{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:NV54W7FPQM6TEZBUWN7CJVMIAN","short_pith_number":"pith:NV54W7FP","canonical_record":{"source":{"id":"2410.07656","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-10T06:55:38Z","cross_cats_sorted":[],"title_canon_sha256":"949a63701b088acf85ac2b448cd5a850b06c2c5aebe4dff7a76b5fe00c4d3d14","abstract_canon_sha256":"8930806c1bd410beab53aaca40851380f875ee24a74f23c8e72a68b5b6bde9ce"},"schema_version":"1.0"},"canonical_sha256":"6d7bcb7caf833d326434b37e24d5880375887d9f4f51014efb54ddd163a567ff","source":{"kind":"arxiv","id":"2410.07656","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.07656","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"2410.07656v3","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.07656","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"NV54W7FPQM6T","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"pith_short_16","alias_value":"NV54W7FPQM6TEZBU","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"pith_short_8","alias_value":"NV54W7FP","created_at":"2026-07-05T10:22:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:NV54W7FPQM6TEZBUWN7CJVMIAN","target":"record","payload":{"canonical_record":{"source":{"id":"2410.07656","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-10T06:55:38Z","cross_cats_sorted":[],"title_canon_sha256":"949a63701b088acf85ac2b448cd5a850b06c2c5aebe4dff7a76b5fe00c4d3d14","abstract_canon_sha256":"8930806c1bd410beab53aaca40851380f875ee24a74f23c8e72a68b5b6bde9ce"},"schema_version":"1.0"},"canonical_sha256":"6d7bcb7caf833d326434b37e24d5880375887d9f4f51014efb54ddd163a567ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:22:07.144929Z","signature_b64":"JgCfT4UKHvJlOhoTp+mlJ9h3A4MDIuJxlRR/oZ09ka7n4MLT0KUI44wx/y0UThX05KN/+z8eiOJIYKV1sJTUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d7bcb7caf833d326434b37e24d5880375887d9f4f51014efb54ddd163a567ff","last_reissued_at":"2026-07-05T10:22:07.144373Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:22:07.144373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.07656","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/xUuuM0GHXYXcY/7SBYQSWOjP17riSzwvk2hsPfUNNk4EPOUczTnIZ15iY+THcuyN7trvp20GrATYJ+nyoH4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T14:35:57.779764Z"},"content_sha256":"ec9be4434bcd410fc13111933f99bca9ac6d7bc1ae90e9dd6be70e47800310c3","schema_version":"1.0","event_id":"sha256:ec9be4434bcd410fc13111933f99bca9ac6d7bc1ae90e9dd6be70e47800310c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:NV54W7FPQM6TEZBUWN7CJVMIAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mechanistic Permutability: Match Features Across Layers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Daniil Gavrilov, Ian Maksimov, Nikita Balagansky","submitted_at":"2024-10-10T06:55:38Z","abstract_excerpt":"Understanding how features evolve across layers in deep neural networks is a fundamental challenge in mechanistic interpretability, particularly due to polysemanticity and feature superposition. While Sparse Autoencoders (SAEs) have been used to extract interpretable features from individual layers, aligning these features across layers has remained an open problem. In this paper, we introduce SAE Match, a novel, data-free method for aligning SAE features across different layers of a neural network. Our approach involves matching features by minimizing the mean squared error between the folded"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.07656","kind":"arxiv","version":3},"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/2410.07656/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":"2026-07-05T10:22:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WDTyzYanOrE7L2Mgp57BpaT2XF1y/k/CiuPVIoSUURSTkwMhotyhGCaIrwDUqCIWbT9VmbE6hsk2Mmi6Kg8xBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T14:35:57.780307Z"},"content_sha256":"a2749238916a0dfb0b95bb2aeef905ec34920825e5c57df944eaebb5b5274eff","schema_version":"1.0","event_id":"sha256:a2749238916a0dfb0b95bb2aeef905ec34920825e5c57df944eaebb5b5274eff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NV54W7FPQM6TEZBUWN7CJVMIAN/bundle.json","state_url":"https://pith.science/pith/NV54W7FPQM6TEZBUWN7CJVMIAