{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:S5K2EEPXYSZKF3MWRRPUJSGL4P","short_pith_number":"pith:S5K2EEPX","schema_version":"1.0","canonical_sha256":"9755a211f7c4b2a2ed968c5f44c8cbe3fae37ddcb3e98773e0320b09d695180b","source":{"kind":"arxiv","id":"2607.20552","version":1},"attestation_state":"computed","paper":{"title":"Thermodynamic Weight Decay: Exploring Grokking Acceleration via Attention Specific Heat","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Chitraansh Pandey","submitted_at":"2026-07-15T09:25:17Z","abstract_excerpt":"Grokking -- the delayed generalization of neural networks long after they have memorized their training data -- wastes thousands of training epochs and is notoriously unpredictable. Building on the recent result that Transformer attention is formally isomorphic to a thermodynamic system, we treat the variance of attention logits as a specific heat Cv and show that its peak reliably precedes the generalization transition. We introduce CvAdamW, a drop-in AdamW variant that monitors Cv online and injects thermal energy by dynamically scaling weight decay when a phase transition is detected. Throu"},"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":"2607.20552","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-15T09:25:17Z","cross_cats_sorted":[],"title_canon_sha256":"161c9a6816bb3c28bb4416a7858f0a3159c942583941be7b03ab9bc0f2844a4c","abstract_canon_sha256":"5c746ac272aec0421772baa28fd09abc9d657e739c66e773e7437b6a364ad332"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T00:23:22.206331Z","signature_b64":"0hoXP+ihdcOzytCPRgUajWg8zzrM2Z27sgoKEF4z5/eRhCZkhktv3BzhjkyBCO3/ELHBKlSaRXW5U6cOrh/QBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9755a211f7c4b2a2ed968c5f44c8cbe3fae37ddcb3e98773e0320b09d695180b","last_reissued_at":"2026-07-24T00:23:22.205412Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T00:23:22.205412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Thermodynamic Weight Decay: Exploring Grokking Acceleration via Attention Specific Heat","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Chitraansh Pandey","submitted_at":"2026-07-15T09:25:17Z","abstract_excerpt":"Grokking -- the delayed generalization of neural networks long after they have memorized their training data -- wastes thousands of training epochs and is notoriously unpredictable. Building on the recent result that Transformer attention is formally isomorphic to a thermodynamic system, we treat the variance of attention logits as a specific heat Cv and show that its peak reliably precedes the generalization transition. We introduce CvAdamW, a drop-in AdamW variant that monitors Cv online and injects thermal energy by dynamically scaling weight decay when a phase transition is detected. Throu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20552","kind":"arxiv","version":1},"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/2607.20552/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.20552","created_at":"2026-07-24T00:23:22.205864+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.20552v1","created_at":"2026-07-24T00:23:22.205864+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20552","created_at":"2026-07-24T00:23:22.205864+00:00"},{"alias_kind":"pith_short_12","alias_value":"S5K2EEPXYSZK","created_at":"2026-07-24T00:23:22.205864+00:00"},{"alias_kind":"pith_short_16","alias_value":"S5K2EEPXYSZKF3MW","created_at":"2026-07-24T00:23:22.205864+00:00"},{"alias_kind":"pith_short_8","alias_value":"S5K2EEPX","created_at":"2026-07-24T00:23:22.205864+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S5K2EEPXYSZKF3MWRRPUJSGL4P","json":"https://pith.science/pith/S5K2EEPXYSZKF3MWRRPUJSGL4P.json","graph_json":"https://pith.science/api/pith-number/S5K2EEPXYSZKF3MWRRPUJSGL4P/graph.json","events_json":"https://pith.science/api/pith-number/S5K2EEPXYSZKF3MWRRPUJSGL4P/events.json","paper":"https://pith.science/paper/S5K2EEPX"},"agent_actions":{"view_html":"https://pith.science/pith/S5K2EEPXYSZKF3MWRRPUJSGL4P","download_json":"https://pith.science/pith/S5K2EEPXYSZKF3MWRRPUJSGL4P.json","view_paper":"https://pith.science/paper/S5K2EEPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.20552&json=true","fetch_graph":"https://pith.science/api/pith-number/S5K2EEPXYSZKF3MWRRPUJSGL4P/graph.json","fetch_events":"https://pith.science/api/pith-number/S5K2EEPXYSZKF3MWRRPUJSGL4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S5K2EEPXYSZKF3MWRRPUJSGL4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S5K2EEPXYSZKF3MWRRPUJSGL4P/action/storage_attestation","attest_author":"https://pith.science/pith/S5K2EEPXYSZKF3MWRRPUJSGL4P/action/author_attestation","sign_citation":"https://pith.science/pith/S5K2EEPXYSZKF3MWRRPUJSGL4P/action/citation_signature","submit_replication":"https://pith.science/pith/S5K2EEPXYSZKF3MWRRPUJSGL4P/action/replication_record"}},"created_at":"2026-07-24T00:23:22.205864+00:00","updated_at":"2026-07-24T00:23:22.205864+00:00"}