{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Y4TP3YMSNROFUNPRF27EOR6MHZ","short_pith_number":"pith:Y4TP3YMS","canonical_record":{"source":{"id":"2606.01155","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T10:51:18Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"2166b1f712da4277478ec011fe55edd8b099f042278a0aec6c9b96c99cb0ed6b","abstract_canon_sha256":"0d25c3aef4ffc3fed1eecc02835d9766d69dd8e35cfa8540fa01eaf1e9b0fef3"},"schema_version":"1.0"},"canonical_sha256":"c726fde1926c5c5a35f12ebe4747cc3e6e2fea22ca9b743d916f586adbeeccc6","source":{"kind":"arxiv","id":"2606.01155","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01155","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01155v1","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01155","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"Y4TP3YMSNROF","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"Y4TP3YMSNROFUNPR","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"Y4TP3YMS","created_at":"2026-06-02T02:04:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Y4TP3YMSNROFUNPRF27EOR6MHZ","target":"record","payload":{"canonical_record":{"source":{"id":"2606.01155","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T10:51:18Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"2166b1f712da4277478ec011fe55edd8b099f042278a0aec6c9b96c99cb0ed6b","abstract_canon_sha256":"0d25c3aef4ffc3fed1eecc02835d9766d69dd8e35cfa8540fa01eaf1e9b0fef3"},"schema_version":"1.0"},"canonical_sha256":"c726fde1926c5c5a35f12ebe4747cc3e6e2fea22ca9b743d916f586adbeeccc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:25.253158Z","signature_b64":"BvYjldibs7BdoZcyaGtBnatfBkHmzirFHDKpCYZtOX6K5+x7A4PXhncbaxBGK48UOCvrsrVVxpdMNCBqFRhvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c726fde1926c5c5a35f12ebe4747cc3e6e2fea22ca9b743d916f586adbeeccc6","last_reissued_at":"2026-06-02T02:04:25.252719Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:25.252719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.01155","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T02:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcbL9RctVhXEXswsGFQpm0syZ1HfjlXo5yjy/VlrYJ1lwQLnsB7BWSnlB6Vmh5cY7HBVTGV9dIxQwfv0QhE6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:59:34.783025Z"},"content_sha256":"f08dfd0c235ec6b18c1101e9f2ce0c86d66d2d53a0923abf233693c3a399d746","schema_version":"1.0","event_id":"sha256:f08dfd0c235ec6b18c1101e9f2ce0c86d66d2d53a0923abf233693c3a399d746"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Y4TP3YMSNROFUNPRF27EOR6MHZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When Data Is Scarce: Scaling Sparse Language Models with Repeated Training","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Boqian Wu, Decebal Constantin Mocanu, Elena Mocanu, Maurice van Keulen, Mykola Pechenizkiy, Patrik Okanovic, Qiao Xiao, Tomasz Sternal, Torsten Hoefler","submitted_at":"2026-05-31T10:51:18Z","abstract_excerpt":"Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not. In this work, we study sparse training in data-constrained regimes where limited unique tokens require multi-epoch training. Our experiments span models up to 1.92B parameters in the fitting set, sparsity up to 93.75%, unique data budgets up to 2.6B tokens, and total training tokens up to 41.6B over 16 epochs; we further validate extrapolation on held-out dense-equivalent models up to 7.68B parameters. We find that: 1. Sparse scaling in data-limited settings: We introduce a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01155","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/2606.01155/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":"2026-06-02T02:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"10IWW32RaSTFsL+etU4O/UGrr5XvQxvahX9lmKR1NoY/kaCGpo0qBNDK/qQwvCUeLkrEHkgv3qWsMYyf6ksnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:59:34.783410Z"},"content_sha256":"d8d1861b233692dbbf41c2af7e19eae49d14bae89cf8ec0c47ffb615e4b4d278","schema_version":"1.0","event_id":"sha256:d8d1861b233692dbbf41c2af7e19eae49d14bae89cf8ec0c47ffb615e4b4d278"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y4TP3YMSNROFUNPRF27EOR6MHZ/bundle.json","state_url":"https://pith.science/pith/Y4TP3YMSNROFUNPRF27EOR6MHZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y4TP3YMSNROFUNPRF27EOR6MHZ/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":"2026-06-02T09:59:34Z","links":{"resolver":"https://pith.science/pith/Y4TP3YMSNROFUNPRF27EOR6MHZ","bundle":"https://pith.science/pith/Y4TP3YMSNROFUNPRF27EOR6MHZ/bundle.json","state":"https://pith.science/pith/Y4TP3YMSNROFUNPRF27EOR6MHZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y4TP3YMSNROFUNPRF27EOR6MHZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Y4TP3YMSNROFUNPRF27EOR6MHZ","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":"0d25c3aef4ffc3fed1eecc02835d9766d69dd8e35cfa8540fa01eaf1e9b0fef3","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T10:51:18Z","title_canon_sha256":"2166b1f712da4277478ec011fe55edd8b099f042278a0aec6c9b96c99cb0ed6b"},"schema_version":"1.0","source":{"id":"2606.01155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01155","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01155v1","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01155","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"Y4TP3YMSNROF","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"Y4TP3YMSNROFUNPR","created_at":"2026-06-02T02:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"Y4TP3YMS","created_at":"2026-06-02T02:04:25Z"}],"graph_snapshots":[{"event_id":"sha256:d8d1861b233692dbbf41c2af7e19eae49d14bae89cf8ec0c47ffb615e4b4d278","target":"graph","created_at":"2026-06-02T02:04:25Z","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/2606.01155/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not. In this work, we study sparse training in data-constrained regimes where limited unique tokens require multi-epoch training. Our experiments span models up to 1.92B parameters in the fitting set, sparsity up to 93.75%, unique data budgets up to 2.6B tokens, and total training tokens up to 41.6B over 16 epochs; we further validate extrapolation on held-out dense-equivalent models up to 7.68B parameters. We find that: 1. Sparse scaling in data-limited settings: We introduce a s","authors_text":"Boqian Wu, Decebal Constantin Mocanu, Elena Mocanu, Maurice van Keulen, Mykola Pechenizkiy, Patrik Okanovic, Qiao Xiao, Tomasz Sternal, Torsten Hoefler","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T10:51:18Z","title":"When Data Is Scarce: Scaling Sparse Language Models with Repeated Training"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01155","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:f08dfd0c235ec6b18c1101e9f2ce0c86d66d2d53a0923abf233693c3a399d746","target":"record","created_at":"2026-06-02T02:04:25Z","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":"0d25c3aef4ffc3fed1eecc02835d9766d69dd8e35cfa8540fa01eaf1e9b0fef3","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-31T10:51:18Z","title_canon_sha256":"2166b1f712da4277478ec011fe55edd8b099f042278a0aec6c9b96c99cb0ed6b"},"schema_version":"1.0","source":{"id":"2606.01155","kind":"arxiv","version":1}},"canonical_sha256":"c726fde1926c5c5a35f12ebe4747cc3e6e2fea22ca9b743d916f586adbeeccc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c726fde1926c5c5a35f12ebe4747cc3e6e2fea22ca9b743d916f586adbeeccc6","first_computed_at":"2026-06-02T02:04:25.252719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:25.252719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BvYjldibs7BdoZcyaGtBnatfBkHmzirFHDKpCYZtOX6K5+x7A4PXhncbaxBGK48UOCvrsrVVxpdMNCBqFRhvAQ==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:25.253158Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f08dfd0c235ec6b18c1101e9f2ce0c86d66d2d53a0923abf233693c3a399d746","sha256:d8d1861b233692dbbf41c2af7e19eae49d14bae89cf8ec0c47ffb615e4b4d278"],"state_sha256":"7a51e96baf67e8840effd6192d23e469320d2c8a9e3e3ebaca44c82a4ea6caaa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LQ+kzgONOE/JX8n5zonHe9JtO6xazmxb5h4CzWG8g352vs5EDL86CdyNUki/ga/c7gca1o61KGqytZzO0EXKAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T09:59:34.785376Z","bundle_sha256":"f2cb9780be72af09b3c3b149bb7ed3be7176b28ddfd8ecc443330568f72645dd"}}