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In practice, URRs are often replaced by randomized Hadamard transforms (RHTs), which preserve orthogonality while admitting fast implementations. The remaining issue is the performance for worst-case inputs. With a URR, each coordinate is individually distributed as a shifted beta distribution, which converges to a Gaussian distribution in high dimensions. Generally, one RHT is not suitable in the worst case, as individual coordinates can be far from these distributions. We show that after composing two RHTs on any $d$-sized input vector, the marginal distribution of every fixed coordinate of the normalized rotated vector is within $O(d^{-1/2})$ of a standard Gaussian both in K","title":"Quantizing With Randomized Hadamard Transforms: Efficient Heuristic Now Proven","url":"https://arxiv.org/abs/2605.06014","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.06014v1 Announce Type: cross \nAbstract: Uniform random rotations (URRs) are a common preprocessing step in modern quantization approaches used for gradient compression, inference acceleration, KV-cache compression, model weight quantization, and approximate nearest-neighbor search in vector databases. In practice, URRs are often replaced by randomized Hadamard transforms (RHTs), which preserve orthogonality while admitting fast implementations. The remaining issue is the performance for worst-case inputs. With a URR, each coordinate is individually distributed as a shifted beta distribution, which converges to a Gaussian distribution in high dimensions. Generally, one RHT is not suitable in the worst case, as individual coordinates can be far from these distributions. We show that after composing two RHTs on any $d$-sized input vector, the marginal distribution of every fixed coordinate of the normalized rotated vector is within $O(d^{-1/2})$ of a standard Gaussian both in K","title":"Quantizing With Randomized Hadamard Transforms: Efficient Heuristic Now Proven","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-08T04:43:40Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.06014"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c6205ab0cb7ab2222165e756cef62fd97271de122763d2105f5b4fbeeda66d440019c6cc617b09bcf65ad7636c8018f1148935e0e656652ae5f9b4c3348d880c","signer":"crovia.substrate","subject":{"observed_at":"2026-05-08T04:43:40Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.06014"},"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":"6fd35d6352f1807bec4263908be83b9221715412a0e71dd3c5435d93ad641817","leaf_index":120256,"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":"2bbda691e93b454ca6058269ec2b19c909f7215241d27e33baef51df4efc51a1","side":"right"},{"sibling":"19e993377af77045a8f9902740474faf805d41e4af179b284274cf5f9e01a3a6","side":"right"},{"sibling":"e944d3b0f143cce4d09dc2d67ab32786ba07451359dcd22a0d4533a265613e60","side":"right"},{"sibling":"5aa731ca3e3af4c5742869ae6855f8c1b3c862496ecea21edb1fcdfaf646a0c1","side":"right"},{"sibling":"8d933485877d2563715f568507b64b5c1021dca20a59d99667b520dfca046251","side":"right"},{"sibling":"d41dcc5bf8b8ae2caed81c1e085ecd4f2a3c9c10543d4eee2bd0ce498a04ec19","side":"right"},{"sibling":"f8731f97e8f9ae56bf080fa7b1f75b46c0f0aa51627cbe9299dc94fe90595ade","side":"left"},{"sibling":"6f9fbeeae57a07a1aca1b75e07f4ae2c8f837e9a25cd31813866783835b2d912","side":"left"},{"sibling":"34e93c6f591cc4fb93a4c29771210eb73573b454d2c5329963f437f1309fe46f","side":"left"},{"sibling":"b9834433f5bd1deeaab4ced2b3bcc0d91d19763a5d0981fb299d124b63459eb3","side":"right"},{"sibling":"143f33d3924b3840fd6dd8ba12566fc35bf86189e663ef0ad4884d676f295e3a","side":"left"},{"sibling":"b1ed99341c327c7c9ab2489f40af2547ab3b3b4b6a74fb684210164fb891a413","side":"right"},{"sibling":"6ee3be9bdfc9bee55d32f7dbb0075f02fe87d20887d563d3e300caf36b1b88c7","side":"left"},{"sibling":"8ccd9937a2c0d5c04044d07d1557791b7d07bb31eac41a39a675608d44b38f23","side":"right"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","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_948150a590fb1e1f3c5507442b746ecc014ba2aeb8c93c2e35d07c68c673797d"}}