{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:PROFCWZ5G7NFXPULEVL25WF4A5","short_pith_number":"pith:PROFCWZ5","canonical_record":{"source":{"id":"2201.02115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-01-06T15:57:31Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"title_canon_sha256":"8afca2f179e206b877ee0353f814527b5be66118ac47b0e1ab5220b9252f21a0","abstract_canon_sha256":"40a91451ecdb4d31b81b3dd47b549f26bef2603be21e27a16480fb4b1a722158"},"schema_version":"1.0"},"canonical_sha256":"7c5c515b3d37da5bbe8b2557aed8bc076624e61a145be24a234fe477afa4c802","source":{"kind":"arxiv","id":"2201.02115","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.02115","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"2201.02115v2","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.02115","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"PROFCWZ5G7NF","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"pith_short_16","alias_value":"PROFCWZ5G7NFXPUL","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"pith_short_8","alias_value":"PROFCWZ5","created_at":"2026-07-05T04:44:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:PROFCWZ5G7NFXPULEVL25WF4A5","target":"record","payload":{"canonical_record":{"source":{"id":"2201.02115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-01-06T15:57:31Z","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"title_canon_sha256":"8afca2f179e206b877ee0353f814527b5be66118ac47b0e1ab5220b9252f21a0","abstract_canon_sha256":"40a91451ecdb4d31b81b3dd47b549f26bef2603be21e27a16480fb4b1a722158"},"schema_version":"1.0"},"canonical_sha256":"7c5c515b3d37da5bbe8b2557aed8bc076624e61a145be24a234fe477afa4c802","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:44:29.060136Z","signature_b64":"+xVSs4EWIzMwhmU1r3sfieEx6BQ1mqUQA8TAAy6e2LUUhDxl32CPDBOOU5mGEQQcAjOyMpICnqEPeqi6EDH6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c5c515b3d37da5bbe8b2557aed8bc076624e61a145be24a234fe477afa4c802","last_reissued_at":"2026-07-05T04:44:29.059758Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:44:29.059758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.02115","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":"2026-07-05T04:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c1oyYTROniq06DWdsUfo3TqxnztL//bYDLv0owNUa5+4UpBBmuo5LSmwH0+//6uLV0MdZENI+z7U80EYazRTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T11:31:48.393300Z"},"content_sha256":"a37b2d7de572f157b1eb7a72ccfb3b018d30893363b950f76d0d49c6177b1d48","schema_version":"1.0","event_id":"sha256:a37b2d7de572f157b1eb7a72ccfb3b018d30893363b950f76d0d49c6177b1d48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:PROFCWZ5G7NFXPULEVL25WF4A5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The dynamics of representation learning in shallow, non-linear autoencoders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"primary_cat":"stat.ML","authors_text":"Maria Refinetti, Sebastian Goldt","submitted_at":"2022-01-06T15:57:31Z","abstract_excerpt":"Autoencoders are the simplest neural network for unsupervised learning, and thus an ideal framework for studying feature learning. While a detailed understanding of the dynamics of linear autoencoders has recently been obtained, the study of non-linear autoencoders has been hindered by the technical difficulty of handling training data with non-trivial correlations - a fundamental prerequisite for feature extraction. Here, we study the dynamics of feature learning in non-linear, shallow autoencoders. We derive a set of asymptotically exact equations that describe the generalisation dynamics of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.02115","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/2201.02115/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":"2026-07-05T04:44:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+60ZY6w7OBiEJD8gyaLOLnN/tE1qDdcN/HL2xL/hb8vdfPZc53wRuQJV1DI1Z/urcJ5ipVMKdin5TVgf+TcZCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T11:31:48.393703Z"},"content_sha256":"8522076dd8a9206de0e8bf508ec05e4a903adee3532f8df47c1debbe2d3f55c1","schema_version":"1.0","event_id":"sha256:8522076dd8a9206de0e8bf508ec05e4a903adee3532f8df47c1debbe2d3f55c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PROFCWZ5G7NFXPULEVL25WF4A5/bundle.json","state_url":"https://pith.science/pith/PROFCWZ5G7NFXPULEVL25WF4A5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PROFCWZ5G7NFXPULEVL25WF4A5/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":"2026-07-26T11:31:48Z","links":{"resolver":"https://pith.science/pith/PROFCWZ5G7NFXPULEVL25WF4A5","bundle":"https://pith.science/pith/PROFCWZ5G7NFXPULEVL25WF4A5/bundle.json","state":"https://pith.science/pith/PROFCWZ5G7NFXPULEVL25WF4A5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PROFCWZ5G7NFXPULEVL25WF4A5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:PROFCWZ5G7NFXPULEVL25WF4A5","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":"40a91451ecdb4d31b81b3dd47b549f26bef2603be21e27a16480fb4b1a722158","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-01-06T15:57:31Z","title_canon_sha256":"8afca2f179e206b877ee0353f814527b5be66118ac47b0e1ab5220b9252f21a0"},"schema_version":"1.0","source":{"id":"2201.02115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.02115","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"arxiv_version","alias_value":"2201.02115v2","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.02115","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"pith_short_12","alias_value":"PROFCWZ5G7NF","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"pith_short_16","alias_value":"PROFCWZ5G7NFXPUL","created_at":"2026-07-05T04:44:29Z"},{"alias_kind":"pith_short_8","alias_value":"PROFCWZ5","created_at":"2026-07-05T04:44:29Z"}],"graph_snapshots":[{"event_id":"sha256:8522076dd8a9206de0e8bf508ec05e4a903adee3532f8df47c1debbe2d3f55c1","target":"graph","created_at":"2026-07-05T04:44:29Z","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/2201.02115/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Autoencoders are the simplest neural network for unsupervised learning, and thus an ideal framework for studying feature learning. While a detailed understanding of the dynamics of linear autoencoders has recently been obtained, the study of non-linear autoencoders has been hindered by the technical difficulty of handling training data with non-trivial correlations - a fundamental prerequisite for feature extraction. Here, we study the dynamics of feature learning in non-linear, shallow autoencoders. We derive a set of asymptotically exact equations that describe the generalisation dynamics of","authors_text":"Maria Refinetti, Sebastian Goldt","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-01-06T15:57:31Z","title":"The dynamics of representation learning in shallow, non-linear autoencoders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.02115","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:a37b2d7de572f157b1eb7a72ccfb3b018d30893363b950f76d0d49c6177b1d48","target":"record","created_at":"2026-07-05T04:44:29Z","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":"40a91451ecdb4d31b81b3dd47b549f26bef2603be21e27a16480fb4b1a722158","cross_cats_sorted":["cond-mat.dis-nn","cond-mat.stat-mech","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2022-01-06T15:57:31Z","title_canon_sha256":"8afca2f179e206b877ee0353f814527b5be66118ac47b0e1ab5220b9252f21a0"},"schema_version":"1.0","source":{"id":"2201.02115","kind":"arxiv","version":2}},"canonical_sha256":"7c5c515b3d37da5bbe8b2557aed8bc076624e61a145be24a234fe477afa4c802","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c5c515b3d37da5bbe8b2557aed8bc076624e61a145be24a234fe477afa4c802","first_computed_at":"2026-07-05T04:44:29.059758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:44:29.059758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+xVSs4EWIzMwhmU1r3sfieEx6BQ1mqUQA8TAAy6e2LUUhDxl32CPDBOOU5mGEQQcAjOyMpICnqEPeqi6EDH6Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:44:29.060136Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.02115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a37b2d7de572f157b1eb7a72ccfb3b018d30893363b950f76d0d49c6177b1d48","sha256:8522076dd8a9206de0e8bf508ec05e4a903adee3532f8df47c1debbe2d3f55c1"],"state_sha256":"c58b4bc39ba40de55d5f6b05d4367c9eee3a0addd5b0209f4e5c772a6a23fe2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fE9JfeOO40IkcOt6vLWM3yWyAV5/EhQ3Rs9/omCcE1UM1OgxvfFCY5CXsBF8M7zsznl7/Pjs/jsc00K/uSu0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-26T11:31:48.396308Z","bundle_sha256":"dd8181351f6ace6fcdc9069444b1904836cae3c8fe80d2a4a98f3cb0f2bf4819"}}