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These vectors, also known as truth vectors, have been studied in prior work, however how they change when context is introduced remains unexplored. We study this question by measuring (1) the directional change ($\\theta$) between the truth vectors with and without context and (2) the relative magnitude of the truth vectors upon adding context. Across four LLMs and four datasets, we find that (1) truth vectors are roughly orthogonal in early layers, converge in middle layers, and may stabilize or continue increasing in later layers; (2) adding context generally increases the truth vector magnitude, i.e., the separation between true and false representations in the activation space is amplified; (3) larger models distinguish relevant from irrelevant context mainly through directional change ($\\theta$), while sma","title":"How Context Shapes Truth: Geometric Transformations of Statement-level Truth Representations in LLMs","url":"https://arxiv.org/abs/2601.06599","vendor":"arxiv_cs_ai"},"summary":"arXiv:2601.06599v2 Announce Type: replace-cross \nAbstract: Large Language Models (LLMs) often encode whether a statement is true as a vector in their residual stream activations. These vectors, also known as truth vectors, have been studied in prior work, however how they change when context is introduced remains unexplored. We study this question by measuring (1) the directional change ($\\theta$) between the truth vectors with and without context and (2) the relative magnitude of the truth vectors upon adding context. Across four LLMs and four datasets, we find that (1) truth vectors are roughly orthogonal in early layers, converge in middle layers, and may stabilize or continue increasing in later layers; (2) adding context generally increases the truth vector magnitude, i.e., the separation between true and false representations in the activation space is amplified; (3) larger models distinguish relevant from irrelevant context mainly through directional change ($\\theta$), while sma","title":"How Context Shapes Truth: Geometric Transformations of Statement-level Truth Representations in LLMs","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-09T04:43:45Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2601.06599"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:3aa875a3f10bfbba9f3868a87a776daa714e30ace91492dddd4fe26907eb65d42d91417ed407bc0efd0c43e7cb7edc58c76d155296d4486b71dfb15271116e0f","signer":"crovia.substrate","subject":{"observed_at":"2026-06-09T04:43:45Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2601.06599"},"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":"71b5bad793c9b329ddb0dfc6bcf1a49df106c78b0a994220fb125d5f33eaeed2","leaf_index":224573,"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":"bbe61f26ebf792537ccf94b7072c0053011ab9564366e7aa38ee06621b310d3d","side":"left"},{"sibling":"2067578af9e9a2a329ead263a2cbc370a3c47043c4c3dafad58351aefe074f98","side":"right"},{"sibling":"e1b9841a15367f4b3eff3c2c6004bd3c0c21de08655edda34ce22f6151e17073","side":"left"},{"sibling":"47325bea240beac04f8f6ddde9de775513915d1d65f76c93758dd29c42097416","side":"left"},{"sibling":"e5236674cb4b894b7d0f295b862334f7e0a26fe940a4b3d041e2c02264a98c02","side":"left"},{"sibling":"8cb8d803d2ce30194ad0ac084483b71b61aef7a447a22d4937d90f5d6854b6a7","side":"left"},{"sibling":"7e5dbd67aa1e8898289b0ff2e3ec46622c5fc90def2622ec8f9fb42d76c33dae","side":"right"},{"sibling":"ce39e453038de7aa49f7571634d02890601b8ad6700079b4c6e4dc3e1d2e8b38","side":"right"},{"sibling":"f54580a307d4bb82e453931aa73e9a0c590486cb8df06af79ad4674f1c4f6963","side":"left"},{"sibling":"b2df6a4bb3e928f0b447931cc688ae01d2415773a2b07cfed0b1cba689078aed","side":"right"},{"sibling":"b1c9ec856caa0fd46bb47b46f18c59ebcd295d774ca17adb3b46f05d394a6a5d","side":"left"},{"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_39ee81547f7d0c6719ca910f545be849b086f4ff569d4ccd4d8b0177de0a7a4e"}}