{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:65EOGNL3BLPOAS5YIZ3FNOCD5Z","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":"5ec0f876cdaf69a00de0836d3ea74b450b9a343a7fc97b434279a00014f414cc","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T19:48:40Z","title_canon_sha256":"6d73f9e65f232e1649471da5beb35c8702fb877fee7cc49187b42ad8264556e3"},"schema_version":"1.0","source":{"id":"2605.20441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20441","created_at":"2026-05-21T01:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20441v1","created_at":"2026-05-21T01:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20441","created_at":"2026-05-21T01:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"65EOGNL3BLPO","created_at":"2026-05-21T01:04:38Z"},{"alias_kind":"pith_short_16","alias_value":"65EOGNL3BLPOAS5Y","created_at":"2026-05-21T01:04:38Z"},{"alias_kind":"pith_short_8","alias_value":"65EOGNL3","created_at":"2026-05-21T01:04:38Z"}],"graph_snapshots":[{"event_id":"sha256:bd316ee83e958ba1b815a72824ed5cdd83e8fd6da1337dd9baf9550a85960a95","target":"graph","created_at":"2026-05-21T01:04:38Z","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/2605.20441/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Transformers trained on modular arithmetic exhibit sharp transitions between memorization, generalization, and collapse. We show that weight decay acts as a scalar empirical control parameter for these regimes, and introduce two cheap online diagnostics, mean pairwise attention-head cosine similarity and entropy standard deviation, that track training dynamics from attention activations alone and complement loss-landscape diagnostics at lower compute cost. Across eleven experimental conditions and three model scales (0.82M to 85M parameters), the weight-decay axis separates memorization, devel","authors_text":"Lucky Verma","cross_cats":["cs.AI","cs.NE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T19:48:40Z","title":"Weight Decay Regimes in Grokking Transformers: Cheap Online Diagnostics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20441","kind":"arxiv","version":1},"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:c999f5e821c42f815387350d84d421ec4abbde9607904f36488b8406361cd058","target":"record","created_at":"2026-05-21T01:04:38Z","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":"5ec0f876cdaf69a00de0836d3ea74b450b9a343a7fc97b434279a00014f414cc","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T19:48:40Z","title_canon_sha256":"6d73f9e65f232e1649471da5beb35c8702fb877fee7cc49187b42ad8264556e3"},"schema_version":"1.0","source":{"id":"2605.20441","kind":"arxiv","version":1}},"canonical_sha256":"f748e3357b0adee04bb8467656b843ee5858d712acee1983a334140e60130f2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f748e3357b0adee04bb8467656b843ee5858d712acee1983a334140e60130f2d","first_computed_at":"2026-05-21T01:04:38.150450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:38.150450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fdJ0wAGkqsbN0AHbpSqUOu6BZDmNt2ndUSOyB3F4OTAzbjeBhBWEdugelX4bV8I0puYyXqTMi7QmcYnVsGbICQ==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:38.151047Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c999f5e821c42f815387350d84d421ec4abbde9607904f36488b8406361cd058","sha256:bd316ee83e958ba1b815a72824ed5cdd83e8fd6da1337dd9baf9550a85960a95"],"state_sha256":"c87b1e1a40449dba867d0e0100152adbbac4ef6872cfeb128eb0a6ec13ab8a4f"}