Pith Number

pith:G47DM2E7

pith:2013:G47DM2E7KSZ4XLNYA4UDVURBCR

not attested not anchored not stored refs pending

On the number of response regions of deep feed forward networks with piece-wise linear activations

Guido Montufar, Razvan Pascanu, Yoshua Bengio

arxiv:1312.6098 v5 · 2013-12-20 · cs.LG · cs.NE

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\usepackage{pith}
\pithnumber{G47DM2E7KSZ4XLNYA4UDVURBCR}

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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.

Cited by

6 papers in Pith

Axiomatizing Neural Networks via Pursuit of Subspaces

A Lower Bound for the Number of Linear Regions of Ternary ReLU Regression Neural Networks

Sparsity is Combinatorial Depth: Quantifying MoE Expressivity via Tropical Geometry

HyParLyVe: Hyperplane Partitioning for Neural Lyapunov Verification

Complexity of Linear Regions in Self-supervised Deep ReLU Networks

Receipt and verification

First computed	2026-05-18T02:59:05.798595Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

373e36689f54b3cbadb807283ad221145766f261ed919a16e0a790dd99b879d8

Aliases

arxiv: 1312.6098 · arxiv_version: 1312.6098v5 · doi: 10.48550/arxiv.1312.6098 · pith_short_12: G47DM2E7KSZ4 · pith_short_16: G47DM2E7KSZ4XLNY · pith_short_8: G47DM2E7

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/G47DM2E7KSZ4XLNYA4UDVURBCR \
  | 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: 373e36689f54b3cbadb807283ad221145766f261ed919a16e0a790dd99b879d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ada344723ea177281bb1f0f5f7828e5e8445924ceba8fcdb28bc74dcc11973b",
    "cross_cats_sorted": [
      "cs.NE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2013-12-20T20:22:31Z",
    "title_canon_sha256": "3cb17ee59156b17c72b79cd7bfaef02a4f7148f203d737faa406eb9a41b8897e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6098",
    "kind": "arxiv",
    "version": 5
  }
}