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In this work, we introduce Bayesian-LoRA, which reformulates the deterministic LoRA update as a probabilistic low-rank representation inspired by Sparse Gaussian Processes. We identify a structural isomorphism between LoRA's factorization and Kronecker-factored SGP posteriors, and show that LoRA emerges as a limiting case when posterior uncertainty collapses. We conduct extensive experiments on various LLM architectures across commonsense reasoning benchmarks. 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We identify a structural isomorphism between LoRA's factorization and Kronecker-factored SGP posteriors, and show that LoRA emerges as a limiting case when posterior uncertainty collapses. We conduct extensive experiments on various LLM architectures across commonsense reasoning benchmarks. With only approximately 0.42M additional parameters and ${\\approx}1.2{\\times}$ training cost relative to standard LoRA, Bayesian-LoRA significantly improves calibration across models up to 30B, achieving up to 84% ECE reduction and 76% NLL","title":"Bayesian-LoRA: Probabilistic Low-Rank Adaptation of Large Language Models","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-28T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2601.21003"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:591f2c961b1fb9bfe8993d0bef92f37b448945b8bfccff4fa3126b85d3de190e1493c2cdb76bd0220df0e6868fb66abc6dda64e69a2a279c0effa836d205610f","signer":"crovia.substrate","subject":{"observed_at":"2026-07-28T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2601.21003"},"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":"40eff5f6b270ab836eb0dee0f839ec09456306b6da00553fb41c7fed6e8759f3","leaf_index":360726,"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":"0399afa1c652ea699e67dfad3729aa33c5eeb648575850241514b647e4419eda","side":"right"},{"sibling":"3bf09823aaf90f585d698033b92e5008a2915019c86fbd069b6fb9d89d1148a7","side":"left"},{"sibling":"181e15573d3ba29a5f5118878c72af3525f861aed527e5060d537dcc3f7f2112","side":"left"},{"sibling":"5c943c4042c6266ed7f54b5ab3aeb485e1a11ea96b93af674d52238bc61f26b9","side":"right"},{"sibling":"b74542b5f40827eb44692b9c68a7de2c10c32743c9bad4f57147027649293955","side":"left"},{"sibling":"3e4968f900e536361cecc93a0df80981cf8da335339dd547beda582609e629b3","side":"right"},{"sibling":"c055cde9457517dcbc597b5ba365b33ee313ae69f23793917b237a63c02a9c03","side":"right"},{"sibling":"80654268ff95f1daa72785465b969eee9ea2b22da6f8dfc0d2cf6148d4718a52","side":"right"},{"sibling":"f05fa4d2088913dc5410109b6c9f2c28b5e413f06a98f46cd68973c567c3b416","side":"left"},{"sibling":"fe03c6d0b083c4097049d7fc6d7d08dfdb05d9c198b2786336689712d66eabf0","side":"right"},{"sibling":"590ea76fdfc1b9e8072055c378be3182f916709e8d06bd955232e650a7188b86","side":"right"},{"sibling":"d92781c59301ffd5bfb0bad75d9fdf6d73879f715518149d383f7362213e0daf","side":"right"},{"sibling":"f315303d4402b57497416d48eb4c4bb50405b40862d41c7caf318cb3d29c5237","side":"right"},{"sibling":"36973eb5f586cd67e0c0dc055dd87e734aa544c35d4400d2c9f932f8ef8fb27f","side":"right"},{"sibling":"e39f7900355489c4718b21cc2d3d06382e1d2f22b864d10be9ebc9d498b279a1","side":"right"},{"sibling":"1f9a970b25dd938c98cabc9e0a55c5a6f46292b9fa37cc89d90ef0cbb1e05a8c","side":"left"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"3b50864499c874394ea0928567747666eaf59b01380e46cd52164ec5acec0f71","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":361008,"merkle_root":"3065e8369ea437c06beba806dc4e4bb159979adeb21fe632242c1906a7204647","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260728T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-28T05:38:48Z","sig_algorithm":"ed25519","signature":"9141644407577a82611c1579110f667de2d46dc6b93c6322edf26f4c3056ea99f0e56502853908e30d87c38bcf95eb6e0ab5130525aa51505bd6f61938120609","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_c82737a90506f59742c0b98ed1ef0d879b0991efa7b6a7c81f8399bb61587f93"}}