Thinking by Subtraction: Confidence-Driven Contrastive Decoding for LLM Reasoning

• URL: http://arxiv.org/abs/2602.18232v1
• Date: Fri, 20 Feb 2026 14:13:22 GMT
• Title: Thinking by Subtraction: Confidence-Driven Contrastive Decoding for LLM Reasoning
• Authors: Lexiang Tang, Weihao Gao, Bingchen Zhao, Lu Ma, Qiao jin, Bang Yang, Yuexian Zou,
• Abstract summary: Thinking by Subtraction is a confidence-driven contrastive decoding approach.<n>A small subset of low-confidence tokens disproportionately contributes to reasoning errors and unnecessary output expansion.<n>Our method, Confidence-Driven Contrastive Decoding, detects low-confidence tokens during decoding and intervenes at these positions.
• Score: 58.331709210563616
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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