{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:6VVXL2XWBWB7SAAC4LW5O62VDX","short_pith_number":"pith:6VVXL2XW","canonical_record":{"source":{"id":"2312.09016","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-14T15:06:48Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3d3e86161b0681911444621788bbcb46f1381f10886f4dde42ece52fb8c9faca","abstract_canon_sha256":"7a027f675f48156e071d63ff3cce5ebff7ffd21022ff97dab5b92e598deeb964"},"schema_version":"1.0"},"canonical_sha256":"f56b75eaf60d83f90002e2edd77b551df8034cc58a8c2b7f9c1de469d3354b96","source":{"kind":"arxiv","id":"2312.09016","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.09016","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"arxiv_version","alias_value":"2312.09016v2","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.09016","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"pith_short_12","alias_value":"6VVXL2XWBWB7","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"pith_short_16","alias_value":"6VVXL2XWBWB7SAAC","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"pith_short_8","alias_value":"6VVXL2XW","created_at":"2026-07-05T07:59:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:6VVXL2XWBWB7SAAC4LW5O62VDX","target":"record","payload":{"canonical_record":{"source":{"id":"2312.09016","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-14T15:06:48Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"3d3e86161b0681911444621788bbcb46f1381f10886f4dde42ece52fb8c9faca","abstract_canon_sha256":"7a027f675f48156e071d63ff3cce5ebff7ffd21022ff97dab5b92e598deeb964"},"schema_version":"1.0"},"canonical_sha256":"f56b75eaf60d83f90002e2edd77b551df8034cc58a8c2b7f9c1de469d3354b96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:59:20.380249Z","signature_b64":"plXvnwnI/9S/xrRbFHY0FPdTF7uKCn+/pqJ4ufD79N10F8F327E6+Z8y48ZT+MnOgiTIlKwiL68R+op0a1f+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f56b75eaf60d83f90002e2edd77b551df8034cc58a8c2b7f9c1de469d3354b96","last_reissued_at":"2026-07-05T07:59:20.379829Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:59:20.379829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.09016","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":"2026-07-05T07:59:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kcJYxqoGKOpVRF6dGSrl7emYHiXXzTreqjAfCxNKUkYY+2hdBLb81UNU/0Ozgxg0c7w6uAaeCrKuQ+XcfVKeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:29:27.810023Z"},"content_sha256":"b84c793220d033ee7bc9ce65304fd3e5cd01855250a635f4c543e1889192aa05","schema_version":"1.0","event_id":"sha256:b84c793220d033ee7bc9ce65304fd3e5cd01855250a635f4c543e1889192aa05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:6VVXL2XWBWB7SAAC4LW5O62VDX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry Breaking and Equivariant Neural Networks","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"S\\'ekou-Oumar Kaba, Siamak Ravanbakhsh","submitted_at":"2023-12-14T15:06:48Z","abstract_excerpt":"Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not always obvious. Here, we analyze a key limitation that arises in equivariant functions: their incapacity to break symmetry at the level of individual data samples. In response, we introduce a novel notion of 'relaxed equivariance' that circumvents this limitation. We further demonstrate how to incorporate this relaxation into equivariant multilayer perceptrons "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.09016","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.09016/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":"2026-07-05T07:59:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xpUpb3cxmsxk8a3YHV9vrrRNgaRfeYV+fjwt3JP1dVsOUWctEwDrrAKuANHicUSHs+NV+jLJ5rqLP8cltTGVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T16:29:27.810541Z"},"content_sha256":"ac780203b21c8f158df92238be1d2d7fee36852d093d7f957977f1b24a34fd56","schema_version":"1.0","event_id":"sha256:ac780203b21c8f158df92238be1d2d7fee36852d093d7f957977f1b24a34fd56"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6VVXL2XWBWB7SAAC4LW5O62VDX/bundle.json","state_url":"https://pith.science/pith/6VVXL2XWBWB7SAAC4LW5O62VDX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6VVXL2XWBWB7SAAC4LW5O62VDX/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":"2026-08-11T16:29:27Z","links":{"resolver":"https://pith.science/pith/6VVXL2XWBWB7SAAC4LW5O62VDX","bundle":"https://pith.science/pith/6VVXL2XWBWB7SAAC4LW5O62VDX/bundle.json","state":"https://pith.science/pith/6VVXL2XWBWB7SAAC4LW5O62VDX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6VVXL2XWBWB7SAAC4LW5O62VDX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:6VVXL2XWBWB7SAAC4LW5O62VDX","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":"7a027f675f48156e071d63ff3cce5ebff7ffd21022ff97dab5b92e598deeb964","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-14T15:06:48Z","title_canon_sha256":"3d3e86161b0681911444621788bbcb46f1381f10886f4dde42ece52fb8c9faca"},"schema_version":"1.0","source":{"id":"2312.09016","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.09016","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"arxiv_version","alias_value":"2312.09016v2","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.09016","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"pith_short_12","alias_value":"6VVXL2XWBWB7","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"pith_short_16","alias_value":"6VVXL2XWBWB7SAAC","created_at":"2026-07-05T07:59:20Z"},{"alias_kind":"pith_short_8","alias_value":"6VVXL2XW","created_at":"2026-07-05T07:59:20Z"}],"graph_snapshots":[{"event_id":"sha256:ac780203b21c8f158df92238be1d2d7fee36852d093d7f957977f1b24a34fd56","target":"graph","created_at":"2026-07-05T07:59:20Z","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/2312.09016/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not always obvious. Here, we analyze a key limitation that arises in equivariant functions: their incapacity to break symmetry at the level of individual data samples. In response, we introduce a novel notion of 'relaxed equivariance' that circumvents this limitation. We further demonstrate how to incorporate this relaxation into equivariant multilayer perceptrons ","authors_text":"S\\'ekou-Oumar Kaba, Siamak Ravanbakhsh","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-14T15:06:48Z","title":"Symmetry Breaking and Equivariant Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.09016","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:b84c793220d033ee7bc9ce65304fd3e5cd01855250a635f4c543e1889192aa05","target":"record","created_at":"2026-07-05T07:59:20Z","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":"7a027f675f48156e071d63ff3cce5ebff7ffd21022ff97dab5b92e598deeb964","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2023-12-14T15:06:48Z","title_canon_sha256":"3d3e86161b0681911444621788bbcb46f1381f10886f4dde42ece52fb8c9faca"},"schema_version":"1.0","source":{"id":"2312.09016","kind":"arxiv","version":2}},"canonical_sha256":"f56b75eaf60d83f90002e2edd77b551df8034cc58a8c2b7f9c1de469d3354b96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f56b75eaf60d83f90002e2edd77b551df8034cc58a8c2b7f9c1de469d3354b96","first_computed_at":"2026-07-05T07:59:20.379829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:59:20.379829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"plXvnwnI/9S/xrRbFHY0FPdTF7uKCn+/pqJ4ufD79N10F8F327E6+Z8y48ZT+MnOgiTIlKwiL68R+op0a1f+Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:59:20.380249Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.09016","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b84c793220d033ee7bc9ce65304fd3e5cd01855250a635f4c543e1889192aa05","sha256:ac780203b21c8f158df92238be1d2d7fee36852d093d7f957977f1b24a34fd56"],"state_sha256":"2e97f4093d3c227cdaf4845c43f51c87794d3f7a34e0b0a4b892434635fc02af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w576SrkRrg5UqaWaidp+UKDoawVjHh/3tTt/fp0ejXokzkA7dkkCk5eFu/xu2FfjM6sEduB7JrPjyZoZJSM3AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T16:29:27.814999Z","bundle_sha256":"bd7187f530b5adead6d33d89a3e26f01c3cdaafd12a7ac8942f87ee83b0ca763"}}