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NV54W7FPQM6TEZBUWN7CJVMIAN/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":"2026-08-15T14:35:57Z","links":{"resolver":"https://pith.science/pith/NV54W7FPQM6TEZBUWN7CJVMIAN","bundle":"https://pith.science/pith/NV54W7FPQM6TEZBUWN7CJVMIAN/bundle.json","state":"https://pith.science/pith/NV54W7FPQM6TEZBUWN7CJVMIAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NV54W7FPQM6TEZBUWN7CJVMIAN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NV54W7FPQM6TEZBUWN7CJVMIAN","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":"8930806c1bd410beab53aaca40851380f875ee24a74f23c8e72a68b5b6bde9ce","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-10T06:55:38Z","title_canon_sha256":"949a63701b088acf85ac2b448cd5a850b06c2c5aebe4dff7a76b5fe00c4d3d14"},"schema_version":"1.0","source":{"id":"2410.07656","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.07656","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"arxiv_version","alias_value":"2410.07656v3","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.07656","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"pith_short_12","alias_value":"NV54W7FPQM6T","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"pith_short_16","alias_value":"NV54W7FPQM6TEZBU","created_at":"2026-07-05T10:22:07Z"},{"alias_kind":"pith_short_8","alias_value":"NV54W7FP","created_at":"2026-07-05T10:22:07Z"}],"graph_snapshots":[{"event_id":"sha256:a2749238916a0dfb0b95bb2aeef905ec34920825e5c57df944eaebb5b5274eff","target":"graph","created_at":"2026-07-05T10:22:07Z","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/2410.07656/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Understanding how features evolve across layers in deep neural networks is a fundamental challenge in mechanistic interpretability, particularly due to polysemanticity and feature superposition. While Sparse Autoencoders (SAEs) have been used to extract interpretable features from individual layers, aligning these features across layers has remained an open problem. In this paper, we introduce SAE Match, a novel, data-free method for aligning SAE features across different layers of a neural network. Our approach involves matching features by minimizing the mean squared error between the folded","authors_text":"Daniil Gavrilov, Ian Maksimov, Nikita Balagansky","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-10T06:55:38Z","title":"Mechanistic Permutability: Match Features Across Layers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.07656","kind":"arxiv","version":3},"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:ec9be4434bcd410fc13111933f99bca9ac6d7bc1ae90e9dd6be70e47800310c3","target":"record","created_at":"2026-07-05T10:22:07Z","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":"8930806c1bd410beab53aaca40851380f875ee24a74f23c8e72a68b5b6bde9ce","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-10T06:55:38Z","title_canon_sha256":"949a63701b088acf85ac2b448cd5a850b06c2c5aebe4dff7a76b5fe00c4d3d14"},"schema_version":"1.0","source":{"id":"2410.07656","kind":"arxiv","version":3}},"canonical_sha256":"6d7bcb7caf833d326434b37e24d5880375887d9f4f51014efb54ddd163a567ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d7bcb7caf833d326434b37e24d5880375887d9f4f51014efb54ddd163a567ff","first_computed_at":"2026-07-05T10:22:07.144373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:22:07.144373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JgCfT4UKHvJlOhoTp+mlJ9h3A4MDIuJxlRR/oZ09ka7n4MLT0KUI44wx/y0UThX05KN/+z8eiOJIYKV1sJTUAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:22:07.144929Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.07656","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec9be4434bcd410fc13111933f99bca9ac6d7bc1ae90e9dd6be70e47800310c3","sha256:a2749238916a0dfb0b95bb2aeef905ec34920825e5c57df944eaebb5b5274eff"],"state_sha256":"52ad12242a3158b8f27e54b9e3a16f6edc32f45505321815ce7f205baa51a6e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IcSKuHWy0bklkRXCJnxeIxeJPQ6X+/SS7HuXRTb3cO42rGHLhaxgJwfuBqsECMlzdP8DxW50GFeGJq9xlyiSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T14:35:57.786207Z","bundle_sha256":"a6d49b0d6a9017c7c8974eac94d907c6e36d515ee2939d4f585f934f959e671e"}}