Chain-of-thought (CoT) reasoning improves LLM accuracy on complex tasks, but CoTs are often unfaithful; that is, the model does not rely on the stated reasoning steps to produce its answer. Existing methods to improve faithfulness require human annotations. We propose LIFT, which automatically scores each reasoning step by its causal influence: we replace it with a domain-matched but irrelevant fact and measure the drop in answer log-probability. We fine-tune on high-scoring CoT traces where interventions successfully disrupted reasoning, jointly optimizing for faithfulness and accuracy. LIFT improves faithfulness across three models (Mistral-7B-Instruct, Qwen3-8B, and Qwen3-4B-Instruct) and three benchmarks, with accuracy comparable to a model fine-tuned solely for accuracy.

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