One-Token Verification for Reasoning Correctness Estimation

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.

Large language models (LLMs) have demonstrated impressive reasoning capabilities by scaling test-time compute via long Chain-of-Thought (CoT). However, recent findings suggest that raw token counts are unreliable proxies for reasoning quality: increased generation length does not consistently correlate with accuracy and may instead signal "overthinking," leading to performance degradation. In this work, we quantify inference-time effort by identifying deep-thinking tokens -- tokens where internal predictions undergo significant revisions in deeper model layers prior to convergence. Across four challenging mathematical and scientific benchmarks (AIME 24/25, HMMT 25, and GPQA-diamond) and a diverse set of reasoning-focused models (GPT-OSS, DeepSeek-R1, and Qwen3), we show that deep-thinking ratio (the proportion of deep-thinking tokens in a generated sequence) exhibits a robust and consistently positive correlation with accuracy, substantially outperforming both length-based and confidence-based baselines. Leveraging this insight, we introduce Think@n, a test-time scaling strategy that prioritizes samples with high deep-thinking ratios. We demonstrate that Think@n matches or exceeds standard self-consistency performance while significantly reducing inference costs by enabling the early rejection of unpromising generations based on short prefixes.

Explicitly eliciting reasoning substantially improves LLM performance. Existing approaches require a predefined characterization of reasoning, whether through CoT prompt design, contrastive CoT directions, or via SAE derived reasoning features. For mathematical reasoning with verifiable answers, we show that a much simpler signal suffices, which is the correctness of the model's own direct answer attempts. This signal yields a latent direction that elicits reasoning. This direction is decodable within the activations of most attention heads, but only a small subset of them can be effectively intervened. We introduce COMPASS, an inference-time steering method that identifies these heads using a logit-space attribution score and steers their activations along the correctness direction, requiring only per-head activation statistics. Across three model families and multiple math benchmarks, COMPASS outperforms the activation-steering baselines we compare against, improves GSM8K accuracy by 16 percentage points on average, and approaches CoT accuracy with 20-70% fewer generated tokens. Interventions transfer without re-fitting to unseen benchmarks, and ablations show that both the correctness direction and the small set of heads carrying it are necessary, with the effect concentrated in remarkably few heads.