SKILL.md
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:
Parameter
Value
Rationale
max_tokens
4096
Proofs need space for chain-of-thought
temperature
0.6
Higher creativity for tactic exploration
top_p
0.95
Allow 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
Parameter
Value
Rationale
max_tokens
2048
Sufficient for most functions
temperature
0.2-0.4
Prefer deterministic output
Creative / Exploration Tasks
Parameter
Value
Rationale
max_tokens
4096
Space for exploration
temperature
0.8-1.0
Maximum 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