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However, most existing CoT methods use reasoning chains mainly as inference-time prompts, while the generated reasoning traces are rarely reused as semi-supervised learning signals. In this report, we define \\textbf{Semi-supervised Chain-of-Thought Learning} and propose \\textbf{Semi-CoT}, a simple framework that uses unlabeled questions to construct pseudo reasoning supervision. Semi-CoT samples multiple pseudo-CoTs for each unlabeled question, estimates answer-level semantic entropy, and selects low-entropy reasoning chains as reliable pseudo-CoT demonstrations. This extends the self-training view of CoT from inference-time refinement to semi-supervised pseudo-supervision. Pilot experiments on AQuA, SVAMP, GSM8K, and MultiArith show that the entropy gate selects high-precision pseudo-CoTs, with pse","title":"Revisiting Chain-of-Thought Reasoning under Limited Supervision: Semi-supervised Chain-of-Thought Learning","url":"https://arxiv.org/abs/2607.01511","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.01511v1 Announce Type: new \nAbstract: Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent reasoning capabilities in large language models. However, most existing CoT methods use reasoning chains mainly as inference-time prompts, while the generated reasoning traces are rarely reused as semi-supervised learning signals. In this report, we define \\textbf{Semi-supervised Chain-of-Thought Learning} and propose \\textbf{Semi-CoT}, a simple framework that uses unlabeled questions to construct pseudo reasoning supervision. Semi-CoT samples multiple pseudo-CoTs for each unlabeled question, estimates answer-level semantic entropy, and selects low-entropy reasoning chains as reliable pseudo-CoT demonstrations. This extends the self-training view of CoT from inference-time refinement to semi-supervised pseudo-supervision. Pilot experiments on AQuA, SVAMP, GSM8K, and MultiArith show that the entropy gate selects high-precision pseudo-CoTs, with pse","title":"Revisiting Chain-of-Thought Reasoning under Limited Supervision: Semi-supervised Chain-of-Thought Learning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-03T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.01511"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:bdd09e479974d095d455f4039b19e7100e22460361ddb8bdb81ba808b5dd0bd9cbbdf74a7c6416ce5eb938fbdaec6eb26c3b4a277511ec50408d6b2c98b7a90b","signer":"crovia.substrate","subject":{"observed_at":"2026-07-03T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.01511"},"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":"faab14d8639a9acd318e46182b9f080e0259e2cb4ba5c9074d7668dee5bc85f9","leaf_index":275347,"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":"19531e5c1446fff58538d406961d527d8234600e1ab67f944878638528abb413","side":"left"},{"sibling":"a956543db217e884ecd7da5842db8c0a17a4d73e516f8439d8950d67c6a131dd","side":"left"},{"sibling":"401d2a852ec0168e6bdfbf0a2cd50ee23462d831ad651bbbc2c781c3e4ec65d0","side":"right"},{"sibling":"b62794f93be3ee6c8eeae3a8bcb5bd3d33f4b02a49a93fdbb3df0d3b96483bef","side":"right"},{"sibling":"7e59aae2362757391cd72c8d5e1bac54afee04e0dda7f3c5062da7bc1c130d72","side":"left"},{"sibling":"b08b6abe334210fa93c8ff98b879ec0c0d19a9a4a6d894942756c60b1eaf5240","side":"right"},{"sibling":"90e9fb2a20374342836f11695e291756a1f8a0197a80f5da7958594a976dd668","side":"right"},{"sibling":"fd055e725b36f5bebbaeb18583f9d7011c4d8c2a608a11cbd2c166cd895e7a85","side":"left"},{"sibling":"e1a65581e9d68211aa8ba0d138c8d2a4e80afd551e6d1b00c4575c39085df705","side":"left"},{"sibling":"92c062f377cd53076b8dfe55c25ab217059e20113433673cc5747b9348b07e01","side":"left"},{"sibling":"e36f7633c67452f41a7377a7bec9b2d454442688d26539321eebf92cae9db0f0","side":"right"},{"sibling":"4dbd8247ba08a5432c7d6540711da9acb2f59e6189865aa8552dee37f69286a9","side":"right"},{"sibling":"41cd1885dc3fcb51e49eeb887d6d22ec2cfa58df0e4f8d7c7dddf3a1b0ce8249","side":"left"},{"sibling":"8a09562f6b247c1c3cd1fea36cb3b8f1cf5c575479dd514573856a380a964bf5","side":"left"},{"sibling":"723981908169653ca6d835aa9b8381a8c7ad3e3e3830d0792bc32032cda615ee","side":"right"},{"sibling":"c0594fa1ee81d5f019cccc7b5e51af603c6d7e43995498c451012060c7d06165","side":"right"},{"sibling":"4de6a2fb22efbb50c84dc62abeb0f2cbc8c663a9540aeba9e758ebfdfe3e86dd","side":"right"},{"sibling":"fdbb3519f8dc411a4043dfb5abdbfea5441e130326183ac2247c42584033f152","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":275799,"merkle_root":"2581d0d6e5fa345cdf2e8ab3b191ace76d6b14189901ab0e4c2291ca1d1ae1e6","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260703T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-03T05:38:09Z","sig_algorithm":"ed25519","signature":"e44a386a5ae00c0e7fc67b1179bb9060bf0fefc006e454fec70e27668182ff497d1e2faf0c3b22de0917beefb7c80e880dae925a3f67e1b16aa0eb44bf947407","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_93d2dde3273ec498f67e6415f002e8f208992eaf8293651f270ddc2fc1c3db25"}}