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In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix $\\Sigma_X$ of the columns of the second factor is available. This setting arises in the ubiquitous task of weight-only post-training quantization of LLMs.\n  Weight-only quantization is related to the problem of weighted mean squared error (WMSE) source coding, whose classical (reverse) waterfilling solution dictates how one should distribute rate between coordinates of the vector. We show how waterfilling can be used to improve practical LLM quantization algorithms (GPTQ), which at present allocate rate equally. A recent scheme (known as ``WaterSIC'') that only uses scalar INT quantizers is analyzed and its high-rate performance is shown to be (a) basis free (i.e., characterized by the determinant of $\\Sigma_X$ and, thus","title":"High-Rate Quantized Matrix Multiplication II","url":"https://arxiv.org/abs/2605.13768","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.13768v1 Announce Type: cross \nAbstract: This is the second part of the work investigating quantized matrix multiplication (MatMul). In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix $\\Sigma_X$ of the columns of the second factor is available. This setting arises in the ubiquitous task of weight-only post-training quantization of LLMs.\n  Weight-only quantization is related to the problem of weighted mean squared error (WMSE) source coding, whose classical (reverse) waterfilling solution dictates how one should distribute rate between coordinates of the vector. We show how waterfilling can be used to improve practical LLM quantization algorithms (GPTQ), which at present allocate rate equally. A recent scheme (known as ``WaterSIC'') that only uses scalar INT quantizers is analyzed and its high-rate performance is shown to be (a) basis free (i.e., characterized by the determinant of $\\Sigma_X$ and, thus","title":"High-Rate Quantized Matrix Multiplication II","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-14T04:43:36Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.13768"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:53bb4e9fe7b64d62910c74cf6948c1a793be3c7fb6c55b34bd08546e376fd7e181670d367fb58a10ac1b277975b7568841f4b492295e59e3cecf6838358e2d02","signer":"crovia.substrate","subject":{"observed_at":"2026-05-14T04:43:36Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.13768"},"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":"0f319ae57d835ed057b824da7cfdea5f34b5753b6c1cb6b878dff02c5b41754b","leaf_index":132665,"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":"94d3ecdaf8ddb69318433915ec4ce062193e39f0efc0e99ef3c7e406ad21d342","side":"left"},{"sibling":"2344cbf822f2c9c32ca635a694fefb3f80a43d36bfe12358ba7cc9ad3e5fe14b","side":"right"},{"sibling":"90d22a61f4b6230c7fb2c971d3823dc190bf395f114aedc0a03b6390a6d1b196","side":"right"},{"sibling":"a3df18ce8a1613dd6876f1b9e8f83b27d2f761c0e0bfc4c289f6050e13971cad","side":"left"},{"sibling":"7eac46ad660d92452b5d3e0e4e161fd64201465d3b99a4ba8a18b6be59676733","side":"left"},{"sibling":"bd0857de3ddbbe18a2122a8ad20f9fe94e8837ca5472083a9985cdd38da82647","side":"left"},{"sibling":"990ccbf7dece9bb81548c1b76f72b61af8fe51b5fc9416a0e16fc1cc6d4a4e96","side":"right"},{"sibling":"d5482331e2cc5acdd0d08391a6a4507a80863b313a18e39660a4565d5c9fa7ea","side":"right"},{"sibling":"2ae8cbb1d93652ee36f693c3d63e733765fbafcd7765d6d596692bf393ce0a1d","side":"right"},{"sibling":"a957418f640d5dc3181a7628c2646bb86c6da0ea6888670b451e534693a0c7cb","side":"left"},{"sibling":"c03f0a468f574a08ffe8b17e1a17bd88216e1359f0e33a54447e160cd8675da0","side":"left"},{"sibling":"038ff12da6f55509125ef0d96e1e57dda29a2fe63bf03fba2af4cf7cbcd88b36","side":"right"},{"sibling":"b0419206fe62ef216df3900ca93cffd44df267435a4643dda354c1310079cf91","side":"right"},{"sibling":"0d4a9c03674f9d0ce64df15c15e9f656a54b41f93c428aac8e615fda26291956","side":"right"},{"sibling":"7856d920f3f1f1d2194c1ed7351bf0d674440df3cb423a6911f89cb3e9578c0b","side":"right"},{"sibling":"6ac6396bdd2e9df315427a46155531476e7f9012b4bd962e0d2d6d1209b11723","side":"right"},{"sibling":"7c8dc85cbfe43e19ac759ad176cfa11dba2467ae17927c471d5c55663c4f490d","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":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_c16fdb6aa7bbe39f36554f4f47ddb171b44148858c989c4caab6b25f787893d5"}}