llm-tuning-patterns

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