{"paper":{"title":"Matrix-Decoupled Concentration for Autoregressive Sequences: Dimension-Free Guarantees for Sparse Long-Context Rewards","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Matrix decoupling of causal dependencies yields dimension-free O(1) variance bounds for sparse rewards in autoregressive sequences.","cross_cats":["math.PR"],"primary_cat":"cs.LG","authors_text":"Pei-Sen Li","submitted_at":"2026-05-07T11:12:59Z","abstract_excerpt":"Sequence-level evaluations in autoregressive Large Language Models (LLMs) rely on highly dependent token generation. Establishing tight concentration bounds for these processes remains a challenge due to two fundamental bottlenecks in existing frameworks: (i) classical inequalities typically separate dependency structures from target sensitivities, leading to a scalar collapse that inflates the variance proxy to a suboptimal $\\mathcal{O}(N)$ for sparse terminal rewards; (ii) conversely, while certain spatial methods achieve tighter bounds, they lack the strictly causal filtration required by s"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we establish a sharp McDiarmid-type inequality for dependent sequences, governed strictly by the exact matrix-vector multiplication of the causal dependency resolvent and the target sensitivity vector. This Matrix-Decoupled Concentration (MDC) framework natively recovers optimal constants for Markov chains and exploits directed d-separation to yield order-optimal bounds for causal trees. Crucially, by exactly preserving the coordinate-wise sparsity of rewards within a strictly causal framework, MDC mathematically prevents scalar collapse, guaranteeing a dimension-free O(1) variance proxy","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The process admits a strictly causal filtration whose dependency structure can be represented by a well-defined resolvent matrix that exactly decouples the target sensitivity vector while preserving coordinate-wise sparsity of the reward.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Matrix-Decoupled Concentration achieves dimension-free O(1) variance bounds for sparse rewards in strictly causal autoregressive sequences by decoupling via the exact matrix-vector product of the dependency resolvent and sensitivity vector.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Matrix decoupling of causal dependencies yields dimension-free O(1) variance bounds for sparse rewards in autoregressive sequences.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1ccd6b49ab1f01a6acc238b2471dece2cf0e70f3bef4fabf17f18324ac40db77"},"source":{"id":"2605.06017","kind":"arxiv","version":2},"verdict":{"id":"eebf5833-054d-45b5-8d30-c01ed6847db6","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T15:26:29.067015Z","strongest_claim":"we establish a sharp McDiarmid-type inequality for dependent sequences, governed strictly by the exact matrix-vector multiplication of the causal dependency resolvent and the target sensitivity vector. This Matrix-Decoupled Concentration (MDC) framework natively recovers optimal constants for Markov chains and exploits directed d-separation to yield order-optimal bounds for causal trees. Crucially, by exactly preserving the coordinate-wise sparsity of rewards within a strictly causal framework, MDC mathematically prevents scalar collapse, guaranteeing a dimension-free O(1) variance proxy","one_line_summary":"Matrix-Decoupled Concentration achieves dimension-free O(1) variance bounds for sparse rewards in strictly causal autoregressive sequences by decoupling via the exact matrix-vector product of the dependency resolvent and sensitivity vector.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The process admits a strictly causal filtration whose dependency structure can be represented by a well-defined resolvent matrix that exactly decouples the target sensitivity vector while preserving coordinate-wise sparsity of the reward.","pith_extraction_headline":"Matrix decoupling of causal dependencies yields dimension-free O(1) variance bounds for sparse rewards in autoregressive sequences."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06017/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.185866Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T13:04:19.359377Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"022b29305ce0177b831f76e52e1947c57d2010d1e7e605dfed21c5849bdf4990"},"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"}