Thinking by Subtraction: Confidence-Driven Contrastive Decoding for LLM Reasoning
This work provides a training-free method to enhance reasoning reliability for users of LLMs, though it is incremental as it builds on existing contrastive decoding approaches.
The paper tackles the problem of improving reasoning reliability in large language models by addressing localized uncertainty in low-confidence tokens, resulting in significant accuracy gains across mathematical reasoning benchmarks and reduced output length with minimal computational overhead.
Recent work on test-time scaling for large language model (LLM) reasoning typically assumes that allocating more inference-time computation uniformly improves correctness. However, prior studies show that reasoning uncertainty is highly localized: a small subset of low-confidence tokens disproportionately contributes to reasoning errors and unnecessary output expansion. Motivated by this observation, we propose Thinking by Subtraction, a confidence-driven contrastive decoding approach that improves reasoning reliability through targeted token-level intervention. Our method, Confidence-Driven Contrastive Decoding, detects low-confidence tokens during decoding and intervenes selectively at these positions. It constructs a contrastive reference by replacing high-confidence tokens with minimal placeholders, and refines predictions by subtracting this reference distribution at low-confidence locations. Experiments show that CCD significantly improves accuracy across mathematical reasoning benchmarks while substantially reducing output length, with minimal KV-cache overhead. As a training-free method, CCD enhances reasoning reliability through targeted low-confidence intervention without computational redundancy. Our code will be made available at: https://github.com/bolo-web/CCD.