Indirect Reasoning with LLMs (DIR)
Direct-Indirect Reasoning augments standard CoT with contrapositive and proof-by-contradiction templates, giving LLMs an explicit way to attack problems they can't solve forward.
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Two-step pipeline: Step 1 augments the data with contrapositive versions of rules to expand what the LLM can reason over; Step 2 uses prompt templates that steer the model into proof-by-contradiction when needed.
Factual reasoning: +27.33% accuracy over direct reasoning baselines on factual reasoning benchmarks, averaged across models.
Math proofs: +31.43% improvement on math proof tasks, where indirect reasoning is often the only tractable route.
Backbone agnostic: Works across GPT-3.5-turbo and Gemini Pro, suggesting the technique generalizes beyond any particular LLM family.