{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FIFJ7MNFFUR2STA7QTGLIPZXVL","short_pith_number":"pith:FIFJ7MNF","schema_version":"1.0","canonical_sha256":"2a0a9fb1a52d23a94c1f84ccb43f37aaf0167cebab49b54a1efacb77d7e90a37","source":{"kind":"arxiv","id":"1511.06464","version":4},"attestation_state":"computed","paper":{"title":"Unitary Evolution Recurrent Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","stat.ML"],"primary_cat":"cs.LG","authors_text":"Amar Shah, Martin Arjovsky, Yoshua Bengio","submitted_at":"2015-11-20T00:37:33Z","abstract_excerpt":"Recurrent neural networks (RNNs) are notoriously difficult to train. When the eigenvalues of the hidden to hidden weight matrix deviate from absolute value 1, optimization becomes difficult due to the well studied issue of vanishing and exploding gradients, especially when trying to learn long-term dependencies. To circumvent this problem, we propose a new architecture that learns a unitary weight matrix, with eigenvalues of absolute value exactly 1. The challenge we address is that of parametrizing unitary matrices in a way that does not require expensive computations (such as eigendecomposit"},"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":"1511.06464","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-11-20T00:37:33Z","cross_cats_sorted":["cs.NE","stat.ML"],"title_canon_sha256":"bce6c9952abad4b509aca2c2792a3022f5c53b507f526b64270c14fb03a4f5c5","abstract_canon_sha256":"398025e1e703650402bcdba69148bc7ca99ba6af788e7a121bdd1c64be3c45cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:30.955664Z","signature_b64":"Zc94C2kQwX1nDexdbri5G8hvZ3P2Cg8Lq8MKwqG/D4e9f+P4pb7W2J4jLi1vSw1FZw2Bgo+CvObOXMP5dufaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a0a9fb1a52d23a94c1f84ccb43f37aaf0167cebab49b54a1efacb77d7e90a37","last_reissued_at":"2026-05-18T01:02:30.955097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:30.955097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unitary Evolution Recurrent Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","stat.ML"],"primary_cat":"cs.LG","authors_text":"Amar Shah, Martin Arjovsky, Yoshua Bengio","submitted_at":"2015-11-20T00:37:33Z","abstract_excerpt":"Recurrent neural networks (RNNs) are notoriously difficult to train. When the eigenvalues of the hidden to hidden weight matrix deviate from absolute value 1, optimization becomes difficult due to the well studied issue of vanishing and exploding gradients, especially when trying to learn long-term dependencies. To circumvent this problem, we propose a new architecture that learns a unitary weight matrix, with eigenvalues of absolute value exactly 1. The challenge we address is that of parametrizing unitary matrices in a way that does not require expensive computations (such as eigendecomposit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06464","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1511.06464","created_at":"2026-05-18T01:02:30.955202+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.06464v4","created_at":"2026-05-18T01:02:30.955202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06464","created_at":"2026-05-18T01:02:30.955202+00:00"},{"alias_kind":"pith_short_12","alias_value":"FIFJ7MNFFUR2","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FIFJ7MNFFUR2STA7","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FIFJ7MNF","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1909.01066","citing_title":"Language Models as Knowledge Bases?","ref_index":93,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FIFJ7MNFFUR2STA7QTGLIPZXVL","json":"https://pith.science/pith/FIFJ7MNFFUR2STA7QTGLIPZXVL.json","graph_json":"https://pith.science/api/pith-number/FIFJ7MNFFUR2STA7QTGLIPZXVL/graph.json","events_json":"https://pith.science/api/pith-number/FIFJ7MNFFUR2STA7QTGLIPZXVL/events.json","paper":"https://pith.science/paper/FIFJ7MNF"},"agent_actions":{"view_html":"https://pith.science/pith/FIFJ7MNFFUR2STA7QTGLIPZXVL","download_json":"https://pith.science/pith/FIFJ7MNFFUR2STA7QTGLIPZXVL.json","view_paper":"https://pith.science/paper/FIFJ7MNF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.06464&json=true","fetch_graph":"https://pith.science/api/pith-number/FIFJ7MNFFUR2STA7QTGLIPZXVL/graph.json","fetch_events":"https://pith.science/api/pith-number/FIFJ7MNFFUR2STA7QTGLIPZXVL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FIFJ7MNFFUR2STA7QTGLIPZXVL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FIFJ7MNFFUR2STA7QTGLIPZXVL/action/storage_attestation","attest_author":"https://pith.science/pith/FIFJ7MNFFUR2STA7QTGLIPZXVL/action/author_attestation","sign_citation":"https://pith.science/pith/FIFJ7MNFFUR2STA7QTGLIPZXVL/action/citation_signature","submit_replication":"https://pith.science/pith/FIFJ7MNFFUR2STA7QTGLIPZXVL/action/replication_record"}},"created_at":"2026-05-18T01:02:30.955202+00:00","updated_at":"2026-05-18T01:02:30.955202+00:00"}