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Based on empirical analyses of the Qwen-2.5 model family on math reasoning benchmarks, we find that more proficient reasoning is associated with fewer reasoning steps but higher information density per step, a property we term Dense Reasoning. Motivated by this observation, we propose DenseSteer, a training-free inference-time steering framework that enhances small-model reasoning by modulating internal representations toward dense reasoning patterns. Experiments show that our method yields consistent accuracy improvements without increasing token-level Negative Log-Likelihood, highlighting dense reasoning as an effective structural approach to mathematical problem solving.","title":"DenseSteer: Steering Small Language Models towards Dense Math Reasoning","url":"https://arxiv.org/abs/2605.29247","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.29247v1 Announce Type: new \nAbstract: Large language models (LLMs) demonstrate strong chain-of-thought (CoT) reasoning abilities, while smaller models (<= 3B parameters) significantly underperform on multi-step reasoning tasks. Based on empirical analyses of the Qwen-2.5 model family on math reasoning benchmarks, we find that more proficient reasoning is associated with fewer reasoning steps but higher information density per step, a property we term Dense Reasoning. Motivated by this observation, we propose DenseSteer, a training-free inference-time steering framework that enhances small-model reasoning by modulating internal representations toward dense reasoning patterns. Experiments show that our method yields consistent accuracy improvements without increasing token-level Negative Log-Likelihood, highlighting dense reasoning as an effective structural approach to mathematical problem solving.","title":"DenseSteer: Steering Small Language Models towards Dense Math Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-29T04:43:58Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.29247"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:21d64ccb93d7f49bfb940e3678abb3f5a0cb45bcdd9854e98d4d525f8d05740b905f5aba7a2788a42c96ec900ca3e5510313fc1882ba686c46c862b57a143009","signer":"crovia.substrate","subject":{"observed_at":"2026-05-29T04:43:58Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.29247"},"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":"6cbf5f2a09dca26a6003e2817dfbf42b1f7cc3dabe5e9be86275478cbc8f72d3","leaf_index":157676,"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":"b8c1c005b7ead7c72afbc6b0ae11836ccdec30671b85b8dcac164bdf2ee11bbe","side":"right"},{"sibling":"25c266ac0f512a1c1a023481086c1c644cf946e129887022ab07f70ec8dedf77","side":"right"},{"sibling":"673d500718399b4f14a83ce6c86e5767fa5528ba24126ed1e010c875f6c667ad","side":"left"},{"sibling":"1400968afc0d5d44dbf5445f9d1a54ae49d7a0a770024bd094dc20a4ceef0265","side":"left"},{"sibling":"1dec423965f2bf69ef076bd5035cd732f74f244143f86714cbbf14699621b04a","side":"right"},{"sibling":"1eead04ebe1be8d8dddce54b72650927fcf3982f00346da13e29805b59a5f05a","side":"left"},{"sibling":"f65c4257e1e3e5a8d1432a336a21d8e806501313e0c2888ff215dba80f4c4cfe","side":"left"},{"sibling":"27e5f392a568b11659ecd5aed52502b5e6d88eea7862dffac806a2d7b5a9ef78","side":"left"},{"sibling":"ece7b043912367e6be374d77e09128de032af83a2b87e39b397350dd279ebe83","side":"left"},{"sibling":"39ec45a73732c5ed1abe96972bd3bc32a517083704467dde1c8117578609124d","side":"left"},{"sibling":"68b4895a8015cdde1c1baeaf63a8382cf574ce4d2ad88d596d4217ce2238245e","side":"left"},{"sibling":"0bc831354843fa27f7ba6a4b3080a72fd440b9a76d1bac63429adfbfe6549bca","side":"right"},{"sibling":"995b421824624a8282c7f44e64c64ee35344800f477ae1845b41be14d3fab94c","side":"right"},{"sibling":"66331bac84ca0f8983eb09fac7eaf95af234f1b82680b793eabff4ee25caac40","side":"left"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"eef0e8906a749d3470f89beeedc723f37a5737010bbb0dcc7cf91515338e5a3e","side":"right"},{"sibling":"1a07e481a9407d71aad078ce854cdeee362163c887fe10f889b0ecf0b5e749ad","side":"right"},{"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":158251,"merkle_root":"485e6b31fe60c8beba5b394808c7e4c32448b2ff65c2482c480ca0e2a2eda718","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260529T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-29T05:37:37Z","sig_algorithm":"ed25519","signature":"bbf9f005201182fce4f9d94c7a9d01a508b56daf7d9611bd73514f5f616bc059d0e5e1f2edfc95716e6fe08ef5fae38b558cbf7f2fd8f9d5dfe4c34a54c83005","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_57374050e34563bb9d60d4923250c061d835cc3cc3221e1e006c7d7656969f92"}}