{"paper":{"title":"Continuous-Depth Field Theory for Transformer Patching and Mechanistic Interpretability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Antonio F. P\\'erez Rodr\\'iguez, David N. Olivieri","submitted_at":"2026-05-24T19:26:25Z","abstract_excerpt":"Mechanistic interpretability often uses activation patching, causal tracing, path patching, and steering directions to reveal behaviorally meaningful directions in Transformer activation space. This paper develops a field-theoretic framework for organizing and predicting such interventions. Treating the residual stream as a depth-token field, we formulate patching as localized source insertion, patch effects as sensitivity-field predictions, downstream propagation as empirical Green-function response, and patch selection as an adjoint variational problem. Empirically, we test the forward respo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25225","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/2605.25225/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"}