{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:RO6VUTXG4PLBQJCBDVWPE3WOZJ","short_pith_number":"pith:RO6VUTXG","canonical_record":{"source":{"id":"2006.08426","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-15T14:26:56Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"28ec54904b936f6b7f5da71ca3bafeb6f20ffd04b52daaf97f889a7c4b328619","abstract_canon_sha256":"3f1e1682dcc5e243b0566d6d67496a6a3cf4b235a54444a16d5afb082a274bdc"},"schema_version":"1.0"},"canonical_sha256":"8bbd5a4ee6e3d61824411d6cf26ececa59c203d76230ea1752d6fd708dfd4003","source":{"kind":"arxiv","id":"2006.08426","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.08426","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"2006.08426v4","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08426","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"RO6VUTXG4PLB","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"pith_short_16","alias_value":"RO6VUTXG4PLBQJCB","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"pith_short_8","alias_value":"RO6VUTXG","created_at":"2026-07-05T06:45:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:RO6VUTXG4PLBQJCBDVWPE3WOZJ","target":"record","payload":{"canonical_record":{"source":{"id":"2006.08426","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-15T14:26:56Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"28ec54904b936f6b7f5da71ca3bafeb6f20ffd04b52daaf97f889a7c4b328619","abstract_canon_sha256":"3f1e1682dcc5e243b0566d6d67496a6a3cf4b235a54444a16d5afb082a274bdc"},"schema_version":"1.0"},"canonical_sha256":"8bbd5a4ee6e3d61824411d6cf26ececa59c203d76230ea1752d6fd708dfd4003","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:45:55.875589Z","signature_b64":"xoJOysA0tD4Ck6abRTNsbXP6x1VC0VjpSre9S58osPSgKTcrZQuerpitH73RZlDb5EDE0funJ7xOKogpRe72Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bbd5a4ee6e3d61824411d6cf26ececa59c203d76230ea1752d6fd708dfd4003","last_reissued_at":"2026-07-05T06:45:55.875114Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:45:55.875114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.08426","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V3/mfIuGHmzJXOrRyU496Wrm7la8Sjfq6QLdGF2I3MpMRwXB8ZG+eXjULFhnkMm2C4d87xs4wwfIsZYGLbSAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T07:45:25.882082Z"},"content_sha256":"a8f454d973645803f4d2c904cb661bcd22482997cda744896f07666e918f10c8","schema_version":"1.0","event_id":"sha256:a8f454d973645803f4d2c904cb661bcd22482997cda744896f07666e918f10c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:RO6VUTXG4PLBQJCBDVWPE3WOZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Walking in the Shadow: A New Perspective on Descent Directions for Constrained Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Hassan Mortagy, Sebastian Pokutta, Swati Gupta","submitted_at":"2020-06-15T14:26:56Z","abstract_excerpt":"Descent directions such as movement towards Descent directions, including movement towards Frank-Wolfe vertices, away-steps, in-face away-steps and pairwise directions, have been an important design consideration in conditional gradient descent (CGD) variants. In this work, we attempt to demystify the impact of the movement in these directions towards attaining constrained minimizers. The optimal local direction of descent is the directional derivative (i.e., shadow) of the projection of the negative gradient. We show that this direction is the best away-step possible, and the continuous-time "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08426","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.08426/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":"2026-07-05T06:45:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shZC/m4Xh/m32/Thghh98jKAKWlC//ycvPA0sDmYtjENULQW+g5K5gkEEHyW+ZX7ZaVl5o3NU7+zZq9e0SNsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T07:45:25.882469Z"},"content_sha256":"e293d62ca90d588c6d7987c75f01c93785c14a49caa7bf5a42e4dbf743752444","schema_version":"1.0","event_id":"sha256:e293d62ca90d588c6d7987c75f01c93785c14a49caa7bf5a42e4dbf743752444"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RO6VUTXG4PLBQJCBDVWPE3WOZJ/bundle.json","state_url":"https://pith.science/pith/RO6VUTXG4PLBQJCBDVWPE3WOZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