{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:LL6CSBDLGGX7ELCPO4Q5DY3X3H","short_pith_number":"pith:LL6CSBDL","canonical_record":{"source":{"id":"2305.17332","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-05-27T02:27:27Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"title_canon_sha256":"8f8bb7fd759e241de170feea9a55c8d08c3e38616d1ada7fd47a07c0bd725345","abstract_canon_sha256":"5804ed4249d4a8675d7a0a2165b5c5a3c22320843716c22bec20043d26b78862"},"schema_version":"1.0"},"canonical_sha256":"5afc29046b31aff22c4f7721d1e377d9f73a4616dd2836a229f20ca51f4604ff","source":{"kind":"arxiv","id":"2305.17332","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.17332","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"arxiv_version","alias_value":"2305.17332v2","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.17332","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_12","alias_value":"LL6CSBDLGGX7","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_16","alias_value":"LL6CSBDLGGX7ELCP","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_8","alias_value":"LL6CSBDL","created_at":"2026-07-05T09:22:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:LL6CSBDLGGX7ELCPO4Q5DY3X3H","target":"record","payload":{"canonical_record":{"source":{"id":"2305.17332","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-05-27T02:27:27Z","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"title_canon_sha256":"8f8bb7fd759e241de170feea9a55c8d08c3e38616d1ada7fd47a07c0bd725345","abstract_canon_sha256":"5804ed4249d4a8675d7a0a2165b5c5a3c22320843716c22bec20043d26b78862"},"schema_version":"1.0"},"canonical_sha256":"5afc29046b31aff22c4f7721d1e377d9f73a4616dd2836a229f20ca51f4604ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:22:59.372936Z","signature_b64":"mJemIc5aV0Y5v7KHAfpWtfOjBsAOaS/w7Ew/CNLVY64fw1nil2k7NQei7utOm5+7sYC73IFO7p23oEPIbNSwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5afc29046b31aff22c4f7721d1e377d9f73a4616dd2836a229f20ca51f4604ff","last_reissued_at":"2026-07-05T09:22:59.372440Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:22:59.372440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.17332","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":"2026-07-05T09:22:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gf35V4KhtNBAYZD5Iwn8FiMg9o7hF1b9IUexFGPvTJLi+1Nl5Fg/TC3KQVidsvj33KZzFafgev1jV+v3+TsKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:01:04.965298Z"},"content_sha256":"ffea3e6267f08c5c0061f601db659bc7b27a876eddaad5aa5c924a603e693f8e","schema_version":"1.0","event_id":"sha256:ffea3e6267f08c5c0061f601db659bc7b27a876eddaad5aa5c924a603e693f8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:LL6CSBDLGGX7ELCPO4Q5DY3X3H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Capacity: A Measure of the Effective Dimensionality of a Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML"],"primary_cat":"cs.LG","authors_text":"Daiwei Chen, Pratik Chaudhari, Wei-Kai Chang","submitted_at":"2023-05-27T02:27:27Z","abstract_excerpt":"We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective dimensionality of a model. We show that the learning capacity is a useful notion of the complexity because (a) it correlates well with the test loss and it is a tiny fraction of the number of parameters for many deep networks trained on typical datasets, (b) it depends upon the number of samples used for training, (c) it is numerically consistent with notions of capacit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.17332","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/2305.17332/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":"2026-07-05T09:22:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GHsgMDqz+CiFSKhC5dxxu16OMKZhY2Tv2Ad6FlvNvzrISl96UiZsKz8EFxEZVcpOnYzcPFl+Cz83q8A7P+PJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T05:01:04.966156Z"},"content_sha256":"dac11e6b61b777f629a13417eb12985fd839533585184ed9ed3271d6938848d2","schema_version":"1.0","event_id":"sha256:dac11e6b61b777f629a13417eb12985fd839533585184ed9ed3271d6938848d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LL6CSBDLGGX7ELCPO4Q5DY3X3H/bundle.json","state_url":"https://pith.science/pith/LL6CSBDLGGX7ELCPO4Q5DY3X3H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LL6CSBDLGGX7ELCPO4Q5DY3X3H/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":"2026-08-07T05:01:04Z","links":{"resolver":"https://pith.science/pith/LL6CSBDLGGX7ELCPO4Q5DY3X3H","bundle":"https://pith.science/pith/LL6CSBDLGGX7ELCPO4Q5DY3X3H/bundle.json","state":"https://pith.science/pith/LL6CSBDLGGX7ELCPO4Q5DY3X3H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LL6CSBDLGGX7ELCPO4Q5DY3X3H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LL6CSBDLGGX7ELCPO4Q5DY3X3H","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":"5804ed4249d4a8675d7a0a2165b5c5a3c22320843716c22bec20043d26b78862","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-05-27T02:27:27Z","title_canon_sha256":"8f8bb7fd759e241de170feea9a55c8d08c3e38616d1ada7fd47a07c0bd725345"},"schema_version":"1.0","source":{"id":"2305.17332","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.17332","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"arxiv_version","alias_value":"2305.17332v2","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.17332","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_12","alias_value":"LL6CSBDLGGX7","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_16","alias_value":"LL6CSBDLGGX7ELCP","created_at":"2026-07-05T09:22:59Z"},{"alias_kind":"pith_short_8","alias_value":"LL6CSBDL","created_at":"2026-07-05T09:22:59Z"}],"graph_snapshots":[{"event_id":"sha256:dac11e6b61b777f629a13417eb12985fd839533585184ed9ed3271d6938848d2","target":"graph","created_at":"2026-07-05T09:22:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.17332/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective dimensionality of a model. We show that the learning capacity is a useful notion of the complexity because (a) it correlates well with the test loss and it is a tiny fraction of the number of parameters for many deep networks trained on typical datasets, (b) it depends upon the number of samples used for training, (c) it is numerically consistent with notions of capacit","authors_text":"Daiwei Chen, Pratik Chaudhari, Wei-Kai Chang","cross_cats":["cs.IT","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-05-27T02:27:27Z","title":"Learning Capacity: A Measure of the Effective Dimensionality of a Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.17332","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:ffea3e6267f08c5c0061f601db659bc7b27a876eddaad5aa5c924a603e693f8e","target":"record","created_at":"2026-07-05T09:22:59Z","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":"5804ed4249d4a8675d7a0a2165b5c5a3c22320843716c22bec20043d26b78862","cross_cats_sorted":["cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-05-27T02:27:27Z","title_canon_sha256":"8f8bb7fd759e241de170feea9a55c8d08c3e38616d1ada7fd47a07c0bd725345"},"schema_version":"1.0","source":{"id":"2305.17332","kind":"arxiv","version":2}},"canonical_sha256":"5afc29046b31aff22c4f7721d1e377d9f73a4616dd2836a229f20ca51f4604ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5afc29046b31aff22c4f7721d1e377d9f73a4616dd2836a229f20ca51f4604ff","first_computed_at":"2026-07-05T09:22:59.372440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:22:59.372440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mJemIc5aV0Y5v7KHAfpWtfOjBsAOaS/w7Ew/CNLVY64fw1nil2k7NQei7utOm5+7sYC73IFO7p23oEPIbNSwBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:22:59.372936Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.17332","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffea3e6267f08c5c0061f601db659bc7b27a876eddaad5aa5c924a603e693f8e","sha256:dac11e6b61b777f629a13417eb12985fd839533585184ed9ed3271d6938848d2"],"state_sha256":"6721175be542501549a26120431335efd79c69ac306d883a2b10eb1ed861c1f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cwi8fVHpPVTIqy7DMqsaZOoepsZcr30upM01Kn83Y5PlUIIxr2Cf291erh9n6YEdXU9BKz2+B+YFMw9FPQE0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T05:01:04.975169Z","bundle_sha256":"1f1e0ea42f6bc80e7d1dbfb33858621e9bdf8d590db5306bec64ca7601b7bedf"}}