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Existing efforts to mitigate this inefficiency typically rely on discrete reasoning modes or fixed budget tiers, lacking a principled criterion of when reasoning is sufficient. In this work, we introduce Minimal Sufficient CoT (MSC), defined as the shortest prefix of a CoT trajectory which is adequate for producing the correct answer. We empirically show that MSC not only reduces reasoning tokens, but also improves accuracy across difficulty levels. Building on MSC, we propose Sufficiency-guided Continuous Adaptive Reasoning (SuCo), a two-stage training framework for autonomous reasoning control along a continuous spectrum. In stage 1, MSC-Aligned Fine-Tuning (MFT) constructs MSC data using problem-adaptive sufficiency thresholds that naturally sca","title":"SuCo: Sufficiency-guided Continuous Adaptive Reasoning","url":"https://arxiv.org/abs/2606.17687","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.17687v1 Announce Type: cross \nAbstract: Despite remarkable performance on complex tasks, Large Reasoning Models (LRMs) often generate excessively long Chain-of-Thoughts (CoT), inflating computational costs even for simple queries. Existing efforts to mitigate this inefficiency typically rely on discrete reasoning modes or fixed budget tiers, lacking a principled criterion of when reasoning is sufficient. In this work, we introduce Minimal Sufficient CoT (MSC), defined as the shortest prefix of a CoT trajectory which is adequate for producing the correct answer. We empirically show that MSC not only reduces reasoning tokens, but also improves accuracy across difficulty levels. Building on MSC, we propose Sufficiency-guided Continuous Adaptive Reasoning (SuCo), a two-stage training framework for autonomous reasoning control along a continuous spectrum. In stage 1, MSC-Aligned Fine-Tuning (MFT) constructs MSC data using problem-adaptive sufficiency thresholds that naturally sca","title":"SuCo: Sufficiency-guided Continuous Adaptive Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-17T04:43:17Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.17687"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:26c5a8208ac260ed136eeec11a45800793ef173887209e5963fcc1cd538a6c967f2a5957af2852eceb17b927a095dbe2aa4662a4a8f878cc494040a30aeee305","signer":"crovia.substrate","subject":{"observed_at":"2026-06-17T04:43:17Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.17687"},"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":"6d74c7f8db9d236959cd0c29108bb53781aaf4ba8ea09b3260215aef9357d5e5","leaf_index":230996,"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":"629577759ce6f8a80d4f4189e930cac37ba9dda594b4e9713c1c6c44911f3326","side":"right"},{"sibling":"a5e63af63fc76f713f05b075f5a00f2bcdb2a7af9c3fb8fefb85d181450c3d9e","side":"right"},{"sibling":"7141b39d5a0951a7819deb980ec09aa0e1b93d768a3dcf3de8306ad78cd81b57","side":"left"},{"sibling":"877c8f892abbe1ab88d2e30ad3aaee8ae3f32c06670b543160be3363a1a8fb7a","side":"right"},{"sibling":"5e77d6396e1cfd34095b5670f9fff36ce3601e2b5fb5645bd9d8e62e9f93b3d2","side":"left"},{"sibling":"b81e03292fa07ff830b444c07ef37ec24747d2035531f28f436dbc6110f3590d","side":"right"},{"sibling":"8daceae0255c786ffdef12a608da0c1a09b9a2ceedfcc067120bfd86b4ab9952","side":"left"},{"sibling":"ce828166a6a4fc2ff2681c985a56053a1f8b683cc245e0b232fa5939310b3ad9","side":"right"},{"sibling":"ebbec9ce4bf43a3f5f71e2c07df4c91301abefa2da727a4d748099a74e980bc3","side":"right"},{"sibling":"1d74941c32baeab8cad08f8700cb49427d8256f231534f2a225b2bb3e84e4ff8","side":"left"},{"sibling":"d5b9f8b1a2c9f6a46e17982dfbe6ce1f3b5fa4e730220397f2253d114dcc8486","side":"left"},{"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_39d2c668f2082b6487c64cfd265aa52b8d95fce4d4629b3fdae04846553a3081"}}