Pith Number

pith:LXK56SLJ

pith:2026:LXK56SLJSI7VILH6G2SYMYOGTO

not attested not anchored not stored refs pending

Information Theory and Statistical Learning

Abbas El Gamal

Divergence measures unify training objectives across regression, autoencoders, GANs, and diffusion models.

arxiv:2605.02989 v2 · 2026-05-04 · cs.IT · eess.SP · math.IT · stat.ML

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\usepackage{pith}
\pithnumber{LXK56SLJSI7VILH6G2SYMYOGTO}

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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

The treatment of the generative diffusion model provides a more systematic and explicit derivation than is typical in the literature.

C2weakest assumption

The reader possesses only basic background in information theory and statistics at the senior undergraduate or first-year graduate level.

C3one line summary

The chapter gives an accessible overview of divergence measures in statistical learning, covering ELBO, f-divergences, Fisher divergence, and a systematic derivation for diffusion models.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:12:54.617044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5dd5df4969923f542cfe36a58661c69ba0300083d2adb06023026f315de23259

Aliases

arxiv: 2605.02989 · arxiv_version: 2605.02989v2 · doi: 10.48550/arxiv.2605.02989 · pith_short_12: LXK56SLJSI7V · pith_short_16: LXK56SLJSI7VILH6 · pith_short_8: LXK56SLJ

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/LXK56SLJSI7VILH6G2SYMYOGTO \
  | 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: 5dd5df4969923f542cfe36a58661c69ba0300083d2adb06023026f315de23259

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c15e20867c9b6fb28dc2ee27dc2f7b83e5a291b7828160a7cb913206e94c511",
    "cross_cats_sorted": [
      "eess.SP",
      "math.IT",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-04T16:52:14Z",
    "title_canon_sha256": "036b1b095d550945ff2993316193d345508cd856c58e4809711940ce09d208e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02989",
    "kind": "arxiv",
    "version": 2
  }
}