{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NKD5LWFNAUQVXWRMFWJMZHVPWU","short_pith_number":"pith:NKD5LWFN","canonical_record":{"source":{"id":"1709.06079","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-16T09:56:55Z","cross_cats_sorted":[],"title_canon_sha256":"f1b7ad29bd7dd983473702f00d4b0b8b2c2ad434a8f8068c573f48e513a841c3","abstract_canon_sha256":"fa738ec6ee980486703c7a884c05ff2bac669aef1d3753cce16bb06619069efa"},"schema_version":"1.0"},"canonical_sha256":"6a87d5d8ad05215bda2c2d92cc9eafb528330cb6ecdcffa389334fef891c4c24","source":{"kind":"arxiv","id":"1709.06079","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06079","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06079v2","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06079","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"NKD5LWFNAUQV","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NKD5LWFNAUQVXWRM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NKD5LWFN","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NKD5LWFNAUQVXWRMFWJMZHVPWU","target":"record","payload":{"canonical_record":{"source":{"id":"1709.06079","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-16T09:56:55Z","cross_cats_sorted":[],"title_canon_sha256":"f1b7ad29bd7dd983473702f00d4b0b8b2c2ad434a8f8068c573f48e513a841c3","abstract_canon_sha256":"fa738ec6ee980486703c7a884c05ff2bac669aef1d3753cce16bb06619069efa"},"schema_version":"1.0"},"canonical_sha256":"6a87d5d8ad05215bda2c2d92cc9eafb528330cb6ecdcffa389334fef891c4c24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:59.894756Z","signature_b64":"nO/06Q0oH+XmB9Ae/majSHNcmFyybg9uMpgcZ8yRamyB38ypuMXIgQiANrByqJdeYzMweuDTEoNh4gs6RNsKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a87d5d8ad05215bda2c2d92cc9eafb528330cb6ecdcffa389334fef891c4c24","last_reissued_at":"2026-05-18T00:29:59.894356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:59.894356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.06079","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lf/u16WLb1u/J6XewB1VNMMN1rrZGrjilcGjmR5z1stFfDojc5L7Jp/gJAJa63jkbRXQ4SLDSj6FeF+9rni4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:36:36.597610Z"},"content_sha256":"acab5744cfa15c2694ba8a1f55da231993c65f261c4f29a656bc39aa56df221d","schema_version":"1.0","event_id":"sha256:acab5744cfa15c2694ba8a1f55da231993c65f261c4f29a656bc39aa56df221d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NKD5LWFNAUQVXWRMFWJMZHVPWU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Adams Wei Yu, Bo Lang, Bo Li, Lei Huang, Xianglong Liu, Yongliang Wang","submitted_at":"2017-09-16T09:56:55Z","abstract_excerpt":"Orthogonal matrix has shown advantages in training Recurrent Neural Networks (RNNs), but such matrix is limited to be square for the hidden-to-hidden transformation in RNNs. In this paper, we generalize such square orthogonal matrix to orthogonal rectangular matrix and formulating this problem in feed-forward Neural Networks (FNNs) as Optimization over Multiple Dependent Stiefel Manifolds (OMDSM). We show that the rectangular orthogonal matrix can stabilize the distribution of network activations and regularize FNNs. We also propose a novel orthogonal weight normalization method to solve OMDSM"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06079","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":""},"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":"2026-05-18T00:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mN40SVJTnS4+bynVBuRhfL2z7XezfGusTbXng/PZEuBNBMgP9DyTEVvkI7mZfVCXN7Na2wpKrMbbpcNcihdhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:36:36.598128Z"},"content_sha256":"d2468334f6522ec391c29d8085548218ee77ead39c5b87557da81670d2720ed5","schema_version":"1.0","event_id":"sha256:d2468334f6522ec391c29d8085548218ee77ead39c5b87557da81670d2720ed5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKD5LWFNAUQVXWRMFWJMZHVPWU/bundle.json","state_url":"https://pith.science/pith/NKD5LWFNAUQVXWRMFWJMZHVPWU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKD5LWFNAUQVXWRMFWJMZHVPWU