{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QOAVYFN2IB3WPY5M6VKLJLA2Y6","short_pith_number":"pith:QOAVYFN2","canonical_record":{"source":{"id":"2405.14131","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-23T03:11:07Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"dde5d9e021f6b25304fc08dbfa85de77f8da58286d5c533dc2e814afd3f81d40","abstract_canon_sha256":"2c702566305c684c046c38c829c710ccf52e3dd5a8cf650836a4eb63c988d062"},"schema_version":"1.0"},"canonical_sha256":"83815c15ba407767e3acf554b4ac1ac7b8d81a1f8b5ef6d99d5b4d3c45080de3","source":{"kind":"arxiv","id":"2405.14131","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.14131","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"2405.14131v3","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.14131","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"QOAVYFN2IB3W","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"pith_short_16","alias_value":"QOAVYFN2IB3WPY5M","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"pith_short_8","alias_value":"QOAVYFN2","created_at":"2026-07-05T10:24:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QOAVYFN2IB3WPY5M6VKLJLA2Y6","target":"record","payload":{"canonical_record":{"source":{"id":"2405.14131","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-23T03:11:07Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"dde5d9e021f6b25304fc08dbfa85de77f8da58286d5c533dc2e814afd3f81d40","abstract_canon_sha256":"2c702566305c684c046c38c829c710ccf52e3dd5a8cf650836a4eb63c988d062"},"schema_version":"1.0"},"canonical_sha256":"83815c15ba407767e3acf554b4ac1ac7b8d81a1f8b5ef6d99d5b4d3c45080de3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:24:53.691236Z","signature_b64":"qbAnTPleb1EHaYS9SV5/W7XDNaoiUnFp8LcAD/bSmGySH92ykvBExSk/yOlUNtP/22ZOQX4euucEg+8J2L/FBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83815c15ba407767e3acf554b4ac1ac7b8d81a1f8b5ef6d99d5b4d3c45080de3","last_reissued_at":"2026-07-05T10:24:53.690346Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:24:53.690346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.14131","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2JzwLPCq4gK+rRh/wWe+VrSRYAjVevDB02q7EMGpsCN9Z5IkL5gcfR/4mhe0JUZJlm+xaW+qEpjWFrGiQ+ImBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:04:32.336692Z"},"content_sha256":"d78202d62620b9a5e8628a0ab2a580a925131d772b101693c19c2efd2190fb2a","schema_version":"1.0","event_id":"sha256:d78202d62620b9a5e8628a0ab2a580a925131d772b101693c19c2efd2190fb2a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QOAVYFN2IB3WPY5M6VKLJLA2Y6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical Advantages of Perturbing Cosine Router in Mixture of Experts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Huy Nguyen, Nhat Ho, Pedram Akbarian, Shujian Zhang, Trang Nguyen, Trang Pham","submitted_at":"2024-05-23T03:11:07Z","abstract_excerpt":"The cosine router in Mixture of Experts (MoE) has recently emerged as an attractive alternative to the conventional linear router. Indeed, the cosine router demonstrates favorable performance in image and language tasks and exhibits better ability to mitigate the representation collapse issue, which often leads to parameter redundancy and limited representation potentials. Despite its empirical success, a comprehensive analysis of the cosine router in MoE has been lacking. Considering the least square estimation of the cosine routing MoE, we demonstrate that due to the intrinsic interaction of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.14131","kind":"arxiv","version":3},"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/2405.14131/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:24:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQvVGsx4GD+5XrAy9vsAK9awJS9fksmGvwnwKmOTsb7iJTcPwen9DsPXScYeS7XlALzs4GgAq/ro5xZ6I6CTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T16:04:32.337083Z"},"content_sha256":"651ee55ca54858562d899dacb981fb1e40a8d50cfe5b7d85ab7ce6eb6314ab37","schema_version":"1.0","event_id":"sha256:651ee55ca54858562d899dacb981fb1e40a8d50cfe5b7d85ab7ce6eb6314ab37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QOAVYFN2IB3WPY5M6VKLJLA2Y6/bundle.json","state_url":"https://pith.science/pith/QOAVYFN2IB3WPY5M6VKLJLA