{"paper":{"title":"All Circuits Lead to Rome: Rethinking Functional Anisotropy in Circuit and Sheaf Discovery for LLMs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A single task in large language models can be performed by multiple structurally distinct circuits or sheaves that are all faithful, sparse, and complete.","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Bangwei Guo, Dimitris N. Metaxas, Gerald Penn, Jingcheng Niu, Jinman Zhao, Mingyu Jin, Xi Chen, Yutao Yue, Yutong Yin, Zhaoran Wang","submitted_at":"2026-05-12T19:21:23Z","abstract_excerpt":"In this paper, we present empirical and theoretical evidence against a central but largely implicit assumption in circuit and sheaf discovery (CSD), which we term the Functional Anisotropy Hypothesis: the idea that functions in large language models (LLMs) are localised to a unique or near-unique internal mechanism. We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete. To systematically uncover such competing mechanisms, we introduce Overlap-Aware Sheaf Repulsion, a method that augm"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the Overlap-Aware Sheaf Repulsion penalty successfully uncovers genuinely distinct mechanisms without introducing methodological artifacts, and that the theoretical analysis of high-dimensional superposition holds under the stated mild assumptions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"LLM tasks are supported by multiple distinct circuits rather than unique mechanisms, demonstrated via Overlap-Aware Sheaf Repulsion and the Distributive Dense Circuit Hypothesis.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A single task in large language models can be performed by multiple structurally distinct circuits or sheaves that are all faithful, sparse, and complete.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a4d99c565994cc02d05d3e383cc99a2c39351108ec19132fe7217e4ddc3f7310"},"source":{"id":"2605.12671","kind":"arxiv","version":1},"verdict":{"id":"411f37ea-c6e1-4de5-a35b-913309568d81","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:48:46.251781Z","strongest_claim":"We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete.","one_line_summary":"LLM tasks are supported by multiple distinct circuits rather than unique mechanisms, demonstrated via Overlap-Aware Sheaf Repulsion and the Distributive Dense Circuit Hypothesis.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the Overlap-Aware Sheaf Repulsion penalty successfully uncovers genuinely distinct mechanisms without introducing methodological artifacts, and that the theoretical analysis of high-dimensional superposition holds under the stated mild assumptions.","pith_extraction_headline":"A single task in large language models can be performed by multiple structurally distinct circuits or sheaves that are all faithful, sparse, and complete."},"references":{"count":300,"sample":[{"doi":"","year":2018,"title":"Abdelmalik, Philip and Peron, Emilie and Schnitzler, Johannes and Fontaine, Julie and Elfenkampera, Eva and Barbozaa, Philippe , year = 2018, journal =","work_id":"81d2a84a-3999-4193-8e69-e5c4d8ed287f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Proceedings of the 25th","work_id":"549a7fd5-5a79-41e6-9bf0-5ca64caef0ee","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"From Language as System to Language as Use:","work_id":"2dcc0e5c-426a-4a83-bbb0-d0f5f7d8d60f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"Ackema, Peter and Neeleman, Ad , year = 2004, publisher =","work_id":"49b766d9-0632-4342-afa8-450c88ca8334","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"Adger, David , year = 2003, publisher =","work_id":"db613369-147f-450d-9861-82a5137dbbcd","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":300,"snapshot_sha256":"be1972d0a73381e38ef6fe77fc85319f8053021e892feaf2c3196a26bdf58e28","internal_anchors":5},"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"}