/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":"2026-05-30T13:36:36Z","links":{"resolver":"https://pith.science/pith/NKD5LWFNAUQVXWRMFWJMZHVPWU","bundle":"https://pith.science/pith/NKD5LWFNAUQVXWRMFWJMZHVPWU/bundle.json","state":"https://pith.science/pith/NKD5LWFNAUQVXWRMFWJMZHVPWU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKD5LWFNAUQVXWRMFWJMZHVPWU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NKD5LWFNAUQVXWRMFWJMZHVPWU","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":"fa738ec6ee980486703c7a884c05ff2bac669aef1d3753cce16bb06619069efa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-16T09:56:55Z","title_canon_sha256":"f1b7ad29bd7dd983473702f00d4b0b8b2c2ad434a8f8068c573f48e513a841c3"},"schema_version":"1.0","source":{"id":"1709.06079","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06079","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06079v2","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06079","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"NKD5LWFNAUQV","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NKD5LWFNAUQVXWRM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NKD5LWFN","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:d2468334f6522ec391c29d8085548218ee77ead39c5b87557da81670d2720ed5","target":"graph","created_at":"2026-05-18T00:29:59Z","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"},"paper":{"abstract_excerpt":"Orthogonal matrix has shown advantages in training Recurrent Neural Networks (RNNs), but such matrix is limited to be square for the hidden-to-hidden transformation in RNNs. In this paper, we generalize such square orthogonal matrix to orthogonal rectangular matrix and formulating this problem in feed-forward Neural Networks (FNNs) as Optimization over Multiple Dependent Stiefel Manifolds (OMDSM). We show that the rectangular orthogonal matrix can stabilize the distribution of network activations and regularize FNNs. We also propose a novel orthogonal weight normalization method to solve OMDSM","authors_text":"Adams Wei Yu, Bo Lang, Bo Li, Lei Huang, Xianglong Liu, Yongliang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-16T09:56:55Z","title":"Orthogonal Weight Normalization: Solution to Optimization over Multiple Dependent Stiefel Manifolds in Deep Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06079","kind":"arxiv","version":2},"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:acab5744cfa15c2694ba8a1f55da231993c65f261c4f29a656bc39aa56df221d","target":"record","created_at":"2026-05-18T00:29:59Z","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":"fa738ec6ee980486703c7a884c05ff2bac669aef1d3753cce16bb06619069efa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-09-16T09:56:55Z","title_canon_sha256":"f1b7ad29bd7dd983473702f00d4b0b8b2c2ad434a8f8068c573f48e513a841c3"},"schema_version":"1.0","source":{"id":"1709.06079","kind":"arxiv","version":2}},"canonical_sha256":"6a87d5d8ad05215bda2c2d92cc9eafb528330cb6ecdcffa389334fef891c4c24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a87d5d8ad05215bda2c2d92cc9eafb528330cb6ecdcffa389334fef891c4c24","first_computed_at":"2026-05-18T00:29:59.894356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:59.894356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nO/06Q0oH+XmB9Ae/majSHNcmFyybg9uMpgcZ8yRamyB38ypuMXIgQiANrByqJdeYzMweuDTEoNh4gs6RNsKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:59.894756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06079","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acab5744cfa15c2694ba8a1f55da231993c65f261c4f29a656bc39aa56df221d","sha256:d2468334f6522ec391c29d8085548218ee77ead39c5b87557da81670d2720ed5"],"state_sha256":"b193da4c6233b18017ca6154e34faf9fe5d70cc7cd7100ac1b5e2bd157511078"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+povfpTvRo29XcJxmek10CgfkwtHiAL+YObxlNg61WMVUckXhscDpn3gMlwJhDswyr6q9qbHaIDgBn+zqbrCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:36:36.600423Z","bundle_sha256":"f2945b891f855a4ef28951cc9d8cf5f08df5dfcc2c9534aa5975790002faa3a4"}}