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The condition is stated for general output dimension $K$, so its sharpness in any particular regime, and its practical implication for the cross-entropy loss actually used in fine-tuning, are open. We give three results that together reduce the prescribed rank to $r = 1$ for binary classification in this regime. First, replacing the symmetric Sard-form count with the non-symmetric LoRA manifold dimension yields a strictly weaker capacity requirement, $r(m+n) - r^2 > C^* \\cdot KN$ with $C^* \\approx 1.35$ under Gaussian-iid features, satisfied at $r = 1$ on canonical setups. Second, in the cross-entropy setting the Polyak--\\L{}ojasiewicz inequality removes t","title":"Rethinking the Rank Threshold for LoRA Fine-Tuning","url":"https://arxiv.org/abs/2605.03724","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.03724v1 Announce Type: cross \nAbstract: A recent landscape analysis of LoRA fine-tuning in the neural tangent kernel regime establishes a sufficient condition $r(r+1)/2 > KN$ on the LoRA rank $r$ for the absence of spurious local minima under squared-error loss, prescribing $r \\geq 12$ on canonical few-shot RoBERTa setups. The condition is stated for general output dimension $K$, so its sharpness in any particular regime, and its practical implication for the cross-entropy loss actually used in fine-tuning, are open. We give three results that together reduce the prescribed rank to $r = 1$ for binary classification in this regime. First, replacing the symmetric Sard-form count with the non-symmetric LoRA manifold dimension yields a strictly weaker capacity requirement, $r(m+n) - r^2 > C^* \\cdot KN$ with $C^* \\approx 1.35$ under Gaussian-iid features, satisfied at $r = 1$ on canonical setups. Second, in the cross-entropy setting the Polyak--\\L{}ojasiewicz inequality removes t","title":"Rethinking the Rank Threshold for LoRA Fine-Tuning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-07T04:43:30Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.03724"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:7669cef762a8d0702cb411aec32bc16f56bfc6b356c9ea4792bb43310f6360826dce4721fd3a843d22ace75ffe5060e8925368389491f4d9fa1c0f4c10e22500","signer":"crovia.substrate","subject":{"observed_at":"2026-05-07T04:43:30Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.03724"},"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":"66bf54145d8fcc772beb0ec78eb9dbc599351f08e996d87189123f903792bb9e","leaf_index":118322,"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":"3e2bcb37ab92dc3ceae05a420565d53fce25567d6613eb77b969bd07c194205f","side":"right"},{"sibling":"0997adf7c581feecfc3517420b43a9e9c32f1103d34706a986007ba115042000","side":"left"},{"sibling":"3a73a94e5547418306d65539770faccdf2f4be6a771d24f0337d0f8f8d955399","side":"right"},{"sibling":"72cfc398067d91301e649077d74d358a872b4ffacfba6edf91f058a16ed2840b","side":"right"},{"sibling":"bb5057ab0c44a195db9d3d6935aa7e67c468a90c937f9533d03fccd78960f0ab","side":"left"},{"sibling":"d3f0f8f917cc535fdafd7262d7572083bec4ab99319b9cd45b1273fde8aa7e68","side":"left"},{"sibling":"d55c45c2d72a75c2e26965d5038dcc3795a5215a1352db031d11fa67366cc442","side":"right"},{"sibling":"432e5b2cf8e49f6f70fd5be7683dbbc02f1ebeff16b82fade70feaeeff078cab","side":"right"},{"sibling":"943780ddf0bc6538ed8b19cdb0e84ad78f5880f72d472b378c67229ade3fd90d","side":"right"},{"sibling":"9e688ad7df5f10379f7d9b9d109c3ea84968c044c36d5562f359706d012cf15b","side":"left"},{"sibling":"8e758a4477dfc0838d2e8ea2bdbd583bc3192683e75fd9cde217ee6a3b2f3ac8","side":"left"},{"sibling":"4219f746e463e594ccd6447debdf736a57e77319b12bcb74d8ece2b5860064c6","side":"left"},{"sibling":"05f89b32c00462e60adf95c1fe4579cdc2791b36e8b17573d8f3b5fd5da95a0b","side":"right"},{"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_2fe2d12869687810aa0a29b8152fa8d934d812f4e396bc3d4909fa4512f208c5"}}