Pith Number

pith:54M7QLOU

pith:2026:54M7QLOULRNBFWNASGVZSE2VVO

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High-Rate Quantized Matrix Multiplication I

Or Ordentlich, Yury Polyanskiy

High-rate quantization theory supplies the exact rate-distortion tradeoff for generic matrix multiplication without calibration data

arxiv:2601.17187 v2 · 2026-01-23 · cs.IT · cs.AI · math.IT

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Claims

C1strongest 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.

C2weakest assumption

The generic MatMul setting can be analyzed under the high-rate quantization regime without any a priori statistical information about the matrix factors.

C3one 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.

References

51 extracted · 51 resolved · 3 Pith anchors

[1] Optimal quantization for matrix multiplication, 2024

[2] OPTQ: Accurate quantization for generative pre-trained transformers, 2023

[3] Quip: 2- bit quantization of large language models with guarantees, 2023

[4] NestQuant: Nested lattice quantization for matrix products and LLMs, 2025

[5] Gpt3. int8 (): 8-bit matrix multiplication for transformers at scale, 2022

Formal links

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Cited by

1 paper in Pith

Contraction-Gauge Preconditioning for Quantized Matrix Multiplication

Receipt and verification

First computed	2026-05-18T02:44:31.871149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef19f82dd45c5a12d9a091ab991355abbe9fcc292adc5f6a24cfec1a8ae3e533

Aliases

arxiv: 2601.17187 · arxiv_version: 2601.17187v2 · doi: 10.48550/arxiv.2601.17187 · pith_short_12: 54M7QLOULRNB · pith_short_16: 54M7QLOULRNBFWNA · pith_short_8: 54M7QLOU

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/54M7QLOULRNBFWNASGVZSE2VVO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ef19f82dd45c5a12d9a091ab991355abbe9fcc292adc5f6a24cfec1a8ae3e533

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-01-23T21:32:44Z",
    "title_canon_sha256": "28bcc846e0410a8e212152795b8654dd2d2f8d8c9d653880774b0defc57e3612"
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