RO6VUTXG4PLBQJCBDVWPE3WOZJ/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":"2026-07-13T07:45:25Z","links":{"resolver":"https://pith.science/pith/RO6VUTXG4PLBQJCBDVWPE3WOZJ","bundle":"https://pith.science/pith/RO6VUTXG4PLBQJCBDVWPE3WOZJ/bundle.json","state":"https://pith.science/pith/RO6VUTXG4PLBQJCBDVWPE3WOZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RO6VUTXG4PLBQJCBDVWPE3WOZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:RO6VUTXG4PLBQJCBDVWPE3WOZJ","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":"3f1e1682dcc5e243b0566d6d67496a6a3cf4b235a54444a16d5afb082a274bdc","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-15T14:26:56Z","title_canon_sha256":"28ec54904b936f6b7f5da71ca3bafeb6f20ffd04b52daaf97f889a7c4b328619"},"schema_version":"1.0","source":{"id":"2006.08426","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.08426","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"arxiv_version","alias_value":"2006.08426v4","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08426","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"pith_short_12","alias_value":"RO6VUTXG4PLB","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"pith_short_16","alias_value":"RO6VUTXG4PLBQJCB","created_at":"2026-07-05T06:45:55Z"},{"alias_kind":"pith_short_8","alias_value":"RO6VUTXG","created_at":"2026-07-05T06:45:55Z"}],"graph_snapshots":[{"event_id":"sha256:e293d62ca90d588c6d7987c75f01c93785c14a49caa7bf5a42e4dbf743752444","target":"graph","created_at":"2026-07-05T06:45:55Z","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/2006.08426/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Descent directions such as movement towards Descent directions, including movement towards Frank-Wolfe vertices, away-steps, in-face away-steps and pairwise directions, have been an important design consideration in conditional gradient descent (CGD) variants. In this work, we attempt to demystify the impact of the movement in these directions towards attaining constrained minimizers. The optimal local direction of descent is the directional derivative (i.e., shadow) of the projection of the negative gradient. We show that this direction is the best away-step possible, and the continuous-time ","authors_text":"Hassan Mortagy, Sebastian Pokutta, Swati Gupta","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-15T14:26:56Z","title":"Walking in the Shadow: A New Perspective on Descent Directions for Constrained Minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08426","kind":"arxiv","version":4},"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:a8f454d973645803f4d2c904cb661bcd22482997cda744896f07666e918f10c8","target":"record","created_at":"2026-07-05T06:45:55Z","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":"3f1e1682dcc5e243b0566d6d67496a6a3cf4b235a54444a16d5afb082a274bdc","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-15T14:26:56Z","title_canon_sha256":"28ec54904b936f6b7f5da71ca3bafeb6f20ffd04b52daaf97f889a7c4b328619"},"schema_version":"1.0","source":{"id":"2006.08426","kind":"arxiv","version":4}},"canonical_sha256":"8bbd5a4ee6e3d61824411d6cf26ececa59c203d76230ea1752d6fd708dfd4003","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bbd5a4ee6e3d61824411d6cf26ececa59c203d76230ea1752d6fd708dfd4003","first_computed_at":"2026-07-05T06:45:55.875114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:45:55.875114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xoJOysA0tD4Ck6abRTNsbXP6x1VC0VjpSre9S58osPSgKTcrZQuerpitH73RZlDb5EDE0funJ7xOKogpRe72Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:45:55.875589Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.08426","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8f454d973645803f4d2c904cb661bcd22482997cda744896f07666e918f10c8","sha256:e293d62ca90d588c6d7987c75f01c93785c14a49caa7bf5a42e4dbf743752444"],"state_sha256":"4ddb47c26342e29249df65059304bd9a500d5da8874ad2cb783ff8c69f96d48f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qMoZwJtMYPxYfmr+Mxs+yiP3/CoTUfol0X0ujdlVY2ncN1q40zSYI46PGcnXW2NZATPaGahuKiCA87Tpft0hAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-13T07:45:25.884845Z","bundle_sha256":"b136c671db44a6736f35c769a66d00983ed9bcc40a50c7235500120d86dbbeed"}}