Pith Number

pith:JBZOYWTE

pith:2026:JBZOYWTEQZRAQS4IOP4MBCKJ5S

not attested not anchored not stored refs pending

Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification

Alexander Marquard, Julian Rodemann, Michele Caprio, Thomas Augustin

Refitting models on their own predictions approximates the posterior predictive distribution directly and improves calibration over classical Laplace methods.

arxiv:2605.12208 v2 · 2026-05-12 · stat.ML · cs.AI · cs.LG · stat.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JBZOYWTEQZRAQS4IOP4MBCKJ5S}

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.

Claims

C1strongest claim

Across a wide array of regression tasks with simulated and real-world datasets, our methods outperform classical Laplace approximations in predictive calibration while remaining computationally efficient.

C2weakest assumption

That refitting the model on self-predicted data effectively approximates the posterior predictive distribution, assuming the initial model predictions are sufficiently reliable to serve as pseudo-labels for uncertainty quantification.

C3one line summary

SSLA approximates the posterior predictive distribution by refitting Bayesian models on self-predicted data, providing a sampling-free method that improves predictive calibration over classical Laplace approximations in regression tasks.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-29T01:05:12.307864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4872ec5a648662084b8873f8c08949ec975aef00bb27c523bfed9896560f7e2d

Aliases

arxiv: 2605.12208 · arxiv_version: 2605.12208v2 · doi: 10.48550/arxiv.2605.12208 · pith_short_12: JBZOYWTEQZRA · pith_short_16: JBZOYWTEQZRAQS4I · pith_short_8: JBZOYWTE

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/JBZOYWTEQZRAQS4IOP4MBCKJ5S \
  | 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: 4872ec5a648662084b8873f8c08949ec975aef00bb27c523bfed9896560f7e2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fe93b5157c2d1916dc32ae588993288bb10e66dae823241734d270dea902d9f",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG",
      "stat.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-12T14:46:08Z",
    "title_canon_sha256": "dbf3db7ed915a678d929033294cc1d6aca7904d99458f3091ad107b6898f7aae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12208",
    "kind": "arxiv",
    "version": 2
  }
}