Reasoning-capable large language models solve hard problems by emitting long chains of thought, paying heavily in latency, GPU time, and energy. Casual inspection of their traces reveals extensive reformulation, verification, and circular self-reflection, yet how much of this deliberation is actually necessary has never been measured at scale or explained from first principles. This paper closes both gaps. We formalise reasoning redundancy directly in terms of the reasoning model itself: the redundancy of a correct trace is the largest fraction of its trailing segmented steps that can be truncated while π, forced to terminate thinking and emit a final answer, still produces the correct answer. A large-scale quantification across four frontier reasoning models and two mathematical benchmarks shows that step-level redundancy is consistently high -- between 61% and 93% across the 8 (model, benchmark) conditions we study, with the median critical prefix equal to a single segmented step in six of the eight conditions -- that the finding is robust to the choice of judge family, and that although ρ decreases with problem difficulty on MATH-500, all four models remain substantially redundant (ρ∈[46%,85%]) even on the hardest Level-5 problems. We then prove that this redundancy is a structural consequence of length-agnostic outcome rewards, not a model-specific artefact: under any such reward, no finite expected stopping time is optimal. The result holds regardless of RL algorithm, base model, data distribution, or whether the policy is obtained via RL or distillation; over-thinking is therefore not a bug to be patched in individual models but a structural property of how current reasoning models are trained. Code: https://github.com/zhiyuanZhai20/how-much-thinking-is-enough
Large Reasoning Models (LRMs) improve performance by generating explicit intermediate reasoning traces through increased test-time compute, yet the assumption that longer reasoning is consistently beneficial remains under-examined. While recent evidence shows that additional reasoning can lead models to overthink, we ask: "Once a model has reached the correct answer, does further reasoning refine the solution, or deviate from it?" To study the dynamics after correctness, we introduce a prefix-level trajectory evaluation protocol grounded in reasoning sufficiency, defining the minimum reasoning budget required for a model to first generate the correct answer. This allows us to disentangle verbose overthinking, where additional reasoning is redundant but harmless, from harmful overthinking, where continued reasoning destabilizes an already-correct trajectory. Starting from multimodal benchmarks, we find that many instances considered reasoning-intensive require surprisingly little reasoning. Moreover, stopping at the first correct prefix improves accuracy over standard reasoning up to 21%, revealing that current models are limited not only by their ability to reason, but also by their inability to stop at the right time. Furthermore, while common efficiency strategies like early stopping substantially reduce verbose overthinking (up to 50%), they fail to mitigate harmful overthinking. Failure analysis reveals that correctness deviations are mainly driven by logical drift and visual reinterpretation. Finally, we show that our findings generalize to language-only reasoning benchmarks, highlighting harmful overthinking as a broader reliability risk. Code available at https://simonecaldarella.github.io/thinking-past-the-answer.
Large reasoning models can produce correct yet unnecessarily long reasoning traces. Existing methods improve reasoning efficiency with trajectory-level objectives or local token- and step-level signals, but rarely model inter-step semantic dependencies. This limits their ability to distinguish redundant steps from those that support later deductions, making it harder to shorten reasoning without sacrificing accuracy. We introduce RECAP (REdundancy-aware Credit Assignment via Propagation), which addresses this limitation by assigning credit where it is due based on both a step's downstream role in the reasoning structure and its contribution to solving the problem correctly. We define structural responsibility to capture the step's downstream role by measuring how strongly later reasoning depends on it, using credit propagated backward from the final-answer node through an outcome-independent, LLM-annotated semantic dependency graph. However, a step can have high structural responsibility yet steer the reasoning away from the correct solution. RECAP therefore introduces step efficacy to measure answer-directed progress through changes in gold-answer log-likelihood as each step is added. Together, these signals reshape rollout-level GRPO advantages into step-specific updates. RECAP requires neither a separately trained process reward model nor preconstructed concise trajectories. Across two 7B models and four mathematical reasoning benchmarks, RECAP improves the accuracy-efficiency trade-off. On Qwen2.5-Math-7B, it improves pass@1 by 2.0-3.7 percentage points while reducing reasoning tokens by 8%-31% relative to GRPO across all four benchmarks. Analysis suggests these savings reflect fewer reasoning operations and less dead-end reasoning, rather than more compact expression.
Reasoning LLMs often spend substantial tokens on long intermediate reasoning traces (e.g., chain-of-thought) when solving new problems. We propose to summarize and store reusable reasoning skills distilled from extensive deliberation and trial-and-error exploration, and to retrieve these skills at inference time to guide future reasoning. Unlike the prevailing \emph{reasoning from scratch} paradigm, our approach first recalls relevant skills for each query, helping the model avoid redundant detours and focus on effective solution paths. We evaluate our method on coding and mathematical reasoning tasks, and find that it significantly reduces reasoning tokens while improving overall performance. The resulting lower per-request cost indicates strong practical and economic potential for real-world deployment.