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We investigate whether this geometric signature persists in production-grade language models. Across Pythia, Phi-2, Llama-3, and Mistral families, we find that last-layer value representations organize along a single dominant axis whose position strongly correlates with predictive entropy, and that domain-restricted prompts collapse this structure into the same low-dimensional manifolds observed in synthetic settings.\n  To probe the role of this geometry, we perform targeted interventions on the entropy-aligned axis of Pythia-410M during in-context learning. Removing or perturbing this axis selectively disrupts the local uncertainty","title":"Geometric Scaling of Bayesian Inference in LLMs","url":"https://arxiv.org/abs/2512.23752","vendor":"arxiv_cs_ai"},"summary":"arXiv:2512.23752v5 Announce Type: replace-cross \nAbstract: Recent work has shown that small transformers trained in controlled \"wind-tunnel'' settings can implement exact Bayesian inference, and that their training dynamics produce a geometric substrate -- low-dimensional value manifolds and progressively orthogonal keys -- that encodes posterior structure. We investigate whether this geometric signature persists in production-grade language models. Across Pythia, Phi-2, Llama-3, and Mistral families, we find that last-layer value representations organize along a single dominant axis whose position strongly correlates with predictive entropy, and that domain-restricted prompts collapse this structure into the same low-dimensional manifolds observed in synthetic settings.\n  To probe the role of this geometry, we perform targeted interventions on the entropy-aligned axis of Pythia-410M during in-context learning. Removing or perturbing this axis selectively disrupts the local uncertainty","title":"Geometric Scaling of Bayesian Inference in LLMs","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-19T04:43:36Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2512.23752"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:1b567b40a7086dfa2bbb80f97d0819ed096fef39e0f1536041280a78aa0a5486fe1ffd522fbd89a6556fd94a0dbb90b454f6ad3f37bf0b90555d4daaf153e202","signer":"crovia.substrate","subject":{"observed_at":"2026-05-19T04:43:36Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2512.23752"},"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":"dc66442df699a1de7aaff41ae5f76ce48005923441e26f98ea60bf1f73f09cdd","leaf_index":143104,"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":"0382fe19207fb46397b605648f2ab3eb8bc86492d83e0797757d94df072e5eec","side":"right"},{"sibling":"a17345e4e205607a63eafb12ffadf38b075b40a24784919d1df0db4c473985b2","side":"right"},{"sibling":"d4d3968186cd77c5365e44e0a69ba75a1e75454ea7b9a663e033a7315714d544","side":"right"},{"sibling":"2c51a8587d98eca25ae38d7a9e823d371944bb6c71d21178706f72edda97f19d","side":"right"},{"sibling":"d0a340c052a6bfab339db17f6821a1c0f96d21af7da733635dd4c3ba6cb7c35b","side":"right"},{"sibling":"0a502c912fd7aa17ca64a16c7636f401b8691b294db6325cf045433da1f21fb0","side":"right"},{"sibling":"85fd29731e65c36b4f2a5f4f39c039cb540b551881d70cd5789c3e56208c17c8","side":"right"},{"sibling":"4b6dab10c74fb2a96436053a067988cc08e1b2f810f1362c194b7439e788d860","side":"right"},{"sibling":"b986468aca0b7804b8a608705cafc663139e79ff550a69be0b9dd58ec70714f7","side":"left"},{"sibling":"db97141c585f6a1e6bebe92b3ea300ea0f38a2321ca286d85850b11b2dd162a6","side":"left"},{"sibling":"202f1bead178ef3785968d50d3d188264a95192a077654c331612e04a34cbfbe","side":"left"},{"sibling":"72249c8c8b068386e35d16f4bd0bbeb9ba820ca217ef0f0d28396c9fe493f5f0","side":"left"},{"sibling":"ea64599340f7ffdf17ad0cbc1d9401ef8870a347e3847bdc106d06b1673df09c","side":"right"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"4db1f363729507e27a60851cf6ed334d7b9acdef194ed7d419aba4d2bd367a4a","side":"right"},{"sibling":"a86ee18c45e7fcc408b6007eaece05aa75b2d9ae30252e9e878462b4dffbef7b","side":"right"},{"sibling":"1d18e7663d43ccff0122ecc7ee12645bb16afb607b218e81b1ea2408f863cb78","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":143302,"merkle_root":"999156d40a7c61d9ddd52b7338f3cbda3e68f53bace070c7b616ea194e23b123","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260519T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-19T05:37:30Z","sig_algorithm":"ed25519","signature":"b1a252cc66ff32bed1d10dd88a6b2a200e3856d3dbcfcc4ee55e02e00f3d548e854ed9c544704b222bd5d315492c4a935ba2d90d727c585a67899b0ad602fc05","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_fc579e76bb16be288874ee68a1e63f8f853876f4296fac34ac1886bf2c04a4e4"}}