending solver-aware evaluation.","lead":"The paper experimentally evaluates automatically generated polynomial symmetry breaking constraints for integer linear programs on bin-packing benchmarks. It finds that their effectiveness depends strongly on the solver and how constraints are handled.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Near half-capacity bin-packing benchmarks may not suffice to establish solver-dependence as a general phenomenon","rationale":"The reader's weakest_assumption directly identifies the same load-bearing point for generalizing the experimental conclusion. No stronger internal inconsistency (e.g., in the algebraic construction itself) is visible from the given abstract and claim; the issue is external validity of the test set.","tokens_in":1596,"tokens_out":297,"duration_ms":20177,"concrete_test":"Apply the identical polynomial breaker generation pipeline to a second benchmark suite (e.g., the MIPLIB scheduling or graph-coloring instances with documented symmetries), re-run the same solver set, and test whether the ranking of quadratic vs. linearized breakers and the magnitude of performance deltas remain consistent with the bin-packing results.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that experiments demonstrate polynomial symmetry breaking effectiveness is strongly solver-dependent, leading to the suggestion that breakers should be evaluated solver-aware. All reported benchmarks are restricted to near half-capacity bin-packing instances, whose symmetries arise from permutations of identical items. This class has a narrow symmetry structure and capacity-induced tightness that may interact with solvers in ways not representative of other ILP families (e.g., those with cyclic, graph automorphism, or variable-subset symmetries). If the observed solver dependence is an artifact of this benchmark family, the broader recommendation does not follow from the data.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper reports an experimental evaluation of automatically generated polynomial symmetry breaking constraints for integer linear programs. Building on a prior ISSAC 2026 method, it compares solver-native quadratic handling, solver-internal reformulation, and explicit linearization on near half-capacity bin-packing benchmarks. Experiments across mathematical programming and SMT solvers indicate that the effectiveness of these breakers is strongly solver-dependent, with compact quadratic families sometimes improving performance while linearization or large sets can degrade it due to model size or search behavior. The authors conclude that such breakers should be evaluated in a solver-aware manner.","tokens_in":1705,"tokens_out":426,"duration_ms":24452,"significance":"If the reported solver dependence holds beyond the tested instances, the work would usefully highlight that algebraic symmetry-breaking techniques cannot be treated as solver-independent additions to models. This could shift evaluation practices in the intersection of symbolic computation and optimization solvers, encouraging more targeted integration of polynomial breakers. The experimental framing provides concrete data on quadratic vs. linearized handling, which is a practical contribution even if limited in scope.","major_comments":[{"comment":"Abstract and benchmark description: All experiments use only near half-capacity bin-packing instances whose symmetries are limited to permutations of identical items under capacity-induced tightness. This narrow symmetry structure and problem class may interact with solvers in ways not representative of other ILP families (e.g., those with cyclic, graph-automorphism, or variable-subset symmetries). Because the central claim of strong solver dependence and the recommendation for solver-aware evaluation rest on these results, the restriction is load-bearing and requires either additional benchmark families or explicit qualification of the scope.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract mentions 'several' solvers and 'statistical analysis' implicitly through performance claims, but lacks explicit details on the number of instances, run-time cutoffs, or variance reporting; adding these would improve verifiability without altering the core findings.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive comment on the scope of our benchmarks. We address it below by agreeing to add explicit qualifications rather than expanding the experimental suite.","responses":[{"response":"We agree that the experiments are restricted to permutation symmetries of identical items in near half-capacity bin-packing instances. This class was selected because it produces well-defined, automatically detectable symmetries that the ISSAC 2026 generation method targets, enabling a controlled comparison of quadratic handling, reformulation, and linearization across solvers. While we believe permutation symmetries are representative of a practically relevant subclass of ILP symmetries, we acknowledge that cyclic, graph-automorphism, or other structures could interact differently with solvers. In the revised version we will add explicit scope qualifications to the abstract, introduction, and conclusions, stating that the reported solver dependence is demonstrated for this symmetry class and problem family, and that extending the evaluation to additional ILP families remains valuable future work. We do not introduce new benchmark families, as that would require substantial new symmetry-generation experiments outside the current study.","revision_made":"yes","referee_comment":"[Abstract] Abstract and benchmark description: All experiments use only near half-capacity bin-packing instances whose symmetries are limited to permutations of identical items under capacity-induced tightness. This narrow symmetry structure and problem class may interact with solvers in ways not representative of other ILP families (e.g., those with cyclic, graph-automorphism, or variable-subset symmetries). Because the central claim of strong solver dependence and the recommendation for solver-aware evaluation rest on these results, the restriction is load-bearing and requires either additional benchmark families or explicit qualification of the scope."