Pith Number

pith:TRYC5IXE

pith:2026:TRYC5IXEOLPQBRIUVX7T4KAWT4

not attested not anchored not stored refs pending

PolySHAP: Extending KernelSHAP with Interaction-Informed Polynomial Regression

Christopher Musco, Fabian Fumagalli, R. Teal Witter

PolySHAP shows that the paired sampling heuristic in KernelSHAP produces exactly the same Shapley approximations as fitting a second-degree polynomial.

arxiv:2601.18608 v3 · 2026-01-26 · cs.AI · 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{TRYC5IXEOLPQBRIUVX7T4KAWT4}

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

We prove that paired sampling outputs exactly the same Shapley value approximations as second-order PolySHAP, without ever fitting a degree 2 polynomial. To the best of our knowledge, this finding provides the first strong theoretical justification for the excellent practical performance of the paired sampling heuristic.

C2weakest assumption

That the underlying cooperative game value function admits a useful low-degree polynomial approximation under the sampling distribution used for KernelSHAP-style estimation.

C3one line summary

PolySHAP approximates Shapley values via polynomial regression and proves paired sampling equals its quadratic version, providing the first theoretical justification for that heuristic.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

QuadraSHAP: Stable and Scalable Shapley Values for Product Games via Gauss-Legendre Quadrature

Receipt and verification

First computed	2026-05-18T02:44:31.853597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c702ea2e472df00c514adff3e28169f1bc2c8060bf23ed748e469c62228e6fc

Aliases

arxiv: 2601.18608 · arxiv_version: 2601.18608v3 · doi: 10.48550/arxiv.2601.18608 · pith_short_12: TRYC5IXEOLPQ · pith_short_16: TRYC5IXEOLPQBRIU · pith_short_8: TRYC5IXE

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/TRYC5IXEOLPQBRIUVX7T4KAWT4 \
  | 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: 9c702ea2e472df00c514adff3e28169f1bc2c8060bf23ed748e469c62228e6fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f06d08e3110b00ae045bca22a30fafe44b2b6f2f8e9d0592ae99b2d8fc2805c",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-01-26T15:47:45Z",
    "title_canon_sha256": "5553daa5904076e2c119b996f7450e9a4cea8eb6f9e6f1579ab8f5e165881b0c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.18608",
    "kind": "arxiv",
    "version": 3
  }
}