Pith Number

pith:PUMJ7S2N

pith:2026:PUMJ7S2NWIEN6IQV7EJWZTXVWD

not attested not anchored not stored refs pending

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects

Jose Israel Rodriguez, Kevin Dao

A minimal filling architecture for polynomial neural networks need not have unimodal hidden-layer widths.

arxiv:2605.09609 v2 · 2026-05-10 · cs.LG · math.AG

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\usepackage{pith}
\pithnumber{PUMJ7S2NWIEN6IQV7EJWZTXVWD}

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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 provide a counterexample to the minimal unimodal conjecture for polynomial neural networks (PNNs) with power activation functions.

C2weakest assumption

The architecture found by frontier search is indeed a minimal filling architecture that is not unimodal, as certified by the recursive dimension bounds and symbolic computation.

C3one line summary

A counterexample disproves the conjecture that minimal filling architectures of polynomial neural networks always have unimodal hidden layer widths.

Cited by

1 paper in Pith

Singular Learning and Occam's Razor in Deep Monomial Networks

Receipt and verification

First computed	2026-06-19T16:12:20.628374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d189fcb4db208df2215f9136ccef5b0f5873237b0cf77be6237ea8d323e9e7a

Aliases

arxiv: 2605.09609 · arxiv_version: 2605.09609v2 · doi: 10.48550/arxiv.2605.09609 · pith_short_12: PUMJ7S2NWIEN · pith_short_16: PUMJ7S2NWIEN6IQV · pith_short_8: PUMJ7S2N

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/PUMJ7S2NWIEN6IQV7EJWZTXVWD \
  | 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: 7d189fcb4db208df2215f9136ccef5b0f5873237b0cf77be6237ea8d323e9e7a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4210a9b371799aca9cfbcff92ad0602a047ad4aac8135ed6c4a5992120b377dd",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-10T15:46:00Z",
    "title_canon_sha256": "1195c39bcb1a48711b3ab359a6c89febaa9c28ad5dad46ae5fa0a4bb78f42bf4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09609",
    "kind": "arxiv",
    "version": 2
  }
}