Pith Number

pith:26JMV5VV

pith:2018:26JMV5VVDOXSKIQP2HRQR2JPLQ

not attested not anchored not stored refs pending

A Tropical Approach to Neural Networks with Piecewise Linear Activations

Petros Maragos, Vasileios Charisopoulos

arxiv:1805.08749 v2 · 2018-05-22 · stat.ML · cs.LG

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{26JMV5VVDOXSKIQP2HRQR2JPLQ}

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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

3 papers in Pith

Sparsity is Combinatorial Depth: Quantifying MoE Expressivity via Tropical Geometry

Most ReLU Networks Admit Identifiable Parameters

Expressivity of Transformers: A Tropical Geometry Perspective

Receipt and verification

First computed	2026-05-17T23:55:07.696735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d792caf6b51baf25220fd1e308e92f5c004a4153e0008237056dbae79364e274

Aliases

arxiv: 1805.08749 · arxiv_version: 1805.08749v2 · doi: 10.48550/arxiv.1805.08749 · pith_short_12: 26JMV5VVDOXS · pith_short_16: 26JMV5VVDOXSKIQP · pith_short_8: 26JMV5VV

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/26JMV5VVDOXSKIQP2HRQR2JPLQ \
  | 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: d792caf6b51baf25220fd1e308e92f5c004a4153e0008237056dbae79364e274

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6115ae28b2596c7c3dc5e4db56114535dce64a2dc42cf08426c88fbcfee124a",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2018-05-22T17:20:51Z",
    "title_canon_sha256": "504daeb6a3845cf58ddfc96a62910424f38068f7ec5608a9b7c2e057c840a22f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.08749",
    "kind": "arxiv",
    "version": 2
  }
}