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Standard GRPO-style training updates the model using only the current step, while full multi-step lookahead can give a better update direction but is too expensive because it needs many backward passes. We propose Gradient Extrapolation-Based Policy Optimization (GXPO), a plug-compatible policy-update rule for GRPO-style reasoning RL. GXPO approximates a longer local lookahead using only three backward passes during an active phase. It reuses the same batch of rollouts, rewards, advantages, and GRPO loss, so it does not require new rollouts or reward computation at the lookahead points. GXPO takes two fast optimizer steps, measures how the gradients change, predicts a virtual K-step lookahead point, moves the policy partway toward that point, and then applies a corrective update using th","title":"Gradient Extrapolation-Based Policy Optimization","url":"https://arxiv.org/abs/2605.06755","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.06755v1 Announce Type: cross \nAbstract: Reinforcement learning is widely used to improve the reasoning ability of large language models, especially when answers can be automatically checked. Standard GRPO-style training updates the model using only the current step, while full multi-step lookahead can give a better update direction but is too expensive because it needs many backward passes. We propose Gradient Extrapolation-Based Policy Optimization (GXPO), a plug-compatible policy-update rule for GRPO-style reasoning RL. GXPO approximates a longer local lookahead using only three backward passes during an active phase. It reuses the same batch of rollouts, rewards, advantages, and GRPO loss, so it does not require new rollouts or reward computation at the lookahead points. GXPO takes two fast optimizer steps, measures how the gradients change, predicts a virtual K-step lookahead point, moves the policy partway toward that point, and then applies a corrective update using th","title":"Gradient Extrapolation-Based Policy Optimization","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-11T04:43:50Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.06755"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:f45f03cd2bcb6113e7e723a56398723d7912fed2531804b532abb0657858a59727330999b19c857019c26b58b5619903f948e7e01acfd6e9906d74629d83970c","signer":"crovia.substrate","subject":{"observed_at":"2026-05-11T04:43:50Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.06755"},"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":"b7a5077464161ebcdac5bd6484a6dbd046068887f72f27dd27a9fcbbc74187a2","leaf_index":126364,"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":"0130684db14058623a1d5609b1a371478c43d4946736c7b6226f301d26e3b8c4","side":"right"},{"sibling":"8c8c1d74469829a0a997a882b835b9d106188eb0f370e7d356874a689407fccb","side":"right"},{"sibling":"968b291f81a5c166dd6a29c51ae5db7826443fcf8a24651694ea9cb1026306c4","side":"left"},{"sibling":"4ba95a6de984e49f852d40d733ab25cc1b6b713b0174e892161a2db390428ff3","side":"left"},{"sibling":"3d486952b5b10eff0a7a00ce77e86a22ca90e9799cc14565a796ee964fa50ea7","side":"left"},{"sibling":"b0ecb971a74e92d84fbc401f296958aee5eba51c73e8dd852d86159cce51cdaa","side":"right"},{"sibling":"155d707ea31ac86e33282c61cf9de432c647507cb7e49b48d8091a83db1fa305","side":"right"},{"sibling":"1affc3278ec6295fa1ae074997c4b0457549f963f09f201e1971c53031c8615e","side":"left"},{"sibling":"d2135da61742c6387f57e5dbeb0f84ba6602653b50838e32a22e26e69c963d0c","side":"left"},{"sibling":"fe7cf0b54f5bf9492865fdc338944ef352cdca1a4f9f377e2991ace599a3bb58","side":"right"},{"sibling":"1a581be91236d1f25e8d47fe5efa0e2b51b7f0f6d706ef76a9093067688e5d56","side":"left"},{"sibling":"878cc30108509c9fa1fc52705a216f519d73b647916fcbdfc30a389934d3364b","side":"left"},{"sibling":"ae7dfff36ba07d9f48c36c28a341482ef244ee13cd0efd49aee2bbef2fd65f87","side":"right"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","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_a0a4b26776210271bd9ea22015976bf576542ff6774d6ebc6a025cb23a2a0384"}}