Pith Number

pith:PA3MCOFJ

pith:2024:PA3MCOFJRIH3GPJFL5NYGDNS46

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Hallucination is Inevitable: An Innate Limitation of Large Language Models

Mohan Kankanhalli, Sanjay Jain, Ziwei Xu

LLMs cannot learn all computable functions and will therefore inevitably hallucinate when used as general problem solvers.

arxiv:2401.11817 v2 · 2024-01-22 · cs.CL · cs.AI · cs.LG

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Claims

C1strongest claim

we show that LLMs cannot learn all the computable functions and will therefore inevitably hallucinate if used as general problem solvers

C2weakest assumption

The formal computable world is representative enough of the real world that the impossibility result carries over directly to practical LLMs.

C3one line summary

Hallucinations are inevitable in LLMs because they cannot learn all computable functions according to learning theory.

References

89 extracted · 89 resolved · 10 Pith anchors

[1] Characterizing Attribution and Fluency Tradeoffs for Retrieval-Augmented Large Language Models 2023

[2] Computational Complexity - A Modern Approach 2009

[3] On the prediction of General Recursive Functions 1972

[4] Learning families of algebraic structures from informant 2020

[5] Airline held liable for its chatbot giving passenger bad advice -- what this means for travellers, February 2024 2024

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Receipt and verification

First computed	2026-05-17T23:38:50.232845Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7836c138a98a0fb33d255f5b830db2e78729ce4a796224c35216fc6cb736bb6e

Aliases

arxiv: 2401.11817 · arxiv_version: 2401.11817v2 · doi: 10.48550/arxiv.2401.11817 · pith_short_12: PA3MCOFJRIH3 · pith_short_16: PA3MCOFJRIH3GPJF · pith_short_8: PA3MCOFJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PA3MCOFJRIH3GPJFL5NYGDNS46 \
  | 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: 7836c138a98a0fb33d255f5b830db2e78729ce4a796224c35216fc6cb736bb6e

Canonical record JSON

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    "abstract_canon_sha256": "248c375cbb4fd5f2746f4d1b73399ec0426c9050dc6345ed0f1bc46fbd9b1bf4",
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      "cs.AI",
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    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2024-01-22T10:26:14Z",
    "title_canon_sha256": "0a5982e2771b534222c546140a26a6e14601bed245b6e35d3b5a1fcd4f37b4cc"
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