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Most existing approaches focus on special cases, such as prescribed symmetries and exact equivariance, without addressing how to discover more general structures that require nonlinear operators to transform and map between continuous state/action systems with isomorphic value functions. We propose \\textbf{VPSD-RL} (Value-Preserving Structure Discovery for Reinforcement Learning). It models continuous RL as a controlled diffusion with value-preserving mappings defined through Lie-group actions and associated pullback operators. We show that a value-preserving structure exists exactly when pulling back the value function and pushing forward actions commute with the controlled generator and reward fu","title":"Operator-Guided Invariance Learning for Continuous Reinforcement Learning","url":"https://arxiv.org/abs/2605.06500","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.06500v1 Announce Type: cross \nAbstract: Reinforcement learning (RL) with continuous time and state/action spaces is often data-intensive and brittle under nuisance variability and shift, motivating methods that exploit value-preserving structures to stabilize and improve learning. Most existing approaches focus on special cases, such as prescribed symmetries and exact equivariance, without addressing how to discover more general structures that require nonlinear operators to transform and map between continuous state/action systems with isomorphic value functions. We propose \\textbf{VPSD-RL} (Value-Preserving Structure Discovery for Reinforcement Learning). It models continuous RL as a controlled diffusion with value-preserving mappings defined through Lie-group actions and associated pullback operators. We show that a value-preserving structure exists exactly when pulling back the value function and pushing forward actions commute with the controlled generator and reward fu","title":"Operator-Guided Invariance Learning for Continuous Reinforcement Learning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-08T04:43:40Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.06500"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:6339483e82d3a122ad3b24da55c20147dca7640997a8b9be133b3ebab60ee9a5885a7aba69e5b23e0317e5fbd59a7069519424697f3b1d704693383c9d3dbf0c","signer":"crovia.substrate","subject":{"observed_at":"2026-05-08T04:43:40Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.06500"},"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":"6b26d5d30c0932d899aef37200266ccbae443e69ad6778b550770005d7b7c980","leaf_index":120330,"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":"883f302ec5fc4ba3c80108c46c7e97f2e5f451b939258d244c2456e07b0174df","side":"right"},{"sibling":"20835276a3d0853e8ae16916649ecb1b0b81f324fedb7cd0fe675ebfd2c32ca9","side":"left"},{"sibling":"694b1eea16a5b38ebae6c79d81604a6b16a92fbb6a1129c54d0f7ec0635a6e84","side":"right"},{"sibling":"9bc0d62e7585cc164eeb308b6a96811118dc74e9565ab6462d930d5fefdd0498","side":"left"},{"sibling":"1dd410888f5c572059febdba5a7907c59838d5b9b159eb0c9399184179bda760","side":"right"},{"sibling":"ee48c805c85a4e43d4a9d14a4f80b704a7a8eb604db6cb321fb8c6fe08a82186","side":"right"},{"sibling":"ff6dfc3e3819926f225fca4697d75146861a953457867e78f1a01b86559feac7","side":"right"},{"sibling":"621ce3a316503da6017cc9f955ea0dca3f50bbc1e8fc10ed72f522e60e814e3f","side":"right"},{"sibling":"7cb9b06d4f6372fac19d788263daadfaf6def57cc0a73d46bed8b284ec0fe014","side":"right"},{"sibling":"42ade783b0aede9d0209c5be94ac7979e635da84dd65ecb4d383719029bbe8f4","side":"left"},{"sibling":"143f33d3924b3840fd6dd8ba12566fc35bf86189e663ef0ad4884d676f295e3a","side":"left"},{"sibling":"b1ed99341c327c7c9ab2489f40af2547ab3b3b4b6a74fb684210164fb891a413","side":"right"},{"sibling":"6ee3be9bdfc9bee55d32f7dbb0075f02fe87d20887d563d3e300caf36b1b88c7","side":"left"},{"sibling":"8ccd9937a2c0d5c04044d07d1557791b7d07bb31eac41a39a675608d44b38f23","side":"right"},{"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_7980fba83b63cad2b7d293282440320eddff623491efe1eb9d99a8285e6f60e4"}}