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llm-tuning-patterns

Choose LLM settings for theorem proving, code generation, and creative exploration. It provides examples for output limits and response variety, plus proof planning prompts and a method for generating multiple proof attempts and selecting the best candidate.

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LLM Tuning Patterns

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이럴 때 유용합니다

  • Choosing LLM settings for theorem proving
  • Adjusting output settings for code generation
  • Increasing response variety for creative exploration
  • Comparing multiple candidate proofs for a hard theorem

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  • SKILL.md1.9 KB

SKILL.md(원문)

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LLM Tuning Patterns

Evidence-based patterns for configuring LLM parameters, based on APOLLO and Godel-Prover research.

Pattern

Different tasks require different LLM configurations. Use these evidence-based settings.

Theorem Proving / Formal Reasoning

Based on APOLLO parity analysis:

ParameterValueRationale
max_tokens4096Proofs need space for chain-of-thought
temperature0.6Higher creativity for tactic exploration
top_p0.95Allow diverse proof paths

Proof Plan Prompt

Always request a proof plan before tactics:

Given the theorem to prove:
[theorem statement]

First, write a high-level proof plan explaining your approach.
Then, suggest Lean 4 tactics to implement each step.

The proof plan (chain-of-thought) significantly improves tactic quality.

Parallel Sampling

For hard proofs, use parallel sampling:

  • Generate N=8-32 candidate proof attempts
  • Use best-of-N selection
  • Each sample at temperature 0.6-0.8

Code Generation

ParameterValueRationale
max_tokens2048Sufficient for most functions
temperature0.2-0.4Prefer deterministic output

Creative / Exploration Tasks

ParameterValueRationale
max_tokens4096Space for exploration
temperature0.8-1.0Maximum creativity

Anti-Patterns

  • Too low tokens for proofs: 512 tokens truncates chain-of-thought
  • Too low temperature for proofs: 0.2 misses creative tactic paths
  • No proof plan: Jumping to tactics without planning reduces success rate

Source Sessions

  • This session: APOLLO parity - increased max_tokens 512->4096, temp 0.2->0.6
  • This session: Added proof plan prompt for chain-of-thought before tactics

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