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While existing reinforcement learning approaches address this by optimizing final response length, they neglect the quality of intermediate reasoning steps, leaving models vulnerable to reward hacking. We argue that verbosity is not merely a length problem, but a symptom of poor intermediate reasoning quality. To investigate this, we conduct an empirical study tracking the per-token predictive entropy of large reasoning models across reasoning trajectories. We find that high-quality reasoning traces exhibit two consistent properties: low uncertainty convergence and fast uncertainty descent. These findings suggest that high-quality reasoning traces are informationally dense, that is, reasoning steps contribute to reaching a low uncertainty level relative to the total reasoni","title":"InfoDensity: Rewarding Information-Dense Traces for Efficient Reasoning","url":"https://arxiv.org/abs/2603.17310","vendor":"arxiv_cs_ai"},"summary":"arXiv:2603.17310v2 Announce Type: replace \nAbstract: Large Language Models (LLMs) with extended reasoning capabilities often generate verbose and redundant reasoning traces, incurring unnecessary computational cost. While existing reinforcement learning approaches address this by optimizing final response length, they neglect the quality of intermediate reasoning steps, leaving models vulnerable to reward hacking. We argue that verbosity is not merely a length problem, but a symptom of poor intermediate reasoning quality. To investigate this, we conduct an empirical study tracking the per-token predictive entropy of large reasoning models across reasoning trajectories. We find that high-quality reasoning traces exhibit two consistent properties: low uncertainty convergence and fast uncertainty descent. These findings suggest that high-quality reasoning traces are informationally dense, that is, reasoning steps contribute to reaching a low uncertainty level relative to the total reasoni","title":"InfoDensity: Rewarding Information-Dense Traces for Efficient Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-06T04:43:19Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2603.17310"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:ae0d4d78475ad48e3d50a2a7e2688304138561a4d2518aa3cf734ea7dc9f82ca60f520932e43cebcb68a7335dd2bb04f371229a05696d9b8de12585328c39404","signer":"crovia.substrate","subject":{"observed_at":"2026-06-06T04:43:19Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2603.17310"},"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":"06b781ecfd17ec603065f829a13d84cd8e57755e6d9692022ec74899cb65778c","leaf_index":219436,"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":"f87ead6aa47f0903154acc230c3ea9987612b975d084eaa965a1cf6086dfc572","side":"right"},{"sibling":"0c5273c8d6e31d3465afd8c98a72102878e2a262e5eed5572254dff62f6f27fb","side":"right"},{"sibling":"4ccd51659073830ac6e3e05b800841894d4ea7ff24e889e0432e2e4666baca92","side":"left"},{"sibling":"a654579595afebbb82a280d5d56d1fc68b3555f6a7f872d78cb771c39db3b374","side":"left"},{"sibling":"e6771f7e0abe1bb2ff4409bdbaefde823f3052d98ce5fc2a1899822d30cb7ca1","side":"right"},{"sibling":"0533945d48fc5cfd005a76d7e01ac78a1ad97725a2e0650037feaf4a36bde567","side":"left"},{"sibling":"c6d85f421226f83ff8cf32aaff89929d6dc9d5d94759254073631ced17a73907","side":"right"},{"sibling":"242ec7690d5995e1b5c2e94f2a8cedd5416b170d2db6fb44c95d0f9fb134a235","side":"right"},{"sibling":"42875175baa73c49869c927a23711e8bef732331ce49af85fa7e86d0903b1066","side":"left"},{"sibling":"84d2509eab51047589142ed6da8c496305d2fbcbe148e0e6755163db2c7a4bc4","side":"right"},{"sibling":"9e3ea17e834fab022f2eabcfedb8ea0ac95c1f9fb57edc5004dded68522d3c9e","side":"right"},{"sibling":"41d58fea95a95071715ee23ef8bcd15f5867a3639da28e62a0641bc95eb83094","side":"left"},{"sibling":"27ad9d6a9ab792d708709017242a61b9ca519da4e035f87a342811aae221d000","side":"left"},{"sibling":"5f303e2a7840c60038ff2d035b1cd911feefb0fba880de2d737c6671ace594d4","side":"right"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"1a61eadbf0217d063ab78291ccafdc0c92907f7d6ccdc3357534ef89f07d78ae","side":"right"},{"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":219672,"merkle_root":"d3e32d3a61ca02ce6b1f0b2db86721107770b250e8a5bf762a2c225d2f03c870","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260606T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-06T05:38:35Z","sig_algorithm":"ed25519","signature":"dab214c2d4d857f01383c8e93a521a774b1aba60eaee5677d4e43e4074f0342b2c6a9b9bfcff0eba74f7ac81fcb490dd0e43727979c1a7e8979c7e11547fb101","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_f06ab32dd7195b7d6f9c385eb898dd63edf7e79881196012c36c312411aede68"}}