{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2I6S3H6I34KWVM3TAOOL34PQEC","short_pith_number":"pith:2I6S3H6I","schema_version":"1.0","canonical_sha256":"d23d2d9fc8df156ab373039cbdf1f020b524dc1e7fe9e71854989f55e1fdceec","source":{"kind":"arxiv","id":"2607.10034","version":1},"attestation_state":"computed","paper":{"title":"MLPs are Hebbians: Constructing Efficient Fact-Storing MLPs for Transformers","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Atri Rudra, Christopher R\\'e, Jerry Liu, Roberto Garcia, Ronny Junkins, Sabri Eyuboglu","submitted_at":"2026-07-10T23:22:48Z","abstract_excerpt":"Large language models (LLMs) store factual knowledge in their parameters. While recent work has shown that this knowledge resides in MLP layers, existing constructive and mechanistic interpretability models of fact-storage in LLMs fail to explain the surprising empirical phenomenon that they store facts at an information-theoretically optimal rate. In this work, we develop a theoretical account of this phenomenon. We develop the first Transformer-compatible fact-storing MLP closed-form construction that satisfies the following three properties empirically observed in LLMs: it (i) attains optim"},"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":"2607.10034","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-10T23:22:48Z","cross_cats_sorted":[],"title_canon_sha256":"d4ff6fca9c3701c0fedda84fd0cebcd006b078c052de2da87eae05b29f37ee4b","abstract_canon_sha256":"5068cb34426050d87129ceac7bec38f055113cc52939e5f9d3e17248a9799bd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T00:18:48.671716Z","signature_b64":"llFt3UgvS0cp53G8L75CHeriykBnDmMQOCA4gN6DPfajlsPIdkcYxFMLJ+3PEXMJiWFcOEyxTq1Ns1PJoHWSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d23d2d9fc8df156ab373039cbdf1f020b524dc1e7fe9e71854989f55e1fdceec","last_reissued_at":"2026-07-14T00:18:48.670889Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T00:18:48.670889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"MLPs are Hebbians: Constructing Efficient Fact-Storing MLPs for Transformers","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Atri Rudra, Christopher R\\'e, Jerry Liu, Roberto Garcia, Ronny Junkins, Sabri Eyuboglu","submitted_at":"2026-07-10T23:22:48Z","abstract_excerpt":"Large language models (LLMs) store factual knowledge in their parameters. While recent work has shown that this knowledge resides in MLP layers, existing constructive and mechanistic interpretability models of fact-storage in LLMs fail to explain the surprising empirical phenomenon that they store facts at an information-theoretically optimal rate. In this work, we develop a theoretical account of this phenomenon. We develop the first Transformer-compatible fact-storing MLP closed-form construction that satisfies the following three properties empirically observed in LLMs: it (i) attains optim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10034","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/2607.10034/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":"2607.10034","created_at":"2026-07-14T00:18:48.671303+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.10034v1","created_at":"2026-07-14T00:18:48.671303+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10034","created_at":"2026-07-14T00:18:48.671303+00:00"},{"alias_kind":"pith_short_12","alias_value":"2I6S3H6I34KW","created_at":"2026-07-14T00:18:48.671303+00:00"},{"alias_kind":"pith_short_16","alias_value":"2I6S3H6I34KWVM3T","created_at":"2026-07-14T00:18:48.671303+00:00"},{"alias_kind":"pith_short_8","alias_value":"2I6S3H6I","created_at":"2026-07-14T00:18:48.671303+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/2I6S3H6I34KWVM3TAOOL34PQEC","json":"https://pith.science/pith/2I6S3H6I34KWVM3TAOOL34PQEC.json","graph_json":"https://pith.science/api/pith-number/2I6S3H6I34KWVM3TAOOL34PQEC/graph.json","events_json":"https://pith.science/api/pith-number/2I6S3H6I34KWVM3TAOOL34PQEC/events.json","paper":"https://pith.science/paper/2I6S3H6I"},"agent_actions":{"view_html":"https://pith.science/pith/2I6S3H6I34KWVM3TAOOL34PQEC","download_json":"https://pith.science/pith/2I6S3H6I34KWVM3TAOOL34PQEC.json","view_paper":"https://pith.science/paper/2I6S3H6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.10034&json=true","fetch_graph":"https://pith.science/api/pith-number/2I6S3H6I34KWVM3TAOOL34PQEC/graph.json","fetch_events":"https://pith.science/api/pith-number/2I6S3H6I34KWVM3TAOOL34PQEC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2I6S3H6I34KWVM3TAOOL34PQEC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2I6S3H6I34KWVM3TAOOL34PQEC/action/storage_attestation","attest_author":"https://pith.science/pith/2I6S3H6I34KWVM3TAOOL34PQEC/action/author_attestation","sign_citation":"https://pith.science/pith/2I6S3H6I34KWVM3TAOOL34PQEC/action/citation_signature","submit_replication":"https://pith.science/pith/2I6S3H6I34KWVM3TAOOL34PQEC/action/replication_record"}},"created_at":"2026-07-14T00:18:48.671303+00:00","updated_at":"2026-07-14T00:18:48.671303+00:00"}