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We identify a counterintuitive \\textbf{Quality-Utility Paradox} in mathematical reasoning distillation. Data refined or synthesized by a stronger Oracle obtains higher perceived quality according to reward models, yet consistently underperforms traces generated by the SLM itself and selected through rejection sampling across Qwen2.5, LLaMA-3, and DeepSeek families. Our analysis shows that Oracle refinement couples logical repair with distributional drift away from the SLM's native reasoning distribution. This drift increases the learner's adaptation cost and can outweigh the benefit of improved reasoning logic. To test this mechanism, we introduce \\textbf{Style-Aligned Refinement}, which preserves the native traje","title":"The Quality-Utility Paradox: Why High-Reward Data Impairs Small Model Mathematical Reasoning","url":"https://arxiv.org/abs/2606.16152","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.16152v1 Announce Type: new \nAbstract: Knowledge distillation from powerful reasoning models is widely used to improve Small Language Models (SLMs) on mathematical reasoning, often assuming that traces with higher reward model scores provide more useful supervision. We identify a counterintuitive \\textbf{Quality-Utility Paradox} in mathematical reasoning distillation. Data refined or synthesized by a stronger Oracle obtains higher perceived quality according to reward models, yet consistently underperforms traces generated by the SLM itself and selected through rejection sampling across Qwen2.5, LLaMA-3, and DeepSeek families. Our analysis shows that Oracle refinement couples logical repair with distributional drift away from the SLM's native reasoning distribution. This drift increases the learner's adaptation cost and can outweigh the benefit of improved reasoning logic. To test this mechanism, we introduce \\textbf{Style-Aligned Refinement}, which preserves the native traje","title":"The Quality-Utility Paradox: Why High-Reward Data Impairs Small Model Mathematical Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-16T04:43:43Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.16152"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:05f9f3c837f0f3f4aacbfbd1e9936a24520789e83dd7e7137dc3be2eb4212fabcfc4dd9f14e429edf4906608c4bc92b48a1d62dc6775a7b7c41c801191fa9b07","signer":"crovia.substrate","subject":{"observed_at":"2026-06-16T04:43:43Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.16152"},"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":"c1fe6d2863d94a5fed0cefe62cc240933db42b9de920b69e9f69fc669ffa3b39","leaf_index":230254,"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":"305a4b4005c40b1fb573a0a95dc0e901be52dcdf6bbdb32cb6b9e5d081bfddab","side":"right"},{"sibling":"b71d81e713d700538ced1494411d8fc3245bc82aa4a38d962d19a580d31403fd","side":"left"},{"sibling":"f33f035cafc7a3cb149ef80c75ff87e185a65ba2f790d161f98307a8dcac9724","side":"left"},{"sibling":"53b0eddcfbfb353bf595f6f5448e5f42a41e4f9e25176eaa47b4efca667aeef3","side":"left"},{"sibling":"fe0907976d8f31b98fbd5d2cb85be488df9f2eb202d8cd54692158c911e17555","side":"right"},{"sibling":"f8cb23847b99c3273ae24b135e5d2ad8918a6996b58fa085c886b72b0ee79ea2","side":"left"},{"sibling":"ab99e8259a1eace4f43b5338489073a2f7f21b0da5b3a1d216f8fbe0780770ab","side":"left"},{"sibling":"0d60a870c104823e0ebbac1aad5395bcb88f28b6928636cce19a16b0cfa21564","side":"right"},{"sibling":"03ebe4791d56166247160f6ee7788c15745bdd7e274c62ec21b2438669941587","side":"left"},{"sibling":"74897e850164dddc689c3c65b33f9bae0268ab0bf429867a4e193d9b9b685040","side":"left"},{"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_255926ccc7404078d2329d390ec4aa6686b4c20a410a9aba050bf6943f207d7b"}}