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We introduce LLQR+SAM, which combines SAM with a learned preconditioner obtained from the recently proposed LLQR framework, a second-order method that recasts steepest descent as a layerwise linear-quadratic regulator problem. The preconditioner is updated sparsely and maintained as a slow exponential moving average, so it captures a smoothed, low-resolution picture of the loss landscape geometry. The SAM perturbation then operates on top of this learned geometry, probing curvature at a faster timescale. We show that this two-timescale structure is not merely a computational convenience: theoretically, the preconditioner amplifies the SAM escape signal in directions that are flat under the average geometry but locally sharp (poth","title":"Navigating Potholes with Geometry-Aware Sharpness Minimization","url":"https://arxiv.org/abs/2605.16134","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.16134v1 Announce Type: cross \nAbstract: Sharpness-aware minimization (SAM) encourages flat minima by perturbing parameters along directions of high loss curvature, but treats all parameter directions uniformly, ignoring the underlying loss geometry. We introduce LLQR+SAM, which combines SAM with a learned preconditioner obtained from the recently proposed LLQR framework, a second-order method that recasts steepest descent as a layerwise linear-quadratic regulator problem. The preconditioner is updated sparsely and maintained as a slow exponential moving average, so it captures a smoothed, low-resolution picture of the loss landscape geometry. The SAM perturbation then operates on top of this learned geometry, probing curvature at a faster timescale. We show that this two-timescale structure is not merely a computational convenience: theoretically, the preconditioner amplifies the SAM escape signal in directions that are flat under the average geometry but locally sharp (poth","title":"Navigating Potholes with Geometry-Aware Sharpness Minimization","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-18T04:43:11Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.16134"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:a724a9ace142af840b2446d0d1709065dc134e86197b6bd9cadf9d21a6de69fa82b4ba5db5f777d5eb617d8461bf6c5522af1fba42605435010764ed50f8430d","signer":"crovia.substrate","subject":{"observed_at":"2026-05-18T04:43:11Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.16134"},"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":"3f566df05e2dfdfbca7959bf7253311c87f5852b326532670d48ccb91e9370fe","leaf_index":140687,"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":"2e3ef23c71b6d72372f43c982ce68bdb000e16d293c132598251dcc9117455ae","side":"left"},{"sibling":"6aab864fba4b19919c4b0871552ee01ca0019c51cd46eff51f2d6684d0911231","side":"left"},{"sibling":"cc46a9dd6dfbd6eed27cbeec306d08f522389f0177084da6b75856f37c15e099","side":"left"},{"sibling":"454650648ca38fe6abf4b5a198e19912e0f1aeec5adc5d01c7375fab184b56db","side":"left"},{"sibling":"58683ddf35d7c3cb9115208c0129b2442e62481772681c4cb2b70868d4f555a7","side":"right"},{"sibling":"ccfc733d99355b280b7859d93aaff9b798cfb41eee6381849bd91a1ab4a17966","side":"right"},{"sibling":"c506700de9fc9cdf32017abe38d10a05938325fe576d9c37ea5fba2a436c2162","side":"right"},{"sibling":"30c60828b6b0ade79197e585b88c06ccf4f348c1e62fbf6710d89ae2c2e9dcfb","side":"left"},{"sibling":"6bedf73520cf3dd8758d8bdedf3be245de9aea97abd42934aae25539176ae1b2","side":"left"},{"sibling":"07abc3bad689e74e6304772503dc9372a118e6f66883b8e88c43414efddac063","side":"right"},{"sibling":"28b78fb112bcf26b6801664db97eb8f52a9bccbf0a7ae6766e11845d443692df","side":"left"},{"sibling":"68d0a4634c1460a19c92edd9480df3aa733b814463e7420d1e14471bf61b2f83","side":"right"},{"sibling":"8af64f275b862349aa3bbb9d5cd7fa9a7fdd5620af3bf1b36b2a4519b0b53bdf","side":"right"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"b98c2afadb358e5387e88f19588f8343a81b488d9b44a6f7e57a032db3a1b030","side":"right"},{"sibling":"11b0c1591747f09f7c8971a6caa19befcd81317ca9dfd417b143234df4e10c79","side":"right"},{"sibling":"87206f3bcc342797c990d87f7235c01f78d32ca59cfaf8ad18d71afc879ba477","side":"right"},{"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":140892,"merkle_root":"6cca56ead155990456b8a014cc50bddbe710f409b26e3d1bfa6fb12b0bfcf6bf","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260518T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-18T05:37:30Z","sig_algorithm":"ed25519","signature":"1e1135f7595f79b14fb11f5fa81a2e17ad31b11b44b427a5e40a7d511cd86447daf492babd368ab571cf26404c8c74c450d460130fca4b064eb2760367489a0f","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_749c4f4658ae16b28e695939b41cf9a22b659dd99f79eb0e43d6c24d151ec760"}}