Paper
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
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.
Metadata
Related papers
Vibe Coding XR: Accelerating AI + XR Prototyping with XR Blocks and Gemini
Ruofei Du, Benjamin Hersh, David Li, Nels Numan, Xun Qian, Yanhe Chen, Zhongy... • 2026-03-25
Comparing Developer and LLM Biases in Code Evaluation
Aditya Mittal, Ryan Shar, Zichu Wu, Shyam Agarwal, Tongshuang Wu, Chris Donah... • 2026-03-25
The Stochastic Gap: A Markovian Framework for Pre-Deployment Reliability and Oversight-Cost Auditing in Agentic Artificial Intelligence
Biplab Pal, Santanu Bhattacharya • 2026-03-25
Retrieval Improvements Do Not Guarantee Better Answers: A Study of RAG for AI Policy QA
Saahil Mathur, Ryan David Rittner, Vedant Ajit Thakur, Daniel Stuart Schiff, ... • 2026-03-25
MARCH: Multi-Agent Reinforced Self-Check for LLM Hallucination
Zhuo Li, Yupeng Zhang, Pengyu Cheng, Jiajun Song, Mengyu Zhou, Hao Li, Shujie... • 2026-03-25
Raw Data (Debug)
{
"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2602.18232v1</id>\n <title>Thinking by Subtraction: Confidence-Driven Contrastive Decoding for LLM Reasoning</title>\n <updated>2026-02-20T14:13:22Z</updated>\n <link href='https://arxiv.org/abs/2602.18232v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2602.18232v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.CL'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.AI'/>\n <published>2026-02-20T14:13:22Z</published>\n <arxiv:primary_category term='cs.CL'/>\n <author>\n <name>Lexiang Tang</name>\n </author>\n <author>\n <name>Weihao Gao</name>\n </author>\n <author>\n <name>Bingchen Zhao</name>\n </author>\n <author>\n <name>Lu Ma</name>\n </author>\n <author>\n <name>Qiao jin</name>\n </author>\n <author>\n <name>Bang Yang</name>\n </author>\n <author>\n <name>Yuexian Zou</name>\n </author>\n </entry>"
}