Pith Number

pith:SQE5VREH

pith:2026:SQE5VREHOCT25NTPKJBURHYNEE

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PrismQuant: Rate-Distortion-Optimal Vector Quantization for Gaussian-Mixture Sources

Bumsu Park, Chanho Park, Namyoon Lee, Youngmok Park

A single global reverse-waterfilling level governs the rate-distortion function for Gaussian-mixture sources.

arxiv:2605.15507 v1 · 2026-05-15 · cs.IT · cs.AI · cs.LG · math.IT

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Claims

C1strongest claim

We prove that the genie-aided conditional RD function is governed by a single global reverse-waterfilling level shared across all components and eigenmodes. Building on this result, we introduce PrismQuant, which transmits the component label losslessly and encodes the residual using the component-matched KLT, followed by scalar quantization, achieving a rate of H(C)/n bits per source dimension of the converse, with a vanishing asymptotic gap.

C2weakest assumption

The source is exactly a finite Gaussian mixture whose component label can be identified and transmitted losslessly at cost H(C)/n per dimension; the proof assumes a genie that reveals the active component before quantization begins.

C3one line summary

PrismQuant achieves near rate-distortion optimality for Gaussian-mixture sources by losslessly transmitting the mixture component label at H(C)/n bits per dimension and applying component-matched KLT plus scalar quantization, with vanishing gap to the genie-aided bound.

References

40 extracted · 40 resolved · 1 Pith anchors

[1] Claude E. Shannon. Coding theorems for a discrete source with a fidelity criterion.IRE National Convention Record, 7(4):142–163, 1959 1959

[2] Prentice-Hall, Englewood Cliffs, NJ, 1971 1971

[3] Cover and Joy A 2006

[4] Vivek K. Goyal. Theoretical foundations of transform coding.IEEE Signal Procesing Magazine, 18(5): 9–21, 2001 2001

[5] Bishop.Pattern recognition and machine learning 2006

Receipt and verification

First computed	2026-05-20T00:01:02.238040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9409dac48770a7aeb66f5243489f0d210c00f457d7c1b188e047b704a1d2cb7a

Aliases

arxiv: 2605.15507 · arxiv_version: 2605.15507v1 · doi: 10.48550/arxiv.2605.15507 · pith_short_12: SQE5VREHOCT2 · pith_short_16: SQE5VREHOCT25NTP · pith_short_8: SQE5VREH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SQE5VREHOCT25NTPKJBURHYNEE \
  | 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: 9409dac48770a7aeb66f5243489f0d210c00f457d7c1b188e047b704a1d2cb7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ff9d458b435b74982ddd2c6099c8f421333f0928c2a6b82a2e1cab6ae0f073c",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-15T01:05:28Z",
    "title_canon_sha256": "a73725cf8b4253467ecb3e8bb0c42c3cdb672a95bbf2dcd0dcd0b234dfd2f528"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15507",
    "kind": "arxiv",
    "version": 1
  }
}