{"paper":{"title":"Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Symmetric spectral diagnostics on attention operators cannot detect the direction of information flow.","cross_cats":["cs.CL","stat.ML"],"primary_cat":"cs.LG","authors_text":"Diego Maniloff, Dominik Dahlem, Mac Misiura","submitted_at":"2026-05-06T13:25:13Z","abstract_excerpt":"When a language model processes a hallucinated response, its attention routing tends to fail in one of two shapes: over-concentrating on a narrow set of positions, or spreading so diffusely that relevance is diluted, and the shape of the failure carries diagnostic signal. We study these shapes as a diagnostic characterization, computed from attention matrices under \\emph{forced scoring} of benchmark-labeled responses rather than during live generation. A widely used family of spectral methods analyzes the symmetric component of the degree-normalized attention operator, which governs transport "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we prove that every transpose-invariant spectral diagnostic of this operator is structurally orientation-blind (it cannot distinguish an operator from its transpose, and therefore cannot detect information-flow direction), with a quantitative converse establishing the asymmetry coefficient G as the unique control parameter for direction.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the dominant hallucination mechanisms in the tested benchmarks are fully captured by the transport capacity and directionality of the degree-normalized attention operator, without substantial confounding from other components such as feed-forward layers, layer norms, or output decoding.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Symmetric spectral diagnostics on attention are structurally blind to flow direction, with asymmetry G as the sole control parameter, yielding a two-axis test that distinguishes bottleneck versus diffuse hallucination modes with opposite polarity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Symmetric spectral diagnostics on attention operators cannot detect the direction of information flow.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f56cbc834fff621944af073139cf63140cc384df46cf9b4cc21a8ab8f195b032"},"source":{"id":"2605.04893","kind":"arxiv","version":2},"verdict":{"id":"31125305-4377-428e-a7bc-4a6cf44940e1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T16:45:03.414461Z","strongest_claim":"we prove that every transpose-invariant spectral diagnostic of this operator is structurally orientation-blind (it cannot distinguish an operator from its transpose, and therefore cannot detect information-flow direction), with a quantitative converse establishing the asymmetry coefficient G as the unique control parameter for direction.","one_line_summary":"Symmetric spectral diagnostics on attention are structurally blind to flow direction, with asymmetry G as the sole control parameter, yielding a two-axis test that distinguishes bottleneck versus diffuse hallucination modes with opposite polarity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the dominant hallucination mechanisms in the tested benchmarks are fully captured by the transport capacity and directionality of the degree-normalized attention operator, without substantial confounding from other components such as feed-forward layers, layer norms, or output decoding.","pith_extraction_headline":"Symmetric spectral diagnostics on attention operators cannot detect the direction of information flow."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.04893/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T10:41:09.837277Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T22:01:23.815473Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:04:04.196495Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ae4de1adb6cae42493d2bdee94f2b1324b8c5fc6172601681dbc232fb227353d"},"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"}