}],"tokens_in":1255,"tokens_out":356,"duration_ms":15482,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper runs their ISSAC 2026 polynomial symmetry breaking method on near half-capacity bin-packing instances and compares how different solvers handle the resulting quadratic constraints versus linearized or reformulated versions. The main finding is that compact quadratic breakers sometimes improve runtimes while larger sets or explicit linearization often erase the benefit through model size or search changes. That difference appears across the tested MP and SMT solvers.\n\nThe work is new as an empirical follow-up. It supplies concrete performance numbers that were not in the earlier paper and makes a practical observation about not treating breakers as solver-independent add-ons.\n\nThe soft spot is the benchmark choice. All instances come from one narrow class where symmetries are just permutations of identical items and the capacity is near half. That structure may interact with solvers in ways that do not appear in other ILPs with cyclic, graph, or subset symmetries. The claim that breakers should be evaluated solver-aware therefore rests on limited evidence; the stress-test concern holds up.\n\nThe experimental design itself looks reasonable on the surface, with no obvious circularity or invented entities. Citations are mostly to their own prior work and standard solver literature.\n\nThis is for people who already work on algebraic symmetry methods inside optimization solvers. A reader who needs data on how quadratic handling plays out across tools will find something usable here. It is not a foundational result but adds a data point worth checking.\n\nI would send it to peer review so the experimental details and statistical support can be examined directly.","headline":"The experiments show solver-dependent effects from polynomial symmetry breakers on these bin-packing cases, but the single benchmark family leaves the general recommendation on shaky ground.","tokens_in":2152,"tokens_out":378,"would_cite":false,"duration_ms":21571,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Polynomial symmetry breaking for integer linear programs works differently depending on the solver used.","keywords":["symmetry breaking","integer linear programming","polynomial constraints","bin-packing","solver performance","mathematical programming","SMT solvers","experimental evaluation"],"falsifier":"A set of experiments on a wider collection of integer linear programs and additional solvers that shows consistent gains from polynomial symmetry breaking regardless of handling method would falsify the solver-dependence claim.","tokens_in":2496,"feed_emoji":"📊","tokens_out":615,"duration_ms":27620,"temperature":0.7,"pith_summary":"The paper evaluates automatically generated polynomial symmetry breaking constraints added to integer linear programs. It compares three ways of handling those constraints—native quadratic support, solver reformulation, and explicit linearization—on near half-capacity bin-packing instances. Experiments across several mathematical programming solvers and SMT solvers reveal that performance changes are strongly tied to the particular solver and handling method. Compact quadratic breaker families sometimes speed up solving, while larger sets or linearization often increase model size and slow search. The study therefore concludes that symmetry breakers cannot be treated as universal, solver-independent additions.","feed_headline":"Symmetry breaking gains vary strongly with solver choice","feed_subtitle":"Bin-packing tests show quadratic breakers boost some solvers but linearization and large sets hurt others overall.","key_machinery":"Automatically generated polynomial symmetry breaking constraints, compared through solver-native quadratic handling, internal reformulation, and explicit linearization.","core_discovery":"Experiments with several mathematical programming solvers and satisfiability modulo theory solvers show that the effectiveness of polynomial symmetry breaking is strongly solver-dependent. Compact quadratic breaker families can improve performance, whereas linearization, large breaker sets, or solver reformulations may offset these gains through increased model size or less favorable search behavior. These results suggest that automatically generated symmetry breakers should be evaluated in a solver-aware manner rather than treated as solver-independent additions to a model.","pith_inferences":["Generator tools for symmetry breakers could be extended to take solver type and native capabilities as input parameters.","The same experimental protocol could be applied to other problem families such as scheduling or graph problems to test whether the solver dependence persists.","Solver portfolios that route instances to the solver best matched to a given breaker family might exploit the observed variation."],"forward_implications":["Compact quadratic breaker families improve performance on the tested bin-packing benchmarks for some solvers.","Explicit linearization of the breakers increases model size and can cancel out any speed gains.","Large breaker families produce less favorable search behavior in the solvers examined.","Solver-internal reformulation of quadratic constraints can reduce the benefit of adding symmetry breakers."],"fun_headline_variants":["Solver choice dictates symmetry breaking success","Symmetry breaking effectiveness varies by solver","Polynomial breakers perform differently per solver","Algebraic symmetry results hinge on solver type"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The near half-capacity bin-packing benchmarks sufficiently represent how symmetry breaking behaves in general integer linear programs.","fun_headline_variants_meta":{"raw":{"variants":["Solver choice dictates symmetry breaking success","Symmetry breaking effectiveness varies by solver","Polynomial breakers perform differently per solver","Algebraic symmetry results hinge on solver type"]},"model":"grok-4.3","cost_usd":0.003355,"raw_usage":{"total_tokens":1741,"prompt_tokens":583,"num_sources_used":0,"completion_tokens":48,"cost_in_usd_ticks":33549500,"prompt_tokens_details":{"text_tokens":583,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1110,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":583,"tokens_out":48,"duration_ms":9874,"temperature":1.0,"reasoning_tokens":1110,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-03T02:15:46.734609+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A set of experiments on a wider collection of integer linear programs and additional solvers that shows consistent gains from polynomial symmetry breaking regardless of handling method would falsify the solver-dependence claim.","supporting_citations":[],"review_version":1}