{"paper":{"title":"Refined Topology-Pass Scheduling: Damped Trust-Region Compensation for Dynamic k-NN Graphs in SE(3)-Equivariant Structure Prediction","arxiv_id":"2610.19246","primary_cat":"cs.LG","submitted_at":"2026-10-13T22:01:49+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Equivariant structure-prediction pipelines alternate coordinate updates with the construction of a k-nearest-neighbour (kNN) graph whose membership is a discrete, piecewise-constant function of the coordinates.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.09,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.11,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.98,"id":"s1","own":false,"role":"background","text":"Rebuilding that graph at every block boundary (PB) is the expensive part of an epoch, whereas reusing one frozen graph (F) is fast but leaves a topology gap.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.29,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.86,"role_probabilities":{"gap":0.02,"method":0.0,"result":0.0,"background":0.98,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.53,"id":"s2","own":true,"role":"method","text":"We study a two-pass design in which the cheap pass records a small amount of state (margins, kNN radii, measured per-boundary displacements) and a second pass compensates conservatively.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.86,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.53,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.47,"interpretation":0.0}},{"i":3,"p":0.69,"id":"s3","own":true,"role":"contribution","text":"We formulate the choice of the graph-construction basis as a damped fixed-point iteration whose unique fixed point is exactly PB, and derive (i) exact non-flip certificates with the two-sided constant $m_i/4$ and one-sided constant $m_i/2$, (ii) the minimum-variance (BLUE) replay gain $\\gamma^*$ and the resulting feasibility crossover, (iii) an $\\ell_\\infty$ trust-region projection that preserves convergence, and (iv) an analytic near-tie spacing law $E[m] \\approx r_k/(3k)$ that matches measurements to 1\\%.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.17,"quantitative":true,"quantitative_p":0.97,"role_probabilities":{"gap":0.0,"method":0.3,"result":0.01,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.69,"interpretation":0.0}},{"i":4,"p":0.95,"id":"s4","own":true,"role":"method","text":"Three compensation levels are implemented in C++ (L1: frozen set with live geometry; L2: margin-gated local repair; L3: damped, projected basis) and validated under a matched-conditions protocol (identical seed, MSA depth and trajectory family, only the topology mode differs).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.06,"quantitative":true,"quantitative_p":0.65,"role_probabilities":{"gap":0.0,"method":0.95,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.05,"interpretation":0.0}},{"i":5,"p":1.0,"id":"s5","own":true,"role":"result","text":"L2 reproduces the PB edge set exactly ($D = 0.0000$ at every boundary), L1 stays within 0.6% and L3 interpolates monotonically: L2 reproduces the PB edge set exactly when the trust region is removed, and L3 interpolates between the frozen and the PB topology.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.26,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":6,"p":1.0,"id":"s6","own":true,"role":"result","text":"The recorded trajectory itself yields a measured $1.5\\times$ Pass-1 and $1.76\\times$ epoch speed-up with no measurable loss gap.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.27,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":7,"p":0.83,"id":"s7","own":true,"role":"contribution","text":"An open-source implementation of the runtime and of all the experiments reported here is available at https://github.com/AlbertHuang96/ProteinPredictMachineLearning.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.72,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.06,"result":0.02,"background":0.0,"limitation":0.0,"future_work":0.09,"contribution":0.83,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.96,"text":"The recorded trajectory itself yields a measured $1.5\\times$ Pass-1 and $1.76\\times$ epoch speed-up with no measurable loss gap.","location":"abstract s6","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":6855,"cost_usd_reported":0.0},"compiled_at":"2026-10-15","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.04,"states_limitation":0.33,"human_participants":0.02,"controlled_comparison":0.93,"randomized_assignment":0.02,"states_quantitative_result":0.99,"compares_with_prior_results":0.91,"mentions_code_or_data_availability":0.98},"evidential_basis":{"p":0.52,"value":"observation or experiment","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":0.11,"analysis_of_existing_data":0.0,"observation_or_experiment":0.52,"simulation_or_computation":0.37}},"contribution_type":{"p":0.99,"value":"method or tool","probabilities":{"review":0.0,"method_or_tool":0.99,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.01,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.55,"text":"We study a two-pass design in which the cheap pass records a small amount of state (margins, kNN radii, measured per-boundary displacements) and a second pass compensates conservatively.","location":"abstract s2"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":8,"sentences_in_abstract":8},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; 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