{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_0160d289c837b7da2c709f9cf3495d12056557de675ff90b63c4ece82c8b3532","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_0160d289c837b7da2c709f9cf3495d12056557de675ff90b63c4ece82c8b3532","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"ec85b79c0e6d5a91d5ee0511a0b56b4838a23346813a953d818bcae43b224a01","published":"Wed, 01 Jul 2026 00:00:00 -0400","receipt_hash":"ec85b79c0e6d5a91d5ee0511a0b56b4838a23346813a953d818bcae43b224a01","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"ec85b79c0e6d5a91d5ee0511a0b56b4838a23346813a953d818bcae43b224a01","observed_at":"2026-07-01T04:43:38.812993Z","parent_run_hash":"0e10ec7d671a375a4e18d8645653df2b4352c82fe16fae2a400af6f7634d6699","published":"Wed, 01 Jul 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2605.09235v2 Announce Type: replace-cross \nAbstract: One-step generative modeling has emerged as a leading approach for amortizing the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and unbounded gradient variance. In this work, we establish a theory that attributes this pathology to a misuse of the conditional velocity field. We show that the conditional velocity plays two distinct statistical roles in the loss: both as an unbiased regression target and as a Monte Carlo control variate in a Jacobi-vector product, with the original MeanFlow loss assigning the wrong coefficient to the latter. We derive the optimal coefficient in closed form and show that a family of fixes in concurrent works corresponds to different practical realizations of the same optimum. A controlled sweep of this coefficient on two-dimensional benchmarks and on a latent Diffusion Transformer recovers t","title":"On Variance Reduction in Learning Mean Flows","url":"https://arxiv.org/abs/2605.09235","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.09235v2 Announce Type: replace-cross \nAbstract: One-step generative modeling has emerged as a leading approach for amortizing the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and unbounded gradient variance. In this work, we establish a theory that attributes this pathology to a misuse of the conditional velocity field. We show that the conditional velocity plays two distinct statistical roles in the loss: both as an unbiased regression target and as a Monte Carlo control variate in a Jacobi-vector product, with the original MeanFlow loss assigning the wrong coefficient to the latter. We derive the optimal coefficient in closed form and show that a family of fixes in concurrent works corresponds to different practical realizations of the same optimum. A controlled sweep of this coefficient on two-dimensional benchmarks and on a latent Diffusion Transformer recovers t","title":"On Variance Reduction in Learning Mean Flows","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-01T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.09235"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:40b17a06d738d5f9fa65441be420f8838ae48cca60f675e45d0e3c2ea17f1e37ab7300a225761cecbd6c1afa55b14c960540ca67c7908cce827a9c8cd655ba0b","signer":"crovia.substrate","subject":{"observed_at":"2026-07-01T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.09235"},"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":"8413a3f72f2a31715a2c64d5439fe699cd85c1480774b9c4fc8c2f72d8e04f95","leaf_index":268717,"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":"c499d0d4a581823b497b5222010e8ec270208f69acd6252fbc548ac9e8861f04","side":"left"},{"sibling":"7d7752a085d2d7cf88748bedbf4016f81babb6e6222e0a13416fdf7a70d3f8e5","side":"right"},{"sibling":"2d33cf590382a7c66df7cbf5a5eea59eef45c5787f301458835f26898847345d","side":"left"},{"sibling":"42d16bad4f7c2800e3e3accea93b27a8ad5a1a8d02585cbc8b1f9af8ca3e2d98","side":"left"},{"sibling":"d9b873370c92e4dc69826859ea55f9515cd72414e290a0e766255ee3ffed8394","side":"right"},{"sibling":"7a1f969ec5b4bf9f076acec001dab3c248a82031e6ffe639dc95059da328f9e9","side":"left"},{"sibling":"4b40722a8676aba99a1cededb6270927be9c50d0f94c30aa826fa53a7a32b4a6","side":"right"},{"sibling":"58c3799598a549d54786b91e80a9c8daea4edcb3c27437b6b16ccadf6dc2889e","side":"left"},{"sibling":"4b14e8ccae46b588748944ffaf410222f66cebc2ac58d936cbe16847b7be9508","side":"left"},{"sibling":"bbd9a20451913e8c7b910f616d5661d9b281a94af70d201ba50b3112d429521b","side":"right"},{"sibling":"85af80e45748c1e0da1e2f42d9d66da8996016888a034f20eb17ff0a73b69eab","side":"right"},{"sibling":"4575fde969d1d9a2984cc01a37ac8441238f74527d42874272dc5582dadebb4f","side":"left"},{"sibling":"f536de281672cbf0b583a3dc46faef1de2823b72bd9265c7b60e889131cc268d","side":"left"},{"sibling":"95b8b0f67237052a17c41fa8cbdce2b79bcb5aeeba3fdb239d4c4497e598115d","side":"right"},{"sibling":"c2f351f771cee329448890504d9436792ba482e50250ca9a19289311131f96c8","side":"right"},{"sibling":"c39bfb2e911ca37ae997690bfc04128ae32e6806ee1cb3908781a7e6685022a0","side":"right"},{"sibling":"a101b4c60ef6854ac3d750eef02d8e2e06c153284b5ecb7111302f97eb129797","side":"right"},{"sibling":"eae2a3de5cb35455ad60125e196cfadaba8a590c53146e95028469f53f70349c","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":268860,"merkle_root":"d098f25810d0569730b6c0e170d57f329a70359d483b47874b5f2fc51d23de65","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260701T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-01T05:38:05Z","sig_algorithm":"ed25519","signature":"64f37f0e3df0556baa55b924a736cab8005643fa0ab65b503f22407de30eab293e6e0bd62904270fda38d05084bb350c8c0d0aadb2c5a6bae5f1c54598e6d30c","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_0160d289c837b7da2c709f9cf3495d12056557de675ff90b63c4ece82c8b3532"}}