{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:S5TQOGLC3ULSFQC3TQZUG4PMUL","short_pith_number":"pith:S5TQOGLC","canonical_record":{"source":{"id":"2510.04930","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-06T15:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"e204f76e7a292198071e2fb1b479687d884cbe25b5cef3c8a58e12e06f4e3c56","abstract_canon_sha256":"a2ae3b492f024cdedf6cdf784671bce35cb2af8e31d44fa27e2e449c9178603c"},"schema_version":"1.0"},"canonical_sha256":"9767071962dd1722c05b9c334371eca2d9b98c29f4aad1365fb8c15dc5ea7bdf","source":{"kind":"arxiv","id":"2510.04930","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.04930","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"2510.04930v3","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.04930","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"S5TQOGLC3ULS","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"pith_short_16","alias_value":"S5TQOGLC3ULSFQC3","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"pith_short_8","alias_value":"S5TQOGLC","created_at":"2026-05-20T00:05:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:S5TQOGLC3ULSFQC3TQZUG4PMUL","target":"record","payload":{"canonical_record":{"source":{"id":"2510.04930","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-06T15:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"e204f76e7a292198071e2fb1b479687d884cbe25b5cef3c8a58e12e06f4e3c56","abstract_canon_sha256":"a2ae3b492f024cdedf6cdf784671bce35cb2af8e31d44fa27e2e449c9178603c"},"schema_version":"1.0"},"canonical_sha256":"9767071962dd1722c05b9c334371eca2d9b98c29f4aad1365fb8c15dc5ea7bdf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:34.339502Z","signature_b64":"Yp5gbG8/N0AHBZjtmkCY5wX0qaaO/wFNkDnfhX/gG6RWEAKHn3Ao2YFJHkIXEzRVhd+tI26RtpkffW9p9tJrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9767071962dd1722c05b9c334371eca2d9b98c29f4aad1365fb8c15dc5ea7bdf","last_reissued_at":"2026-05-20T00:05:34.338835Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:34.338835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2510.04930","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pBvMiyJeVTCfzP/PTg9V/DijTLJL8zpHuMtPas+5DHCV0Xd3AG0utyOJ1PonyMEK0HBFC6hwY4Wdn2bcoeYQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:15:27.980893Z"},"content_sha256":"6ae62a15073a3183ba16454c510482d9b3dd9f3e739a3f20ae6cc7c9ddf60d2c","schema_version":"1.0","event_id":"sha256:6ae62a15073a3183ba16454c510482d9b3dd9f3e739a3f20ae6cc7c9ddf60d2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:S5TQOGLC3ULSFQC3TQZUG4PMUL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ali Saheb Pasand, Elvis Dohmatob","submitted_at":"2025-10-06T15:40:36Z","abstract_excerpt":"Grokking is the phenomenon whereby, unlike the training performance, which peaks early in the training process, the test/generalization performance of a model stagnates over arbitrarily many epochs and then suddenly jumps to usually close to perfect levels. In practice, it is desirable to reduce the length of such plateaus, that is to make the learning process \"grok\" faster. In this work, we provide new insights into grokking. First, we show both empirically and theoretically that grokking can be induced by asymmetric speeds of (stochastic) gradient descent, along different principal (i.e sing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.04930","kind":"arxiv","version":3},"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/2510.04930/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":"2026-05-20T00:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGKy1iIOFEyK0QVT7ThXnOEMJH6HmFKBSRJQ3Blm9I+oxLmic8ckAasqeQzCrpiweU0bMbOunGv4F3mVtnKYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:15:27.981563Z"},"content_sha256":"f9300f4a388170d2a080c078aa18a4ef20820463257cf7440bad2d05bcddaa9c","schema_version":"1.0","event_id":"sha256:f9300f4a388170d2a080c078aa18a4ef20820463257cf7440bad2d05bcddaa9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5TQOGLC3ULSFQC3TQZUG4PMUL/bundle.json","state_url":"https://pith.science/pith/S5TQOGLC3ULSFQC3TQZUG4PMUL