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

arXiv: https://arxiv.org/abs/2602.18232 · HTML: https://mlsanity.com/paper/2602.18232/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 28 of its 52 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 28 of 28)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models](https://mlsanity.com/paper/2309.03883/) (2023)
- [Deep Think with Confidence](https://mlsanity.com/paper/2508.15260/) (2025)
- [Mitigating Hallucinations in Large Vision-Language Models with Instruction Contrastive Decoding](https://mlsanity.com/paper/2403.18715/) (2024)
- [Turning Up the Heat: Min-p Sampling for Creative and Coherent LLM Outputs](https://mlsanity.com/paper/2407.01082/) (2024)
- [From Decoding to Meta-Generation: Inference-time Algorithms for Large Language Models](https://mlsanity.com/paper/2406.16838/) (2024)
- [Confidence Improves Self-Consistency in LLMs](https://mlsanity.com/paper/2502.06233/) (2025)
- [Learning What Reinforcement Learning Can't: Interleaved Online Fine-Tuning for Hardest Questions](https://mlsanity.com/paper/2506.07527/) (2025)
- [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025)
- [Contrastive Decoding Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2309.09117/) (2023)
- [Confidence Is All You Need: Few-Shot RL Fine-Tuning of Language Models](https://mlsanity.com/paper/2506.06395/) (2025)
- [Parallel-R1: Towards Parallel Thinking via Reinforcement Learning](https://mlsanity.com/paper/2509.07980/) (2025)
- [Enhancing Contextual Understanding in Large Language Models through Contrastive Decoding](https://mlsanity.com/paper/2405.02750/) (2024)
- [The Majority is not always right: RL training for solution aggregation](https://mlsanity.com/paper/2509.06870/) (2025)
- [Exploration vs Exploitation: Rethinking RLVR through Clipping, Entropy, and Spurious Reward](https://mlsanity.com/paper/2512.16912/) (2025)
- [Entropy-Gated Branching for Efficient Test-Time Reasoning](https://mlsanity.com/paper/2503.21961/) (2025)
- [Distillation Contrastive Decoding: Improving LLMs Reasoning with Contrastive Decoding and Distillation](https://mlsanity.com/paper/2402.14874/) (2024)
- [Leash: Adaptive Length Penalty and Reward Shaping for Efficient Large Reasoning Model](https://mlsanity.com/paper/2512.21540/) (2025)
- [Confidence Estimation for LLMs in Multi-turn Interactions](https://mlsanity.com/paper/2601.02179/) (2026)
- [Safety Alignment of Large Language Models via Contrasting Safe and Harmful Distributions](https://mlsanity.com/paper/2406.16743/) (2024)
- [Not All Tokens and Heads Are Equally Important: Dual-Level Attention Intervention for Hallucination Mitigation](https://mlsanity.com/paper/2506.12609/) (2025)
- [Less is More: Improving LLM Reasoning with Minimal Test-Time Intervention](https://mlsanity.com/paper/2510.13940/) (2025)
- [GIFT: Reconciling Post-Training Objectives via Variational Finite-Temperature Gibbs Initialization](https://mlsanity.com/paper/2601.09233/) (2026)

## Built on by (most cited first, 6 of 6)

- [Reasoning Denoiser: Denoising Reasoning Traces for Hallucination Detection in Large Reasoning Models](https://mlsanity.com/paper/2607.22098/) (2026)
- [PathCal: State-Aware Reflection-Marker Calibration for Efficient Reasoning](https://mlsanity.com/paper/2605.23074/) (2026)
- [Gradient-Guided Reward Optimization for Inference-time Alignment](https://mlsanity.com/paper/2606.09635/) (2026)
- [Beam Search as Test-Time Self-Distillation via Counterfactual Contexts](https://mlsanity.com/paper/2609.37041/) (2026)
- [Decoding Looped Transformers Better for (Almost) Free](https://mlsanity.com/paper/2610.02185/) (2026)
- [DoubtLess: Training-Free Contrastive Decoding for Efficient Reasoning](https://mlsanity.com/paper/2610.18862/) (2026)

## Abstract (arXiv)

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.