{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_2091f13522d971d5b8dd811f2d6322bf3aaf05ad0a532e0c4bc060c764d5ce31","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_2091f13522d971d5b8dd811f2d6322bf3aaf05ad0a532e0c4bc060c764d5ce31","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"509497f027618e81fcdd5901f3448904403b6f32c1e384848894eadf79061623","published":"Tue, 02 Jun 2026 00:00:00 -0400","receipt_hash":"509497f027618e81fcdd5901f3448904403b6f32c1e384848894eadf79061623","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"509497f027618e81fcdd5901f3448904403b6f32c1e384848894eadf79061623","observed_at":"2026-06-02T04:43:38.825628Z","parent_run_hash":"c2a9665c814770d56765bb764e6a6c7e4fa7d4e9708e157ca0f7440c89927d54","published":"Tue, 02 Jun 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2606.00703v1 Announce Type: cross \nAbstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible. We study a B-bit quantized stochastic first-order oracle: an optimizer interacts for T rounds and receives, each round, a B-bit adaptive public-coin description of its stochastic gradient. Our main contribution is an exact reduction from optimizing a strongly convex quadratic family to interactively compressed Gaussian mean estimation -- under the B-bit oracle the query carries no information, so optimization collapses exactly onto a sequential distributed-estimation problem. This yields two unconditional lower bounds, a communication bound TB = Omega(d) and a statistical bound T = Omega(sigma^2 d / eps^2), and the sharp product-form bound T = Omega((sigma^2 d / eps^2) ma","title":"Information-Theoretic Lower Bounds for Bit-Constrained Stochastic Optimization via a Reduction to Compressed Gaussian Mean Estimation","url":"https://arxiv.org/abs/2606.00703","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.00703v1 Announce Type: cross \nAbstract: Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible. We study a B-bit quantized stochastic first-order oracle: an optimizer interacts for T rounds and receives, each round, a B-bit adaptive public-coin description of its stochastic gradient. Our main contribution is an exact reduction from optimizing a strongly convex quadratic family to interactively compressed Gaussian mean estimation -- under the B-bit oracle the query carries no information, so optimization collapses exactly onto a sequential distributed-estimation problem. This yields two unconditional lower bounds, a communication bound TB = Omega(d) and a statistical bound T = Omega(sigma^2 d / eps^2), and the sharp product-form bound T = Omega((sigma^2 d / eps^2) ma","title":"Information-Theoretic Lower Bounds for Bit-Constrained Stochastic Optimization via a Reduction to Compressed Gaussian Mean Estimation","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-02T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.00703"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:41316cfc21abe2bd0364b8132e83ac039cee9283435a1800b467a10f133f93307a4aec661f7094523adce2bb151e492e4990980dc9f1e0d57886b3b1f537e800","signer":"crovia.substrate","subject":{"observed_at":"2026-06-02T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.00703"},"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":"ff65c2cb2350525787e4aa18a3390cff480633b39f64a7743cd0ef4d02c5ea05","leaf_index":205502,"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":"e02b00f2e53f6648fc519ad52c50caf5a02eb90e2e07b06cac16eb9b82125f78","side":"right"},{"sibling":"b6544460bfb7475239f4ca4562612e4705c64c5e9ccb3a58bb5d1907517e88f9","side":"left"},{"sibling":"db6feb1bfb0351a32eb47fb9e4fdde3ecf4ebf19efd18f25a9d6fc45dc092807","side":"left"},{"sibling":"8279e1b9ff1fb42e277b97f2551b7c9ede04db43b0a9bbef8fcc44ced9ac834f","side":"left"},{"sibling":"83fe3e24039ad8f6f6c442b57a0b07315a92b367a33d908d065979ffde5342b1","side":"left"},{"sibling":"fbf504b5ccbbc2a48b8d724fdd6bf769b7e54bfd85b865f4f01a465c7ecdbf2b","side":"left"},{"sibling":"67e6605f43c5d5ac89be444fb2b5a7f5ed44979491ae31acd4af400d2443d2d0","side":"right"},{"sibling":"4c08f6d1ea280f1117880420bf5d3d8f4cfb29d16b8b643cafca9f868218668c","side":"left"},{"sibling":"24ca17172d6e9b822b45054c27a7852aa461e97a906c83736cd55c5cf9874394","side":"right"},{"sibling":"6620a5008acf732cd3e57b0f2d1437293e88366c2e5b175ebeb7d796fc1e0c62","side":"left"},{"sibling":"a82575bfb494af7afcc13aaae718afa6f74030f09d71b02819ea25efd4186fc4","side":"right"},{"sibling":"e6adead8216db4cae92f0a036d53baebf30eed95a99c0d10758aa75bb7780f2f","side":"right"},{"sibling":"1acc2b7ff453ffd8c97b80ae4db5358780f0c6796874fd75403791dbe99f8cd7","side":"right"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"5f86f58c28b1a86ae06dfff4666bb9fba8866021a81fd4f1d200aa9af4722dfb","side":"right"},{"sibling":"f6cc6f94f6944ae21390afc65ac9e91dc31f84ee6e060681bba5ae08058294bd","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":206226,"merkle_root":"d2a6d32b13cbf343fb143b21a756d0533864ae6577a376ee84ba867b949207ec","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260602T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-02T05:37:46Z","sig_algorithm":"ed25519","signature":"abd9956cfb19dd1fb8142c46a220bac2514848c6abb0e79b8b0940206cc3ebb00894d4daaf9f786427f82a7cc12482e7fda79054ebb06bceaa9b4b97e23fb30e","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_2091f13522d971d5b8dd811f2d6322bf3aaf05ad0a532e0c4bc060c764d5ce31"}}