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5TQOGLC3ULSFQC3TQZUG4PMUL/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":"2026-05-25T18:15:27Z","links":{"resolver":"https://pith.science/pith/S5TQOGLC3ULSFQC3TQZUG4PMUL","bundle":"https://pith.science/pith/S5TQOGLC3ULSFQC3TQZUG4PMUL/bundle.json","state":"https://pith.science/pith/S5TQOGLC3ULSFQC3TQZUG4PMUL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5TQOGLC3ULSFQC3TQZUG4PMUL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:S5TQOGLC3ULSFQC3TQZUG4PMUL","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":"a2ae3b492f024cdedf6cdf784671bce35cb2af8e31d44fa27e2e449c9178603c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-06T15:40:36Z","title_canon_sha256":"e204f76e7a292198071e2fb1b479687d884cbe25b5cef3c8a58e12e06f4e3c56"},"schema_version":"1.0","source":{"id":"2510.04930","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.04930","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"2510.04930v3","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.04930","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"S5TQOGLC3ULS","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"pith_short_16","alias_value":"S5TQOGLC3ULSFQC3","created_at":"2026-05-20T00:05:34Z"},{"alias_kind":"pith_short_8","alias_value":"S5TQOGLC","created_at":"2026-05-20T00:05:34Z"}],"graph_snapshots":[{"event_id":"sha256:f9300f4a388170d2a080c078aa18a4ef20820463257cf7440bad2d05bcddaa9c","target":"graph","created_at":"2026-05-20T00:05:34Z","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/2510.04930/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Grokking is the phenomenon whereby, unlike the training performance, which peaks early in the training process, the test/generalization performance of a model stagnates over arbitrarily many epochs and then suddenly jumps to usually close to perfect levels. In practice, it is desirable to reduce the length of such plateaus, that is to make the learning process \"grok\" faster. In this work, we provide new insights into grokking. First, we show both empirically and theoretically that grokking can be induced by asymmetric speeds of (stochastic) gradient descent, along different principal (i.e sing","authors_text":"Ali Saheb Pasand, Elvis Dohmatob","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-06T15:40:36Z","title":"Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.04930","kind":"arxiv","version":3},"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":"sha256:6ae62a15073a3183ba16454c510482d9b3dd9f3e739a3f20ae6cc7c9ddf60d2c","target":"record","created_at":"2026-05-20T00:05:34Z","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":"a2ae3b492f024cdedf6cdf784671bce35cb2af8e31d44fa27e2e449c9178603c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-10-06T15:40:36Z","title_canon_sha256":"e204f76e7a292198071e2fb1b479687d884cbe25b5cef3c8a58e12e06f4e3c56"},"schema_version":"1.0","source":{"id":"2510.04930","kind":"arxiv","version":3}},"canonical_sha256":"9767071962dd1722c05b9c334371eca2d9b98c29f4aad1365fb8c15dc5ea7bdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9767071962dd1722c05b9c334371eca2d9b98c29f4aad1365fb8c15dc5ea7bdf","first_computed_at":"2026-05-20T00:05:34.338835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:34.338835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yp5gbG8/N0AHBZjtmkCY5wX0qaaO/wFNkDnfhX/gG6RWEAKHn3Ao2YFJHkIXEzRVhd+tI26RtpkffW9p9tJrCw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:34.339502Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.04930","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ae62a15073a3183ba16454c510482d9b3dd9f3e739a3f20ae6cc7c9ddf60d2c","sha256:f9300f4a388170d2a080c078aa18a4ef20820463257cf7440bad2d05bcddaa9c"],"state_sha256":"bde03aa8cfcc630ffad0ece4520700c47317931c6ba1d69bd8a339ec61bf8b1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bsuYAnKJKD8lUfw2RckprlywSgEWYLRkaou2diz2WOCwYTullFGfzsIVOgjjFwFwdVFJcK6BrrLbNhAQuGeKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:15:27.984986Z","bundle_sha256":"d36f1b15f5ec3f007a51473372b1219d53dda960f5413f993f052240d282a6f5"}}