{"paper":{"title":"When Are Two Networks the Same? Tensor Similarity for Mechanistic Interpretability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Tensor similarity is a weight-based metric that algebraically determines when two neural networks implement the same computation by ignoring irrelevant symmetries.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jacob Meyer Cohen, Laurence Wroe, Logan Riggs Smith, Melwina Albuquerque, ML Nissen Gonzalez, Thomas Dooms","submitted_at":"2026-05-14T17:58:27Z","abstract_excerpt":"Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to out-of-distribution mechanisms, or basis-dependent parameters, meaning they disregard weight-space symmetries. To address these issues for the class of tensor-based models, we introduce a weight-based metric, tensor similarity, that is invariant to such symmetries. This metric captures global functional equivalence and accounts for cross-layer mechanisms us"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Tensor similarity captures global functional equivalence and accounts for cross-layer mechanisms using an efficient recursive algorithm. This reduces measuring similarity and verifying faithfulness into a solved algebraic problem rather than one of empirical approximation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the recursive algorithm correctly identifies functional equivalence for all tensor-based models without missing non-linear interactions or symmetries outside weight-space basis changes.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Tensor similarity is a symmetry-invariant metric that measures functional equivalence between tensor-based networks using a recursive algorithm for cross-layer mechanisms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Tensor similarity is a weight-based metric that algebraically determines when two neural networks implement the same computation by ignoring irrelevant symmetries.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4890af74f90e38a0855cccf7b6724135c0954aa81b1e826dd7cd32d69f70e799"},"source":{"id":"2605.15183","kind":"arxiv","version":1},"verdict":{"id":"77df47ca-3fa3-4e3d-acf6-45a3b304390e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T03:13:32.984659Z","strongest_claim":"Tensor similarity captures global functional equivalence and accounts for cross-layer mechanisms using an efficient recursive algorithm. This reduces measuring similarity and verifying faithfulness into a solved algebraic problem rather than one of empirical approximation.","one_line_summary":"Tensor similarity is a symmetry-invariant metric that measures functional equivalence between tensor-based networks using a recursive algorithm for cross-layer mechanisms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the recursive algorithm correctly identifies functional equivalence for all tensor-based models without missing non-linear interactions or symmetries outside weight-space basis changes.","pith_extraction_headline":"Tensor similarity is a weight-based metric that algebraically determines when two neural networks implement the same computation by ignoring irrelevant symmetries."},"references":{"count":30,"sample":[{"doi":"","year":2025,"title":"David Bau, Bolei Zhou, Aditya Khosla, Aude Oliva, and Antonio Torralba","work_id":"823a63dc-e714-4553-a714-37fe028b7fce","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Available: https://arxiv.org/abs/1704.05796","work_id":"4ecff60a-03d5-476d-b6b9-cba59c37a41c","ref_index":2,"cited_arxiv_id":"1704.05796","is_internal_anchor":true},{"doi":"","year":null,"title":"Neural networks learn statistics of increasing complexity","work_id":"3803730c-4a5c-4f3e-aafc-3ff58e1860a6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Convolutional Rectifier Networks as Generalized Tensor Decompositions","work_id":"bc48707b-0c47-4ea8-91b0-97b76c7d0dbe","ref_index":4,"cited_arxiv_id":"1603.00162","is_internal_anchor":true},{"doi":"","year":null,"title":"On the Expressive Power of Deep Learning: A Tensor Analysis","work_id":"13d1579e-096c-46e4-a4fd-f45ad09f3101","ref_index":5,"cited_arxiv_id":"1509.05009","is_internal_anchor":true}],"resolved_work":30,"snapshot_sha256":"805623669fa5bd10d7e6be64a87d80d826136b18482a2628b7157f453d4181cb","internal_anchors":11},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9e63ee3cdb2c5dc9ee44e5923f79d58e73d5d776f03c9605e767cf34da3702c1"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}