Pith Number

pith:IL4K7Q3L

pith:2026:IL4K7Q3LHKDUN2HRFHEULT5MHS

not attested not anchored not stored refs resolved

MaxSketch: Robust Distinct Counting in Streams via Random Projections

Christos Tzamos, Constantine Caramanis, Nikos Tsikouras

A max-linear sketch over random Gaussian projections recovers distinct counts in noisy streams using only logarithmic memory when observations share geometric structure.

arxiv:2605.15571 v1 · 2026-05-15 · stat.ML · cs.LG

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We show that under this assumption m = O~(log n / ε²) random projections (and hence O~(log n/ε²) memory) suffice to recover the true distinct count within a (1+ε) factor.

C2weakest assumption

The input observations possess geometric structure common in learned representations that permits the max-linear sketch over random Gaussian projections to separate latent objects at the claimed memory cost.

C3one line summary

MaxSketch achieves O~(log n / ε²) memory for (1+ε)-approximate distinct counting in streams with geometric structure via max-linear random projections.

References

34 extracted · 34 resolved · 0 Pith anchors

[1] Concentration inequalities 2003

[2] Streaming algorithms for robust distinct elements 2016

[3] Distinct sampling on streaming data with near-duplicates 2018

[4] A simple framework for contrastive learning of visual representations 2020

[5] Loglog counting of large cardinalities 2003

Receipt and verification

First computed	2026-05-20T00:01:05.974067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42f8afc36b3a8746e8f129c945cfac3c8313fa05e9db95db010e29cf57feb330

Aliases

arxiv: 2605.15571 · arxiv_version: 2605.15571v1 · doi: 10.48550/arxiv.2605.15571 · pith_short_12: IL4K7Q3LHKDU · pith_short_16: IL4K7Q3LHKDUN2HR · pith_short_8: IL4K7Q3L

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IL4K7Q3LHKDUN2HRFHEULT5MHS \
  | 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: 42f8afc36b3a8746e8f129c945cfac3c8313fa05e9db95db010e29cf57feb330

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2483a899c2b823513a4580a0b51b4e125059fb09a6c0a0034e4af8c0cbc615fc",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-15T03:29:26Z",
    "title_canon_sha256": "b63376785046f6f7ce9bfa9f0e671ae93fc199a02c24b4baf9e52683117c4795"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15571",
    "kind": "arxiv",
    "version": 1
  }
}