llm-tuning-patterns

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

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

| Parameter | Value | Rationale |

|-----------|-------|-----------|

| max_tokens | 2048 | Sufficient for most functions |

| temperature | 0.2-0.4 | Prefer deterministic output |

| Parameter | Value | Rationale |

|-----------|-------|-----------|

| max_tokens | 4096 | Space for exploration |

| temperature | 0.8-1.0 | Maximum creativity |

• 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

• 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