Pith Number

pith:VPSR4ZIC

pith:2021:VPSR4ZICWER5DNM3ZWX4JTRFRJ

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An Explanation of In-context Learning as Implicit Bayesian Inference

Aditi Raghunathan, Percy Liang, Sang Michael Xie, Tengyu Ma

Large language models perform in-context learning by implicitly inferring latent concepts that explain coherence in both pretraining data and prompt examples.

arxiv:2111.02080 v6 · 2021-11-03 · cs.CL · cs.LG

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4 Citations open

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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

We prove when this occurs despite a distribution mismatch between prompts and pretraining data in a setting where the pretraining distribution is a mixture of HMMs.

C2weakest assumption

That real-world pretraining corpora exhibit long-range coherence driven by latent document-level concepts that can be adequately captured by a mixture-of-HMMs generative process, and that this mechanism dominates the in-context behavior of large-scale models trained on messy web data.

C3one line summary

In-context learning emerges as implicit Bayesian inference of latent concepts when pretraining data has long-range coherence, proven for mixture-of-HMM distributions and replicated on the synthetic GINC dataset.

References

300 extracted · 300 resolved · 7 Pith anchors

[1] Statistical inference for probabilistic functions of finite state markov chains 1966

[2] Blei, Andrew Ng, and M 2003

[3] Language Models are Few-Shot Learners 2005 · arXiv:2005.14165

[4] Le, and Christopher D 2020

[5] A. P. Dempster, Laird N. M., and Rubin D. B. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B, 39 0 (1): 0 1--38, 1977 1977

Formal links

2 machine-checked theorem links

Cited by

27 papers in Pith

Prompt Evolution for Generative AI: A Classifier-Guided Approach

Amortized Inference of Causal Models via Conditional Fixed-Point Iterations

Distributional Alignment as a Criterion for Designing Task Vectors in In-Context Learning

Transformer-like Inference from Optimal Control

ACIL: Auto Chain of Thoughts for In-Context Learning

Receipt and verification

First computed	2026-05-17T23:38:46.404101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abe51e6502b123d1b59bcdafc4ce258a748628095a8fba3c262f049ff320956a

Aliases

arxiv: 2111.02080 · arxiv_version: 2111.02080v6 · doi: 10.48550/arxiv.2111.02080 · pith_short_12: VPSR4ZICWER5 · pith_short_16: VPSR4ZICWER5DNM3 · pith_short_8: VPSR4ZIC

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VPSR4ZICWER5DNM3ZWX4JTRFRJ \
  | 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: abe51e6502b123d1b59bcdafc4ce258a748628095a8fba3c262f049ff320956a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ece93fb738dd7f046125c81a57fa34c43199dcc6730005f0994bac4c271d5308",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2021-11-03T09:12:33Z",
    "title_canon_sha256": "d11121fff8b4527ebb3daba0fca9697ace21e7716128ef726203c70bc0afe3a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.02080",
    "kind": "arxiv",
    "version": 6
  }
}