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Yet the standard policy class draws $K$ independent samples from a single answer distribution, so attempts often collapse onto near-duplicate reasoning paths and waste the budget on redundant rollouts. This failure is costly in competitive programming, where many problems admit multiple distinct algorithmic strategies and pass@$K$ requires only one correct attempt. We propose Coordinated Pass@$K$ Policy Optimization (CPPO), which turns pass@$K$ generation into joint exploration over strategies: a planner emits a tuple of $K{=}4$ alternative high-level methods, and a shared solver attempts one solution per method. CPPO trains this joint policy with a multiplicative planner reward, $R_{\\mathrm{plan}} = J_\\psi \\cdot R_{\\mathrm{out}}$, assigning credit only to valid strategy tuples that lea","title":"Cast a Wider Net: Coordinated Pass@K Policy Optimization for Code Reasoning","url":"https://arxiv.org/abs/2605.27000","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.27000v2 Announce Type: replace-cross \nAbstract: Repeated sampling with a verifier is the standard way to allocate test-time compute for code generation, with pass@$K$ as the canonical metric. Yet the standard policy class draws $K$ independent samples from a single answer distribution, so attempts often collapse onto near-duplicate reasoning paths and waste the budget on redundant rollouts. This failure is costly in competitive programming, where many problems admit multiple distinct algorithmic strategies and pass@$K$ requires only one correct attempt. We propose Coordinated Pass@$K$ Policy Optimization (CPPO), which turns pass@$K$ generation into joint exploration over strategies: a planner emits a tuple of $K{=}4$ alternative high-level methods, and a shared solver attempts one solution per method. CPPO trains this joint policy with a multiplicative planner reward, $R_{\\mathrm{plan}} = J_\\psi \\cdot R_{\\mathrm{out}}$, assigning credit only to valid strategy tuples that lea","title":"Cast a Wider Net: Coordinated Pass@K Policy Optimization for Code Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-02T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.27000"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:376d9566b98b9a17e8d4e74b9588ff351aebc8c5c390274288fc7b37fa2b6012aa6ed824417fee247db88f150d266d50b5611508446b93517d13fa19beca9e01","signer":"crovia.substrate","subject":{"observed_at":"2026-06-02T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.27000"},"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":"60d1d310cab698c34dc631e85f3211c88986c0fff7b40b579214380d56278e9b","leaf_index":206088,"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":"f9d3b0015700d032720b2355879b4a376e4990314d6580a3d8e79a6859c89b4e","side":"right"},{"sibling":"225588c6b67ed67d3e2b7a09c4fa817567aab8928bc37beded2460de95cd16ed","side":"right"},{"sibling":"2e42b8eff9cf15c7dc496eaae0edcb155039b3f6d381e2538e9d7c237317ea14","side":"right"},{"sibling":"3f04de0ed8674b8cc0481170eb5c76dd50f039b7cb2687e1863b53d5062da260","side":"left"},{"sibling":"fd4db5dd1075fe567e72d4e0f51ae13acc9a50dbdfb2f0443b9f221a56091012","side":"right"},{"sibling":"c4bfd63492cdaa1d6ee6b539c444ec0a0a990579a86f49b56e17e430ba1e0cfe","side":"right"},{"sibling":"3063e356890554036d4f0a6e91cc823b3b649b6b41cb63db792f9cd6e94149a7","side":"right"},{"sibling":"a9aea7550ccae0b975ce218792c15e48b92501c5247043b8b2d47da30deee4f9","side":"right"},{"sibling":"4d5351522794a5e3aa2cb050bf38e3174f383de817b6b88500eed49d70c3b786","side":"left"},{"sibling":"5e1949edfad76bc6a73d008dc8be8a0c6fe4a7fb64c8beaf70e5023ca11d35e0","side":"right"},{"sibling":"e4bd1aaaf3f336d9b072b4d1fc234246fc3cf2874ca873b7741c03eaf97911f2","side":"left"},{"sibling":"e6adead8216db4cae92f0a036d53baebf30eed95a99c0d10758aa75bb7780f2f","side":"right"},{"sibling":"1acc2b7ff453ffd8c97b80ae4db5358780f0c6796874fd75403791dbe99f8cd7","side":"right"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"5f86f58c28b1a86ae06dfff4666bb9fba8866021a81fd4f1d200aa9af4722dfb","side":"right"},{"sibling":"f6cc6f94f6944ae21390afc65ac9e91dc31f84ee6e060681bba5ae08058294bd","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":206226,"merkle_root":"d2a6d32b13cbf343fb143b21a756d0533864ae6577a376ee84ba867b949207ec","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260602T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-02T05:37:46Z","sig_algorithm":"ed25519","signature":"abd9956cfb19dd1fb8142c46a220bac2514848c6abb0e79b8b0940206cc3ebb00894d4daaf9f786427f82a7cc12482e7fda79054ebb06bceaa9b4b97e23fb30e","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_f9f99cd57093a020aee264df989202825ba6e3248e2ecaec82e5ff8af638a7c3"}}