Thinking Traps in Long Chain-of-Thought: A Measurable Study and Trap-Aware Adaptive Restart

TL;DR

This work investigates why longer chains of thought do not always yield correct answers, identifying prefix-dominant Thinking Traps where an early wrong commitment governs subsequent reasoning. It introduces Trap-Aware Adaptive Restart (TAAR), a test-time controller that learns to predict a trap location $\hat{t}$ and an escape probability $\hat{p}$ from partial traces, then truncates the prefix before the trap and adaptively restarts decoding with varying perturbation strength. Across five challenging reasoning benchmarks (AIME24/25, GPQA-Diamond, HMMT25, BRUMO25) and multiple base models, TAAR improves accuracy and token efficiency without fine-tuning the base models, particularly for small-to-mid scale reasoners where traps are prevalent. The results demonstrate that reallocating compute to counterfactual re-derivations by removing corrupted prefixes can meaningfully enhance reasoning performance in a fixed-budget setting, and that early online trap detection enables practical, cost-efficient interventions.

Abstract

Scaling test-time compute via Long Chain-of-Thought (Long-CoT) significantly enhances reasoning capabilities, yet extended generation does not guarantee correctness: after an early wrong commitment, models may keep elaborating a self-consistent but incorrect prefix. Through fine-grained trajectory analysis, we identify Thinking Traps, prefix-dominant deadlocks where later reflection, alternative attempts, or verification fails to revise the root error. On a curated subset of DAPO-MATH, 89\% of failures exhibit such traps. To solve this problem, we introduce TAAR (Trap-Aware Adaptive Restart), a test-time control framework that trains a diagnostic policy to predict two signals from partial trajectories: a trap index for where to truncate and an escape probability for whether and how strongly to intervene. At inference time, TAAR truncates the trajectory before the predicted trap segment and adaptively restarts decoding; for severely trapped cases, it applies stronger perturbations, including higher-temperature resampling and an optional structured reboot suffix. Experiments on challenging mathematical and scientific reasoning benchmarks (AIME24, AIME25, GPQA-Diamond, HMMT25, BRUMO25) show that TAAR improves reasoning performance without fine-tuning base model parameters.

Figures (9)

• Figure 1: Conceptual illustration of Thinking Traps. A reasoner facing a trap can leverage Diagnostic Policy Model to choose an appropriate escape strategy: step over (no intervention), jump (mild intervention), or use a ladder (strong intervention).
• Figure 2: Overview of the TAAR framework. Left: Diagnostic Data Construction pipeline that segments trajectories and labels trap indices and escape probabilities via GLM-4.7 annotation with manual verification. Middle: Training of the diagnostic policy $\pi_\phi$. Right: Adaptive restart controller selects intervention based on $\hat{p}$.
• Figure 3: Escape rate by cut strategy. Truncating at the trap segment (Cut@Trap) achieves significantly higher escape rates than keeping the trap and attempting downstream correction (Cut@Post-trap).
• Figure 3: Early diagnosis efficiency. Prefix@X%: the diagnostic policy receives only the first X% of the trajectory. TAAR achieves comparable performance even with partial observations.
• Figure 4: Trap position distribution. Traps concentrate in the early portion of trajectories, with 44.4% occurring before relative position 0.2.