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However, the field faces \\textit{the fundamental gap between token-level behavioral analysis and internal reasoning mechanisms, and the instability of reinforcement learning (RL) for reasoning optimization relying on costly external verifiers}. We identify and formally define \\textbf{Entropy-Gradient Inversion}, a robust negative correlation between token entropy and logit gradients that acts as a definitive geometric fingerprint for LRM reasoning capability. Building on this, we propose \\textbf{Correlation-Regularized Group Policy Optimization (CorR-PO)}, which embeds this inversion signature into RL reward regularization. Extensive experiments on various reasoning bench","title":"Entropy-Gradient Inversion: Moving Toward Internal Mechanism of Large Reasoning Models","url":"https://arxiv.org/abs/2605.17770","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.17770v3 Announce Type: replace \nAbstract: The advancement of Large Reasoning Models (LRMs) has catalyzed a paradigm shift from reactive ``fast thinking'' text generation to systematic, step-by-step ``slow thinking'' reasoning, unlocking state-of-the-art performance in complex mathematical and logical tasks. However, the field faces \\textit{the fundamental gap between token-level behavioral analysis and internal reasoning mechanisms, and the instability of reinforcement learning (RL) for reasoning optimization relying on costly external verifiers}. We identify and formally define \\textbf{Entropy-Gradient Inversion}, a robust negative correlation between token entropy and logit gradients that acts as a definitive geometric fingerprint for LRM reasoning capability. Building on this, we propose \\textbf{Correlation-Regularized Group Policy Optimization (CorR-PO)}, which embeds this inversion signature into RL reward regularization. Extensive experiments on various reasoning bench","title":"Entropy-Gradient Inversion: Moving Toward Internal Mechanism of Large Reasoning Models","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-12T04:43:44Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.17770"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:99d5f4d442081297d9329d076a081c068ee67788b855aeda4d5fabb02f554237815b7b46b9b12d5ce85e21987b3bdd03f4c36a8c04c8dce0a9a384aa3c40db0b","signer":"crovia.substrate","subject":{"observed_at":"2026-06-12T04:43:44Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.17770"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"3158a4d3f4518a3fbd64678220029ac54411ae82f57040f679c670a345d4c2b3","leaf_index":229819,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"325108c6dce574e851909af2460574e1b4eb5ef7e1ce9481db4b61a2a9913746","side":"left"},{"sibling":"456e8aca0ecb24c5bec20183a56d71654577a7a66c8ffb8dbf0e31c23ebcc85d","side":"left"},{"sibling":"b8259873d65011c1a880d6bdc6c54c8d2e8083f8a104bc9c1ea9dac6a4f962b5","side":"right"},{"sibling":"836545b7e3c9c0f2d99da40e2f60e46086e43cad987c067a3c99c6e11216aee8","side":"left"},{"sibling":"a911290c1e1de2836ed3df7c5f27f98ea8e42d4006618d955a65b3f6c813fde1","side":"left"},{"sibling":"f88c40850a92a64a6598b06027c61b5037d7554f528aedc4df6a89a6d87d6bd0","side":"left"},{"sibling":"f8bab1c4b4d78ecdc0c7c24f3f0491d32c6f49b960c42926df1ece7da77ecd89","side":"right"},{"sibling":"ae0aa292f48289283e26aa363532f22206cc7cea51771c75c6c011c898bec69c","side":"left"},{"sibling":"99d288e6cd43a807fba958865176bb1c08b82471afe942f6e4989eaeeb7275aa","side":"left"},{"sibling":"d385017d38a86f6abc492026a7cd60ceb3b3ff2486142dc49e5acb179f4b7d11","side":"right"},{"sibling":"bde25d7e94e64717e426a97f6fcb4907e92b5c61fc89d92d7e0947a2249c3f6b","side":"right"},{"sibling":"d10d772a4984cae00e65ab24af21d1d260e475bbaae3f17871859eb705bd3999","side":"right"},{"sibling":"e79159853f2f35ddae8e3247d515e433c534277b287d65bbd77ae989aa4992fa","side":"right"},{"sibling":"3054319f1840cce0eaaf0bc4b1ae38e5bf8b6210927d924a750775cc7d77cca6","side":"right"},{"sibling":"0fd8b5059f279c4a4a6688de2472fdbc25543fee183df19b21dacca880354cff","side":"right"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":232015,"merkle_root":"62bfb7809bb55667ad7eeebdb48267b9b2c1ee89bb808ea1e6d3a814a15aa402","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260617T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-17T13:39:59Z","sig_algorithm":"ed25519","signature":"930a3563c643cc7518d048b12a1f5392a96a5edce49533ba0a56f11b6cc69319bb1c800aacc46b52a6941c4d05dae255a45cac757d6093c971b96852c24f140e","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_02275d8cfce7e824c61811f081588507a432281b21e71a7cb4c9cd8a090ba22b"}}