Pith Number

pith:DCK7WD6V

pith:2026:DCK7WD6VL37HYQIJGYBA2ANZXX

not attested not anchored not stored refs resolved

Provable Quantization with Randomized Hadamard Transform

Boris Prokhorov, Dmitry Krachun, Michael Kapralov, Piotr Indyk, Ying Feng

Dithered quantization after randomized Hadamard transform matches the error of dense random rotations at linearithmic cost.

arxiv:2605.13810 v1 · 2026-05-13 · cs.LG · cs.DS

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Claims

C1strongest claim

A dithered version of TurboQuant achieves mean squared error (π√3/2 + o(1)) · 4^{-b} at b bits per coordinate, where the o(1) term vanishes uniformly over all unit vectors and all dimensions as the number of quantization levels grows.

C2weakest assumption

The analysis assumes the input vectors are unit vectors and relies on the asymptotic regime where the number of quantization levels grows; the uniformity claim over all dimensions and vectors may require additional technical conditions on the dither distribution that are not fully detailed in the abstract.

C3one line summary

Dithered quantization after a single randomized Hadamard transform yields unbiased estimates whose MSE asymptotically equals that of dense random rotations, specifically (π√3/2 + o(1))·4^{-b} for b-bit TurboQuant.

References

38 extracted · 38 resolved · 3 Pith anchors

[1] Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing , pages=

[2] IEEE Transactions on Pattern Analysis and Machine Intelligence , volume= 2010

[3] Proceedings of the Twentieth Annual Symposium on Computational Geometry , pages=

[4] Proceedings of the 31st annual international ACM SIGIR conference on Research and development in information retrieval , pages=

[5] Proceedings of the AAAI Conference on Artificial Intelligence , volume=

Receipt and verification

First computed	2026-05-18T02:44:15.402305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1895fb0fd55efe7c410936020d01b9bdf634b18ab5816bb150b69d7360ccb8cb

Aliases

arxiv: 2605.13810 · arxiv_version: 2605.13810v1 · doi: 10.48550/arxiv.2605.13810 · pith_short_12: DCK7WD6VL37H · pith_short_16: DCK7WD6VL37HYQIJ · pith_short_8: DCK7WD6V

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DCK7WD6VL37HYQIJGYBA2ANZXX \
  | 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: 1895fb0fd55efe7c410936020d01b9bdf634b18ab5816bb150b69d7360ccb8cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb576d08788a08e09795b4caddc60d07c2486d82f701b785014d55a1aa6482f1",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T17:38:18Z",
    "title_canon_sha256": "3259f4be765356e1b7101b9ec0a7e448db8dfef729936d0c79ccee9ecb121d7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13810",
    "kind": "arxiv",
    "version": 1
  }
}