Pith Number

pith:6WJTXNHU

pith:2026:6WJTXNHUBJJOKPN55B42GDIQC7

not attested not anchored not stored refs pending

Most ReLU Networks Admit Identifiable Parameters

Guido Mont\'ufar, Moritz Grillo

ReLU networks with input and hidden widths at least two admit an open set of identifiable parameters.

arxiv:2605.03601 v2 · 2026-05-05 · cs.LG · cs.DM · math.CO

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\pithnumber{6WJTXNHUBJJOKPN55B42GDIQC7}

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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

Our main result shows that for every architecture whose input and hidden layers have width at least two, there exists an open set of identifiable parameters. This implies that the functional dimension of every such architecture is exactly the number of parameters minus the number of hidden neurons.

C2weakest assumption

The assumption that the architecture has input and hidden layer widths at least two; the result is stated only for open sets of parameters and does not claim identifiability for every parameter vector.

C3one line summary

For ReLU networks with input and hidden widths at least 2, most parameters are identifiable up to symmetry, so the functional dimension equals the parameter count minus the number of hidden neurons.

Receipt and verification

First computed	2026-05-21T01:04:26.728429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f5933bb4f40a52e53dbde879a30d1017c7edc2e69231f152d426bace7d206a21

Aliases

arxiv: 2605.03601 · arxiv_version: 2605.03601v2 · doi: 10.48550/arxiv.2605.03601 · pith_short_12: 6WJTXNHUBJJO · pith_short_16: 6WJTXNHUBJJOKPN5 · pith_short_8: 6WJTXNHU

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6WJTXNHUBJJOKPN55B42GDIQC7 \
  | 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: f5933bb4f40a52e53dbde879a30d1017c7edc2e69231f152d426bace7d206a21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1b1a8bd998b8122674b64d1b2627b4781114aa017e7d3ea2b12b63cc0042308",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-05T10:25:28Z",
    "title_canon_sha256": "8d8de95237a580c8e2cc2a2929b8bfbaf69d3c1624b9d6c310908c60cdca5d60"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03601",
    "kind": "arxiv",
    "version": 2
  }
}