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