Pith Number

pith:FYH2GCCU

pith:2026:FYH2GCCUGLH3UOFJMFQT4BPKY2

not attested not anchored not stored refs pending

Implicit Hypothesis Testing and Divergence Preservation in Neural Network Representations

Kadircan Aksoy, Peter Jung, Protim Bhattacharjee

Neural networks approach Neyman-Pearson optimal rules through monotonic growth in retained KL divergence.

arxiv:2601.20477 v4 · 2026-01-28 · cs.LG · cs.IT · math.IT

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\pithnumber{FYH2GCCUGLH3UOFJMFQT4BPKY2}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

along training trajectories, well-generalizing networks progressively approach Neyman-Pearson optimal decision rules, as measured by monotonic growth in the KL divergence retained by learned representations

C2weakest assumption

That the class-conditional distributions induced by the learned representations are sufficiently well-behaved for the binary hypothesis tests to be meaningfully defined and that monotonic KL growth directly indicates approach to Neyman-Pearson optimality without additional assumptions on the data distribution or network architecture.

C3one line summary

Well-generalizing neural classifiers approach Neyman-Pearson optimal rules as training proceeds, shown by monotonic increase in KL divergence preserved in their representations.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:39.323841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e0fa3085432cfba38a961613e05eac68fd38dea5a6a32e78cba60e1c1e55aef

Aliases

arxiv: 2601.20477 · arxiv_version: 2601.20477v4 · doi: 10.48550/arxiv.2601.20477 · pith_short_12: FYH2GCCUGLH3 · pith_short_16: FYH2GCCUGLH3UOFJ · pith_short_8: FYH2GCCU

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FYH2GCCUGLH3UOFJMFQT4BPKY2 \
  | 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: 2e0fa3085432cfba38a961613e05eac68fd38dea5a6a32e78cba60e1c1e55aef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "929a29e16bb21d11328f993c7140eaf10cd3029d6de0381f2aa5b22165d11321",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-01-28T10:46:44Z",
    "title_canon_sha256": "9fe0143d5a93dd39115324fefc5a76f4a694b79322ec50248e7309f48ea00025"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.20477",
    "kind": "arxiv",
    "version": 4
  }
}