{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:SDLP3RGPCMIXRIA6SF4BHORKLB","short_pith_number":"pith:SDLP3RGP","schema_version":"1.0","canonical_sha256":"90d6fdc4cf131178a01e917813ba2a584b1d2d5b0f0fe1244d915261146f770c","source":{"kind":"arxiv","id":"2312.10794","version":5},"attestation_state":"computed","paper":{"title":"A mathematical perspective on Transformers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"cs.LG","authors_text":"Borjan Geshkovski, Cyril Letrouit, Philippe Rigollet, Yury Polyanskiy","submitted_at":"2023-12-17T19:06:29Z","abstract_excerpt":"Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters emerge in long time. Our study explores the underlying theory and offers new perspectives for mathematicians as well as computer scientists."},"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":"2312.10794","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-12-17T19:06:29Z","cross_cats_sorted":["math.AP","math.DS"],"title_canon_sha256":"a403911af461508b20360d652ac782632ff046b195d78a8a40727be597a9572e","abstract_canon_sha256":"04cc2a93a04c023d63e55e2cca4d66e6ce5e2c21ce0a87a714e49622d58ddc51"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:47.732939Z","signature_b64":"5scIIEfdpbF+8Z+0FXQ/CBZEZG9HxcXHeSb/bQh+OSi7c8no3rzSECk6NBUBXYuPxyo9r1ZFGjivKZUks5NgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90d6fdc4cf131178a01e917813ba2a584b1d2d5b0f0fe1244d915261146f770c","last_reissued_at":"2026-07-05T11:56:47.732462Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:47.732462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A mathematical perspective on Transformers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"cs.LG","authors_text":"Borjan Geshkovski, Cyril Letrouit, Philippe Rigollet, Yury Polyanskiy","submitted_at":"2023-12-17T19:06:29Z","abstract_excerpt":"Transformers play a central role in the inner workings of large language models. We develop a mathematical framework for analyzing Transformers based on their interpretation as interacting particle systems, which reveals that clusters emerge in long time. Our study explores the underlying theory and offers new perspectives for mathematicians as well as computer scientists."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.10794","kind":"arxiv","version":5},"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/2312.10794/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":"2312.10794","created_at":"2026-07-05T11:56:47.732523+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.10794v5","created_at":"2026-07-05T11:56:47.732523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.10794","created_at":"2026-07-05T11:56:47.732523+00:00"},{"alias_kind":"pith_short_12","alias_value":"SDLP3RGPCMIX","created_at":"2026-07-05T11:56:47.732523+00:00"},{"alias_kind":"pith_short_16","alias_value":"SDLP3RGPCMIXRIA6","created_at":"2026-07-05T11:56:47.732523+00:00"},{"alias_kind":"pith_short_8","alias_value":"SDLP3RGP","created_at":"2026-07-05T11:56:47.732523+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":23,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.26749","citing_title":"Structure Before Collapse: Transient semantic geometry in next-token prediction","ref_index":68,"is_internal_anchor":false},{"citing_arxiv_id":"2606.19268","citing_title":"Patnaik-Pearson intrinsic dimension for internal representations of neural networks","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2606.18694","citing_title":"Attention as Frustrated Synchronization","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2606.19268","citing_title":"Patnaik-Pearson intrinsic dimension for internal representations of neural networks","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2606.11585","citing_title":"Kuramoto Attention: Synchronizing Self-Attention on the Torus","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2607.02154","citing_title":"Path-Measure Dynamics of Attention-Driven World Models: A Nonlocal Onsager--Machlup Approach","ref_index":12,"is_internal_anchor":false},{"citing_arxiv_id":"2606.01923","citing_title":"Resonant Context Anchoring: Decoupling Attention Routing and Signal Gain at Inference Time","ref_index":50,"is_internal_anchor":false},{"citing_arxiv_id":"2606.28751","citing_title":"A Path-Space Formulation of Prediction in World Models: From a Single Action to Prediction, Planning, and Irreversibility","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2605.25085","citing_title":"Polynomial Context-Truncation Sensitivity in Autoregressive Language Models: Sequential Wyner-Ziv Bounds for KV Cache Compression","ref_index":27,"is_internal_anchor":false},{"citing_arxiv_id":"2606.11585","citing_title":"Kuramoto Attention: Synchronizing Self-Attention on the Torus","ref_index":6,"is_internal_anchor":false},{"citing_arxiv_id":"2605.23778","citing_title":"The physics of AI weather models","ref_index":17,"is_internal_anchor":false},{"citing_arxiv_id":"2407.01602","citing_title":"Clustering in pure-attention hardmax transformers and its role in sentiment analysis","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2505.24333","citing_title":"Two failure modes of deep transformers and how to avoid them: a unified theory of signal propagation at initialisation","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2605.15608","citing_title":"Transformer-like Inference from Optimal Control","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2509.04154","citing_title":"Robust Filter Attention: Self-Attention as Precision-Weighted State Estimation","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2510.03989","citing_title":"A Mathematical Explanation of Transformers","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2511.01202","citing_title":"Forget BIT, It is All about TOKEN: Towards Semantic Information Theory for LLMs","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2605.05686","citing_title":"Attractor Geometry of Transformer Memory: From Conflict Arbitration to Confident Hallucination","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2605.14258","citing_title":"Dynamics of the Transformer Residual Stream: Coupling Spectral Geometry to Network Topology","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12697","citing_title":"A Unified Framework for Critical Scaling of Inverse Temperature in Self-Attention","ref_index":5,"is_internal_anchor":false},{"citing_arxiv_id":"2605.05686","citing_title":"Attractor Geometry of Transformer Memory: From Conflict Arbitration to Confident Hallucination","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04279","citing_title":"Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04279","citing_title":"Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SDLP3RGPCMIXRIA6SF4BHORKLB","json":"https://pith.science/pith/SDLP3RGPCMIXRIA6SF4BHORKLB.json","graph_json":"https://pith.science/api/pith-number/SDLP3RGPCMIXRIA6SF4BHORKLB/graph.json","events_json":"https://pith.science/api/pith-number/SDLP3RGPCMIXRIA6SF4BHORKLB/events.json","paper":"https://pith.science/paper/SDLP3RGP"},"agent_actions":{"view_html":"https://pith.science/pith/SDLP3RGPCMIXRIA6SF4BHORKLB","download_json":"https://pith.science/pith/SDLP3RGPCMIXRIA6SF4BHORKLB.json","view_paper":"https://pith.science/paper/SDLP3RGP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.10794&json=true","fetch_graph":"https://pith.science/api/pith-number/SDLP3RGPCMIXRIA6SF4BHORKLB/graph.json","fetch_events":"https://pith.science/api/pith-number/SDLP3RGPCMIXRIA6SF4BHORKLB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SDLP3RGPCMIXRIA6SF4BHORKLB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SDLP3RGPCMIXRIA6SF4BHORKLB/action/storage_attestation","attest_author":"https://pith.science/pith/SDLP3RGPCMIXRIA6SF4BHORKLB/action/author_attestation","sign_citation":"https://pith.science/pith/SDLP3RGPCMIXRIA6SF4BHORKLB/action/citation_signature","submit_replication":"https://pith.science/pith/SDLP3RGPCMIXRIA6SF4BHORKLB/action/replication_record"}},"created_at":"2026-07-05T11:56:47.732523+00:00","updated_at":"2026-07-05T11:56:47.732523+00:00"}