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Beyond verbatim reproduction, models can encode subtler traces of their training data that never surface in their outputs yet remain exploitable. We study this regime for Rectified Flows, which are increasingly used in deployed generative systems. We analyse the interpolation path $X_\\lambda = (1-\\lambda)X_0 + \\lambda X_1$ that defines the Rectified Flow training. We show that a gap exists between the reconstruction of train and test data that follows a bell-shaped curve over $\\lambda$, wich accumulates during training, while the validation metrics remain stable. The signal has a maximum whose location we derive in closed form under Gaussian assumptions. We validate these predictions on both audio and images and show that the bell-shaped structure is universal, while the peak prediction holds when our assumpt","title":"Where Rectified Flows Leak: Characterising Membership Signals Along the Interpolation Path","url":"https://arxiv.org/abs/2606.07271","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.07271v1 Announce Type: cross \nAbstract: Understanding what generative models retain from training data remains challenging, with implications for copyright and privacy. Beyond verbatim reproduction, models can encode subtler traces of their training data that never surface in their outputs yet remain exploitable. We study this regime for Rectified Flows, which are increasingly used in deployed generative systems. We analyse the interpolation path $X_\\lambda = (1-\\lambda)X_0 + \\lambda X_1$ that defines the Rectified Flow training. We show that a gap exists between the reconstruction of train and test data that follows a bell-shaped curve over $\\lambda$, wich accumulates during training, while the validation metrics remain stable. The signal has a maximum whose location we derive in closed form under Gaussian assumptions. We validate these predictions on both audio and images and show that the bell-shaped structure is universal, while the peak prediction holds when our assumpt","title":"Where Rectified Flows Leak: Characterising Membership Signals Along the Interpolation Path","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-08T04:44:02Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.07271"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:316408b94a8779e940ed4f01655e3db444e530bac57e832f380852315f216bdbc742a014fcac42a16846c1e21ece770162516d5487a29ef8c4236d1bacbfab03","signer":"crovia.substrate","subject":{"observed_at":"2026-06-08T04:44:02Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.07271"},"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":"bc7a0f3da7113a84db4a1edec61b209544b781bdef57a9b2077d5910faffc72b","leaf_index":223775,"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":"af29da5d5fd26863aa1239dec2ca4312482ed07e7990c2c5de5d729fae5eb4a1","side":"left"},{"sibling":"a12a1bc9a290546004ca52ca2cc85cba996f34ce44d4129f31e52f42821db26d","side":"left"},{"sibling":"1b67b2c3c20966eeec1366db9b6a3a583801101b9868073f473d49932353cab0","side":"left"},{"sibling":"2267de9fb9ed99119e80ae43a73467b1ce0d916a958082dcc39bb01815439fbb","side":"left"},{"sibling":"a38264cf71ddffc043539fed9238d2a29e6f104d24b527b463d9c26cff51b026","side":"left"},{"sibling":"b7b453ef2baf0d34e6ebbd1fa44cad77319e644524315b1f13ce29253a2c9015","side":"right"},{"sibling":"4e304d5d7910cf045b4d600075b2e1b6a8e413ccb358cfc3bad788ceebcc2de9","side":"right"},{"sibling":"4fcf914698d33c1c26df7cb3719b9425a51cc354d8550fca9c3f04fdd2314f2a","side":"right"},{"sibling":"fad4d9627e4b025e7840b4e896082fb8291cbf1a4c05653b3a789c8a4205d4b5","side":"right"},{"sibling":"e8dcea313a54920d83e4f72d5a4223f986c719f264241d171c4712efaaf1fc54","side":"left"},{"sibling":"5480e1ea31f4744f9bd7c4261771fe51f2cdb01e705cc17320bfc202d935ca12","side":"right"},{"sibling":"24fdc29d461691aedb6fa920758206b5bb43851f477ef7a04c34aaed84b8971b","side":"left"},{"sibling":"036922da4e1e2c46d948f070454bfad299b7406fb00735ea9d8bd1e687f5f445","side":"right"},{"sibling":"533d82482604463aa4a281b9d8b85917b383b7c5f924b2b494039524c55e8797","side":"left"},{"sibling":"b2590791b920ca2a4ed39de126d2c0b1a10d9e7e62f572f12425f214e767b6e1","side":"left"},{"sibling":"87c6b850dfec08ac35a693d9db3a3315250a68adb1cfab9b1015f212b63b15bd","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":224761,"merkle_root":"e9f7b49b652e869ab97ffba9c5a31356b2d0e3dc5d00bb28944adf737c46b1e7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260609T103805Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-09T14:15:34Z","sig_algorithm":"ed25519","signature":"8ad8076fb12c8e486ae1d1559a9a7ba8e2ee996a9ad3d8ba7bcdbdbd88ab3a15bcb429707aca6d3e9d8b97e2ba755b3dcc77b1abb6601ccb829842719a6fb30d","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_ba76273fd66a1d5078f8cf3d2aa61685afba85bd24a9aa0df440e78fb0350905"}}