Think Deep, Not Just Long: Measuring LLM Reasoning Effort via Deep-Thinking Tokens

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 \emph{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 \textit{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.