{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:HGD53ZXOMBPR6WB25QYHPAVXNL","short_pith_number":"pith:HGD53ZXO","schema_version":"1.0","canonical_sha256":"3987dde6ee605f1f583aec307782b76ae83803a7d3899d77d364649a86e932ed","source":{"kind":"arxiv","id":"2507.14354","version":2},"attestation_state":"computed","paper":{"title":"Interpretable Gradient Descent for Kalman Gain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"A. Olshevsky, M.A. Belabbas","submitted_at":"2025-07-18T20:20:06Z","abstract_excerpt":"We derive a decomposition for the gradient of the innovation loss with respect to the filter gain in a linear time-invariant system, decomposing as a product of an observability Gramian and a term quantifying the ``non-orthogonality\" between the estimation error and the innovation. We leverage this decomposition to give a convergence proof of gradient descent to the optimal Kalman gain, specifically identifying how recovery of the Kalman gain depends on a non-standard observability condition, and obtaining an interpretable geometric convergence rate."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.14354","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-07-18T20:20:06Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"7cab4b0e04aed5c065f18c6e21897132370b03134c5fa4ff699bd1a872bcfee8","abstract_canon_sha256":"b96a73c2e9f7d2879c538e83e0f1d7af726ddb3c97b9fc61f9336723ff758b6d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:41:26.880066Z","signature_b64":"iKtHKxghHIi3Ur4QEV+CBRIadkR5QQ+EszSsbf+ev33iajlD16J3X7rMPGKwldW53wHxTF10hWXNNdQdiBw3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3987dde6ee605f1f583aec307782b76ae83803a7d3899d77d364649a86e932ed","last_reissued_at":"2026-07-05T11:41:26.879515Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:41:26.879515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Interpretable Gradient Descent for Kalman Gain","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"A. Olshevsky, M.A. Belabbas","submitted_at":"2025-07-18T20:20:06Z","abstract_excerpt":"We derive a decomposition for the gradient of the innovation loss with respect to the filter gain in a linear time-invariant system, decomposing as a product of an observability Gramian and a term quantifying the ``non-orthogonality\" between the estimation error and the innovation. We leverage this decomposition to give a convergence proof of gradient descent to the optimal Kalman gain, specifically identifying how recovery of the Kalman gain depends on a non-standard observability condition, and obtaining an interpretable geometric convergence rate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14354","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.14354/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.14354","created_at":"2026-07-05T11:41:26.879578+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.14354v2","created_at":"2026-07-05T11:41:26.879578+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14354","created_at":"2026-07-05T11:41:26.879578+00:00"},{"alias_kind":"pith_short_12","alias_value":"HGD53ZXOMBPR","created_at":"2026-07-05T11:41:26.879578+00:00"},{"alias_kind":"pith_short_16","alias_value":"HGD53ZXOMBPR6WB2","created_at":"2026-07-05T11:41:26.879578+00:00"},{"alias_kind":"pith_short_8","alias_value":"HGD53ZXO","created_at":"2026-07-05T11:41:26.879578+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.05071","citing_title":"Learning Kalman Policy for Singular Unknown Covariances via Riemannian Regularization","ref_index":32,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HGD53ZXOMBPR6WB25QYHPAVXNL","json":"https://pith.science/pith/HGD53ZXOMBPR6WB25QYHPAVXNL.json","graph_json":"https://pith.science/api/pith-number/HGD53ZXOMBPR6WB25QYHPAVXNL/graph.json","events_json":"https://pith.science/api/pith-number/HGD53ZXOMBPR6WB25QYHPAVXNL/events.json","paper":"https://pith.science/paper/HGD53ZXO"},"agent_actions":{"view_html":"https://pith.science/pith/HGD53ZXOMBPR6WB25QYHPAVXNL","download_json":"https://pith.science/pith/HGD53ZXOMBPR6WB25QYHPAVXNL.json","view_paper":"https://pith.science/paper/HGD53ZXO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.14354&json=true","fetch_graph":"https://pith.science/api/pith-number/HGD53ZXOMBPR6WB25QYHPAVXNL/graph.json","fetch_events":"https://pith.science/api/pith-number/HGD53ZXOMBPR6WB25QYHPAVXNL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HGD53ZXOMBPR6WB25QYHPAVXNL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HGD53ZXOMBPR6WB25QYHPAVXNL/action/storage_attestation","attest_author":"https://pith.science/pith/HGD53ZXOMBPR6WB25QYHPAVXNL/action/author_attestation","sign_citation":"https://pith.science/pith/HGD53ZXOMBPR6WB25QYHPAVXNL/action/citation_signature","submit_replication":"https://pith.science/pith/HGD53ZXOMBPR6WB25QYHPAVXNL/action/replication_record"}},"created_at":"2026-07-05T11:41:26.879578+00:00","updated_at":"2026-07-05T11:41:26.879578+00:00"}