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