2Y6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QOAVYFN2IB3WPY5M6VKLJLA2Y6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-06T16:04:32Z","links":{"resolver":"https://pith.science/pith/QOAVYFN2IB3WPY5M6VKLJLA2Y6","bundle":"https://pith.science/pith/QOAVYFN2IB3WPY5M6VKLJLA2Y6/bundle.json","state":"https://pith.science/pith/QOAVYFN2IB3WPY5M6VKLJLA2Y6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QOAVYFN2IB3WPY5M6VKLJLA2Y6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QOAVYFN2IB3WPY5M6VKLJLA2Y6","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":"2c702566305c684c046c38c829c710ccf52e3dd5a8cf650836a4eb63c988d062","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-23T03:11:07Z","title_canon_sha256":"dde5d9e021f6b25304fc08dbfa85de77f8da58286d5c533dc2e814afd3f81d40"},"schema_version":"1.0","source":{"id":"2405.14131","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.14131","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"2405.14131v3","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.14131","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"QOAVYFN2IB3W","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"pith_short_16","alias_value":"QOAVYFN2IB3WPY5M","created_at":"2026-07-05T10:24:53Z"},{"alias_kind":"pith_short_8","alias_value":"QOAVYFN2","created_at":"2026-07-05T10:24:53Z"}],"graph_snapshots":[{"event_id":"sha256:651ee55ca54858562d899dacb981fb1e40a8d50cfe5b7d85ab7ce6eb6314ab37","target":"graph","created_at":"2026-07-05T10:24:53Z","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/2405.14131/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The cosine router in Mixture of Experts (MoE) has recently emerged as an attractive alternative to the conventional linear router. Indeed, the cosine router demonstrates favorable performance in image and language tasks and exhibits better ability to mitigate the representation collapse issue, which often leads to parameter redundancy and limited representation potentials. Despite its empirical success, a comprehensive analysis of the cosine router in MoE has been lacking. Considering the least square estimation of the cosine routing MoE, we demonstrate that due to the intrinsic interaction of","authors_text":"Huy Nguyen, Nhat Ho, Pedram Akbarian, Shujian Zhang, Trang Nguyen, Trang Pham","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-23T03:11:07Z","title":"Statistical Advantages of Perturbing Cosine Router in Mixture of Experts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.14131","kind":"arxiv","version":3},"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:d78202d62620b9a5e8628a0ab2a580a925131d772b101693c19c2efd2190fb2a","target":"record","created_at":"2026-07-05T10:24:53Z","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":"2c702566305c684c046c38c829c710ccf52e3dd5a8cf650836a4eb63c988d062","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-05-23T03:11:07Z","title_canon_sha256":"dde5d9e021f6b25304fc08dbfa85de77f8da58286d5c533dc2e814afd3f81d40"},"schema_version":"1.0","source":{"id":"2405.14131","kind":"arxiv","version":3}},"canonical_sha256":"83815c15ba407767e3acf554b4ac1ac7b8d81a1f8b5ef6d99d5b4d3c45080de3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83815c15ba407767e3acf554b4ac1ac7b8d81a1f8b5ef6d99d5b4d3c45080de3","first_computed_at":"2026-07-05T10:24:53.690346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:24:53.690346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qbAnTPleb1EHaYS9SV5/W7XDNaoiUnFp8LcAD/bSmGySH92ykvBExSk/yOlUNtP/22ZOQX4euucEg+8J2L/FBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:24:53.691236Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.14131","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d78202d62620b9a5e8628a0ab2a580a925131d772b101693c19c2efd2190fb2a","sha256:651ee55ca54858562d899dacb981fb1e40a8d50cfe5b7d85ab7ce6eb6314ab37"],"state_sha256":"d988b7ad196472856578191ea98ed613fb08f50fdf3560efbb11295edf3d05ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5IgINOAlCni62pkAacv5Y9mD8sfIgyuTPT2PW7Cy9zUSMFmFOEDnM1fbHTUMP35fk9A8fSHPPcI44/tOhVtfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T16:04:32.339858Z","bundle_sha256":"37a675c27f805cf91284f886e76bd4a04205f85dd44fd4090b6100d53b5181e3"}}