{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:O4Y3XCDVYUYJ72TKAJZRTFW5JK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"922bad5e6f866e95f6bb18a0715e8cd475cc8433d3da90ad09001e21c71c0028","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-08T03:59:25Z","title_canon_sha256":"c6207cbb006e746ffd35ed6b0b3fec5c7c3cb86708386cc7c2b89d82decd0e65"},"schema_version":"1.0","source":{"id":"2607.06976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06976","created_at":"2026-07-09T00:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06976v1","created_at":"2026-07-09T00:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06976","created_at":"2026-07-09T00:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"O4Y3XCDVYUYJ","created_at":"2026-07-09T00:19:41Z"},{"alias_kind":"pith_short_16","alias_value":"O4Y3XCDVYUYJ72TK","created_at":"2026-07-09T00:19:41Z"},{"alias_kind":"pith_short_8","alias_value":"O4Y3XCDV","created_at":"2026-07-09T00:19:41Z"}],"graph_snapshots":[{"event_id":"sha256:ce76deac0a0fdbe606246d9b61c40b0ece9c05208b10569d916e6539624c4cd3","target":"graph","created_at":"2026-07-09T00:19:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.06976/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose an efficient hybrid least squares/gradient descent (LSGD) method for MIONets to accelerate training. This method generalizes the LSGD method for DeepONets. Since MIONet is the sum of the entrywise product of multiple branch networks and a trunk network, it can be viewed as a multilinear function with respect to the last layer parameters of each branch network. These sets of parameters can be optimized using the alternating least squares method, where we solve the LS system for a single branch network in turn. To handle the large-sized system matrix, we introduce Krone","authors_text":"Chang-Ock Lee, Jun Choi, Minam Moon","cross_cats":["cs.AI","cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-08T03:59:25Z","title":"Hybrid Least Squares/Gradient Descent Methods for MIONets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06976","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:89df2648a6b4f8b72465fbdff9b5b1610319e14c2b4d0636ae4f9708e8afb093","target":"record","created_at":"2026-07-09T00:19:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"922bad5e6f866e95f6bb18a0715e8cd475cc8433d3da90ad09001e21c71c0028","cross_cats_sorted":["cs.AI","cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-08T03:59:25Z","title_canon_sha256":"c6207cbb006e746ffd35ed6b0b3fec5c7c3cb86708386cc7c2b89d82decd0e65"},"schema_version":"1.0","source":{"id":"2607.06976","kind":"arxiv","version":1}},"canonical_sha256":"7731bb8875c5309fea6a02731996dd4a985c3930f75dd17708c8d873900e2488","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7731bb8875c5309fea6a02731996dd4a985c3930f75dd17708c8d873900e2488","first_computed_at":"2026-07-09T00:19:41.848669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T00:19:41.848669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"02PXR7ZutDac4Tt5jnR7gG2uXL9HzuFHuuXxsY+1T4K02KX4lbq/849Wjrja/X/mk4G9JXjoZysatt6On5q/DQ==","signature_status":"signed_v1","signed_at":"2026-07-09T00:19:41.849082Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89df2648a6b4f8b72465fbdff9b5b1610319e14c2b4d0636ae4f9708e8afb093","sha256:ce76deac0a0fdbe606246d9b61c40b0ece9c05208b10569d916e6539624c4cd3"],"state_sha256":"77eb3f4a309bdc5037d786f088c1bc091b0053c7f1ead9bcce625ecf69cc7126"}