Pith Number

pith:JPBADMBS

pith:2026:JPBADMBSCREE7VLKFBXWFJ736Q

not attested not anchored not stored refs pending

Adalina: Adaptive Linear Approximation for the Shapley Value and Beyond

Bryan Kian Hsiang Low, Weida Li, Yaoliang Yu

A linear-space algorithm approximates Shapley values and semi-values with O(n/ε² log(1/δ)) queries while minimizing mean squared error for any utility.

arxiv:2604.08438 v2 · 2026-04-09 · cs.LG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JPBADMBSCREE7VLKFBXWFJ736Q}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Our algorithm requires O(n/ε² log(1/δ)) utility queries to ensure P(‖φ̂ - φ‖₂ ≥ ε) ≤ δ for all commonly used semi-values... our algorithm allows explicit minimization of the mean square error for each specific utility function... the first adaptive, linear-time, linear-space randomized algorithm, Adalina, that theoretically achieves improved mean square error.

C2weakest assumption

The framework relies on a vector concentration inequality to derive the query bounds under a Θ(n) space constraint; if this inequality does not apply tightly to the semi-value estimators, the claimed complexities may not hold.

C3one line summary

Introduces Adalina, the first adaptive linear-time linear-space randomized algorithm for semi-value approximation with provable O(n/ε² log(1/δ)) query complexity and explicit MSE minimization.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-04T01:08:49.704520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4bc201b03214484fd56a286f62a7fbf43c6e310c3a6194fbff6e11e4c2608144

Aliases

arxiv: 2604.08438 · arxiv_version: 2604.08438v2 · doi: 10.48550/arxiv.2604.08438 · pith_short_12: JPBADMBSCREE · pith_short_16: JPBADMBSCREE7VLK · pith_short_8: JPBADMBS

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JPBADMBSCREE7VLKFBXWFJ736Q \
  | 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: 4bc201b03214484fd56a286f62a7fbf43c6e310c3a6194fbff6e11e4c2608144

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d55164f24eae6d753b025f36cb17a061e020b092a82cd99f0d64b03cecc14476",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-09T16:38:14Z",
    "title_canon_sha256": "b84431360dda8abe46294e537bf01c12b4deb3e91bf76002adeec910ea9cb143"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.08438",
    "kind": "arxiv",
    "version": 2
  }
}