Pith Number

pith:VFYWKNVU

pith:2025:VFYWKNVUDTKTN4QINHB2V4CWFP

not attested not anchored not stored refs pending

Position: A Theory of Deep Learning Must Include Compositional Sparsity

David A. Danhofer, Davide D'Ascenzo, Rafael Dubach, Tomaso Poggio

arxiv:2507.02550 v1 · 2025-07-03 · cs.LG · cs.AI

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VFYWKNVUDTKTN4QINHB2V4CWFP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

5 papers in Pith

Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation

Compositionality Emerges in a Narrow Depth-Connectivity Regime: Architecture Constraints and Solution Manifolds

Compositional Sparsity as an Inductive Bias for Neural Architecture Design

Learning Sparse Compositional Functions with Norm-Constrained Neural Networks

From Mechanistic to Compositional Interpretability

Receipt and verification

First computed	2026-07-05T11:31:30.735744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9716536b41cd536f20869c3aaf0562bed8ff98d51ffb8ec4ab2dfbcd2bec1f7

Aliases

arxiv: 2507.02550 · arxiv_version: 2507.02550v1 · doi: 10.48550/arxiv.2507.02550 · pith_short_12: VFYWKNVUDTKT · pith_short_16: VFYWKNVUDTKTN4QI · pith_short_8: VFYWKNVU

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/VFYWKNVUDTKTN4QINHB2V4CWFP \
  | 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: a9716536b41cd536f20869c3aaf0562bed8ff98d51ffb8ec4ab2dfbcd2bec1f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba0a7edfe3c51ba6b7709fee519eb0dcb2ea4b008339bc3ffddbdc9e6b767f3d",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-07-03T11:49:56Z",
    "title_canon_sha256": "b87e40a9b9ab50a9583e00de595ad3b701b4a39884496e46e5d5ddfc16c18237"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.02550",
    "kind": "arxiv",
    "version": 1
  }
}