pith:OXXTT4OH
From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step
A progressive fine-tuning method lets language models internalize chain-of-thought steps so they can solve harder reasoning tasks without producing explicit intermediate outputs.
arxiv:2405.14838 v1 · 2024-05-23 · cs.CL · cs.AI · cs.LG
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\pithnumber{OXXTT4OHRETB3KWT7POHNLCMVB}
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Claims
Our approach enables a GPT-2 Small model to solve 9-by-9 multiplication with up to 99% accuracy, whereas standard training cannot solve beyond 4-by-4 multiplication.
That performance gains arise specifically from internalizing the removed reasoning steps rather than from increased task exposure, regularization, or other side effects of the progressive fine-tuning schedule.
Gradual fine-tuning that removes explicit CoT steps lets GPT-2 Small reach 99% accuracy on 9x9 multiplication and Mistral 7B exceed 50% on GSM8K with no intermediate outputs.
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Receipt and verification
| First computed | 2026-05-17T23:38:47.988012Z |
|---|---|
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | Pith Ed25519
(pith-v1-2026-05) · public key |
| Schema | pith-number/v1.0 |
Canonical hash
75ef39f1c789261daad3fbdc76ac4ca85ed7cc2c883c7920c4c44a61de79c7fc
Aliases
· · · · ·Agent API
Verify this Pith Number yourself
curl -sH 'Accept: application/ld+json' https://pith.science/pith/OXXTT4OHRETB3KWT7POHNLCMVB \
| 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: 75ef39f1c789261daad3fbdc76ac4ca85ed7cc2c883c7920c4c44a61de79c7fc
Canonical record JSON
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