Pith Number

pith:75ARSMLE

pith:2026:75ARSMLEIPA5N2TTRGROR4HIRE

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Understanding Self-Supervised Learning via Latent Distribution Matching

Fabian A Mikulasch, Friedemann Zenke

Self-supervised learning works by matching representations to an assumed latent model while maximizing their entropy to avoid collapse.

arxiv:2605.03517 v2 · 2026-05-05 · cs.LG · stat.ML

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Claims

C1strongest claim

We cast SSL as latent distribution matching (LDM): learning representations that maximize their log-probability under an assumed latent model (alignment), while maximizing latent entropy to prevent collapse (uniformity). This view unifies independent component analysis with contrastive, non-contrastive, and predictive SSL methods... We further prove that predictive LDM yields identifiable latent representations under mild assumptions, even with nonlinear predictors.

C2weakest assumption

The existence and suitability of an 'assumed latent model' whose log-probability can be maximized, plus the 'mild assumptions' required for the identifiability proof; without the full derivations it is unclear how restrictive these are or whether they are satisfied by standard SSL objectives.

C3one line summary

Self-supervised learning is cast as latent distribution matching that aligns representations to a model while enforcing uniformity, unifying multiple SSL families and proving identifiability for predictive variants even with nonlinear predictors.

Receipt and verification

First computed	2026-05-20T00:05:45.907367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff4119316443c1d6ea7389a2e8f0e889210b655147fbe85974e0bbcd6fd76fb2

Aliases

arxiv: 2605.03517 · arxiv_version: 2605.03517v2 · doi: 10.48550/arxiv.2605.03517 · pith_short_12: 75ARSMLEIPA5 · pith_short_16: 75ARSMLEIPA5N2TT · pith_short_8: 75ARSMLE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/75ARSMLEIPA5N2TTRGROR4HIRE \
  | 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: ff4119316443c1d6ea7389a2e8f0e889210b655147fbe85974e0bbcd6fd76fb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7ce7975143800a7b5b8c6c81fc1a0663a8ffce46868a898538ad651689c5e33",
    "cross_cats_sorted": [
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-05T08:53:00Z",
    "title_canon_sha256": "22e38605503f4afc6f2631c9c4851a56388e9d647616cd20ef2234670bf7595d"
  },
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  "source": {
    "id": "2605.03517",
    "kind": "arxiv",
    "version": 2
  }
}