{"paper":{"title":"High-Rate Quantized Matrix Multiplication I","license":"http://creativecommons.org/licenses/by/4.0/","headline":"High-rate quantization theory supplies the exact rate-distortion tradeoff for generic matrix multiplication without calibration data","cross_cats":["cs.AI","math.IT"],"primary_cat":"cs.IT","authors_text":"Or Ordentlich, Yury Polyanskiy","submitted_at":"2026-01-23T21:32:44Z","abstract_excerpt":"This paper investigates the problem of quantized matrix multiplication (MatMul), which has become crucial for the efficient deployment of large language models (LLMs). We consider a Generic MatMul setting, where both matrices must be quantized (weight+activation quantization) without specific apriori (calibration) statistical information about the factors. We review the fundamental information-theoretic tradeoff between quantization rate and distortion (high-rate theory), and contrast those with the performance of popular quantization schemes (absmax INT and floating-point (FP)), for which we "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We review the fundamental information-theoretic tradeoff between quantization rate and distortion (high-rate theory), and contrast those with the performance of popular quantization schemes (absmax INT and floating-point (FP)), for which we also derive accurate heuristic approximations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The generic MatMul setting can be analyzed under the high-rate quantization regime without any a priori statistical information about the matrix factors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"High-rate quantization theory yields accurate approximations for the distortion of absmax INT and FP schemes in generic weight-plus-activation matrix multiplication.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"High-rate quantization theory supplies the exact rate-distortion tradeoff for generic matrix multiplication without calibration data","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7bc443eb058df2aed8e51aed07ee7cc0485c7aeb5ebbf2c6651408dafed870ee"},"source":{"id":"2601.17187","kind":"arxiv","version":2},"verdict":{"id":"d982e895-9e5a-4c8d-8015-8dd24e07edad","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T11:16:04.954721Z","strongest_claim":"We review the fundamental information-theoretic tradeoff between quantization rate and distortion (high-rate theory), and contrast those with the performance of popular quantization schemes (absmax INT and floating-point (FP)), for which we also derive accurate heuristic approximations.","one_line_summary":"High-rate quantization theory yields accurate approximations for the distortion of absmax INT and FP schemes in generic weight-plus-activation matrix multiplication.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The generic MatMul setting can be analyzed under the high-rate quantization regime without any a priori statistical information about the matrix factors.","pith_extraction_headline":"High-rate quantization theory supplies the exact rate-distortion tradeoff for generic matrix multiplication without calibration data"},"references":{"count":51,"sample":[{"doi":"","year":2024,"title":"Optimal quantization for matrix multiplication,","work_id":"67e0dada-22c6-4282-81b0-f8ec7b786c89","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"OPTQ: Accurate quantization for generative pre-trained transformers,","work_id":"3902ff1c-dfb5-4adc-870b-c8ec9abfbb82","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Quip: 2- bit quantization of large language models with guarantees,","work_id":"0aba206f-56c2-4635-8de8-d421053e5962","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"NestQuant: Nested lattice quantization for matrix products and LLMs,","work_id":"f992de1c-558b-403e-b88e-f81e0e9e5949","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Gpt3. int8 (): 8-bit matrix multiplication for transformers at scale,","work_id":"e5a95f16-d998-4ef7-9f71-01077b057362","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":51,"snapshot_sha256":"3a839c1fa857ae7801c55a43c41d51102551b6338778401aeb66350a17eb72a9","internal_anchors":3},"formal_canon":{"evidence_count":3,"snapshot_sha256":"c0909d9ee5197e0c66e99c03234a7c7d4d637ab52bff298a627b8bde1ce34325"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}