{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4SNADUXPSAKWATBNEQDRP6W5GR","short_pith_number":"pith:4SNADUXP","schema_version":"1.0","canonical_sha256":"e49a01d2ef9015604c2d240717fadd346160e46938a0df1ef76b2e7eb2729f57","source":{"kind":"arxiv","id":"1612.04642","version":2},"attestation_state":"computed","paper":{"title":"Harmonic Networks: Deep Translation and Rotation Equivariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.CV","authors_text":"Daniel E. Worrall, Daniyar Turmukhambetov, Gabriel J. Brostow, Stephan J. Garbin","submitted_at":"2016-12-14T14:01:11Z","abstract_excerpt":"Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typically sought through data augmentation, but patch-wise equivariance is more difficult. We present Harmonic Networks or H-Nets, a CNN exhibiting equivariance to patch-wise translation and 360-rotation. We achieve this by replacing regular CNN filters with circular harmonics, return"},"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":"1612.04642","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-12-14T14:01:11Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"3e7c6d45864274f1cfbca861e43845ada791b19a74673f0943f62c362f5f01ea","abstract_canon_sha256":"b0a551bee54aa4f0507d791f05795c64d1f8f709a94fa66d2c16e9c9913e8093"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:38.500611Z","signature_b64":"TCOnTx1jk9TMU8k+lsd9xM1DAc/hCqYAOEPntSx96rdC7Y45B8tXVgGOqBRyA8w2B2o6LTJrDC/IyXqx7/QvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e49a01d2ef9015604c2d240717fadd346160e46938a0df1ef76b2e7eb2729f57","last_reissued_at":"2026-05-18T00:46:38.499790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:38.499790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Harmonic Networks: Deep Translation and Rotation Equivariance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.CV","authors_text":"Daniel E. Worrall, Daniyar Turmukhambetov, Gabriel J. Brostow, Stephan J. Garbin","submitted_at":"2016-12-14T14:01:11Z","abstract_excerpt":"Translating or rotating an input image should not affect the results of many computer vision tasks. Convolutional neural networks (CNNs) are already translation equivariant: input image translations produce proportionate feature map translations. This is not the case for rotations. Global rotation equivariance is typically sought through data augmentation, but patch-wise equivariance is more difficult. We present Harmonic Networks or H-Nets, a CNN exhibiting equivariance to patch-wise translation and 360-rotation. We achieve this by replacing regular CNN filters with circular harmonics, return"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04642","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.04642","created_at":"2026-05-18T00:46:38.499922+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.04642v2","created_at":"2026-05-18T00:46:38.499922+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04642","created_at":"2026-05-18T00:46:38.499922+00:00"},{"alias_kind":"pith_short_12","alias_value":"4SNADUXPSAKW","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4SNADUXPSAKWATBN","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4SNADUXP","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.08435","citing_title":"Interaction-and-Aggregation Network for Person Re-identification","ref_index":52,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4SNADUXPSAKWATBNEQDRP6W5GR","json":"https://pith.science/pith/4SNADUXPSAKWATBNEQDRP6W5GR.json","graph_json":"https://pith.science/api/pith-number/4SNADUXPSAKWATBNEQDRP6W5GR/graph.json","events_json":"https://pith.science/api/pith-number/4SNADUXPSAKWATBNEQDRP6W5GR/events.json","paper":"https://pith.science/paper/4SNADUXP"},"agent_actions":{"view_html":"https://pith.science/pith/4SNADUXPSAKWATBNEQDRP6W5GR","download_json":"https://pith.science/pith/4SNADUXPSAKWATBNEQDRP6W5GR.json","view_paper":"https://pith.science/paper/4SNADUXP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.04642&json=true","fetch_graph":"https://pith.science/api/pith-number/4SNADUXPSAKWATBNEQDRP6W5GR/graph.json","fetch_events":"https://pith.science/api/pith-number/4SNADUXPSAKWATBNEQDRP6W5GR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4SNADUXPSAKWATBNEQDRP6W5GR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4SNADUXPSAKWATBNEQDRP6W5GR/action/storage_attestation","attest_author":"https://pith.science/pith/4SNADUXPSAKWATBNEQDRP6W5GR/action/author_attestation","sign_citation":"https://pith.science/pith/4SNADUXPSAKWATBNEQDRP6W5GR/action/citation_signature","submit_replication":"https://pith.science/pith/4SNADUXPSAKWATBNEQDRP6W5GR/action/replication_record"}},"created_at":"2026-05-18T00:46:38.499922+00:00","updated_at":"2026-05-18T00:46:38.499922+00:00"}