{"paper":{"title":"Matrix-Product Belief Propagation for continuous-state-space variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Matrix-Product Belief Propagation extends to continuous variables through a Hilbert basis expansion.","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alfredo Braunstein, Federico Florio","submitted_at":"2026-05-14T08:06:32Z","abstract_excerpt":"Computation of observables in discrete stochastic, possibly conditioned, dynamics over large sparse networks is at the basis of a myriad of applications. The Matrix-Product Belief Propagation method allows a semi-analytical estimation of such observables with a controlled error that depends on the size of the employed matrices, called bond size. Its computational cost is linear in the time horizon and the network size for a large family of models with discrete degrees of freedom. Here, a generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is presented, using a tunable expansion in a Hilbert function basis.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a finite expansion in the chosen Hilbert basis (e.g., Fourier) can accurately represent the continuous degrees of freedom with controlled error for the target models.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Generalizes matrix-product belief propagation to continuous variables using Hilbert basis expansions, enabling linear-cost computation of dynamics and large deviations in mixed-state kinetic Ising models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Matrix-Product Belief Propagation extends to continuous variables through a Hilbert basis expansion.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8c7838b6944073c5fdfa85d25551930d27ef7479f3f2abe700924954c864e329"},"source":{"id":"2605.14522","kind":"arxiv","version":1},"verdict":{"id":"d1fafaa4-cf1b-4557-adc1-071153cb7699","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:19:18.083370Z","strongest_claim":"A generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is presented, using a tunable expansion in a Hilbert function basis.","one_line_summary":"Generalizes matrix-product belief propagation to continuous variables using Hilbert basis expansions, enabling linear-cost computation of dynamics and large deviations in mixed-state kinetic Ising models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a finite expansion in the chosen Hilbert basis (e.g., Fourier) can accurately represent the continuous degrees of freedom with controlled error for the target models.","pith_extraction_headline":"Matrix-Product Belief Propagation extends to continuous variables through a Hilbert basis expansion."},"references":{"count":19,"sample":[{"doi":"","year":2014,"title":"N. 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Newman, Message passing ap- proach for general epidemic models, Physical Review E 82, 016101 (2010)","work_id":"e559fbe1-d5b6-480d-8f86-0d70e3c915eb","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"A. Braunstein, G. Catania, L. Dall’Asta, M. Mariani, F. Mazza, and M. Tarabolo, Small-coupling dynamic cav- ity: A Bayesian mean-field framework for epidemic infer- ence, Physical Review Research7, 02","work_id":"ede4dc89-8428-402e-99f1-bd94768620de","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":19,"snapshot_sha256":"6eacbc42ca9740b9085107de4a0f7cd2d617a218633ccc45f2e0a74dd4bc6f83","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"17a02ec95d336c14cb01d13f78517d901c7271aa5d5fd77a99572183228a2332"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}