Daily Papers

We find that the response length of reasoning LLMs, whether trained by reinforcement learning or supervised learning, drastically increases for ill-posed questions with missing premises (MiP), ending up with redundant and ineffective thinking. This newly introduced scenario exacerbates the general overthinking issue to a large extent, which we name as the MiP-Overthinking. Such failures are against the ``test-time scaling law'' but have been widely observed on multiple datasets we curated with MiP, indicating the harm of cheap overthinking and a lack of critical thinking. Surprisingly, LLMs not specifically trained for reasoning exhibit much better performance on the MiP scenario, producing much shorter responses that quickly identify ill-posed queries. This implies a critical flaw of the current training recipe for reasoning LLMs, which does not encourage efficient thinking adequately, leading to the abuse of thinking patterns. To further investigate the reasons behind such failures, we conduct fine-grained analyses of the reasoning length, overthinking patterns, and location of critical thinking on different types of LLMs. Moreover, our extended ablation study reveals that the overthinking is contagious through the distillation of reasoning models' responses. These results improve the understanding of overthinking and shed novel insights into mitigating the problem.

Large Reasoning Models (LRMs) demonstrate exceptional capability in tackling complex mathematical, logical, and coding tasks by leveraging extended Chain-of-Thought (CoT) reasoning. Test-time scaling methods, such as prolonging CoT with explicit token-level exploration, can push LRMs' accuracy boundaries, but they incur significant decoding overhead. A key inefficiency source is LRMs often generate redundant thinking CoTs, which demonstrate clear structured overthinking and underthinking patterns. Inspired by human cognitive reasoning processes and numerical optimization theories, we propose TrimR, a verifier-based, training-free, efficient framework for dynamic CoT compression to trim reasoning and enhance test-time scaling, explicitly tailored for production-level deployment. Our method employs a lightweight, pretrained, instruction-tuned verifier to detect and truncate redundant intermediate thoughts of LRMs without any LRM or verifier fine-tuning. We present both the core algorithm and asynchronous online system engineered for high-throughput industrial applications. Empirical evaluations on Ascend NPUs and vLLM show that our framework delivers substantial gains in inference efficiency under large-batch workloads. In particular, on the four MATH500, AIME24, AIME25, and GPQA benchmarks, the reasoning runtime of Pangu Pro MoE, Pangu-R-38B, QwQ-32B, and DeepSeek-R1-Distill-Qwen-32B is improved by up to 70% with negligible impact on accuracy.

Modern language models can imitate complex patterns through few-shot learning, enabling them to complete challenging tasks without fine-tuning. However, imitation can also lead models to reproduce inaccuracies or harmful content if present in the context. We study harmful imitation through the lens of a model's internal representations, and identify two related phenomena: "overthinking" and "false induction heads". The first phenomenon, overthinking, appears when we decode predictions from intermediate layers, given correct vs. incorrect few-shot demonstrations. At early layers, both demonstrations induce similar model behavior, but the behavior diverges sharply at some "critical layer", after which the accuracy given incorrect demonstrations progressively decreases. The second phenomenon, false induction heads, are a possible mechanistic cause of overthinking: these are heads in late layers that attend to and copy false information from previous demonstrations, and whose ablation reduces overthinking. Beyond scientific understanding, our results suggest that studying intermediate model computations could be a promising avenue for understanding and guarding against harmful model behaviors.

Recent advances in Large Language Models (LLMs) have introduced Reasoning Large Language Models (RLLMs), which employ extended thinking processes with reflection and self-correction capabilities, demonstrating the effectiveness of test-time scaling. RLLMs exhibit innate Chain-of-Thought (CoT) reasoning capability obtained from training, leading to a natural question: "Is CoT prompting, a popular In-Context Learning (ICL) method for chat LLMs, necessary to enhance the reasoning capability of RLLMs?" In this work, we present the first comprehensive analysis of the impacts of Zero-shot CoT and Few-shot CoT on RLLMs across mathematical reasoning tasks. We examine models ranging from 1.5B to 32B parameters, finding that contrary to concerns, CoT prompting significantly enhances RLLMs' performance in most scenarios. Our results reveal distinct patterns: large-capacity models show minimal improvement on simple tasks but substantial gains on complex problems, while smaller models exhibit the opposite behavior. Further analysis demonstrates that CoT prompting effectively controls the distribution of the numbers of thinking tokens and reasoning steps, reducing excessive reflections by approximately 90% in some cases. Moreover, attention logits analysis reveals the RLLMs' overfitting to reflection-related words, which is mitigated by external CoT guidance. Notably, our experiments indicate that for RLLMs, one-shot CoT consistently yields superior performance compared to Few-shot CoT approaches. Our findings provide important insights for optimizing RLLMs' performance through appropriate prompting strategies.

Large Reasoning Models (LRMs) represent a breakthrough in AI problem-solving capabilities, but their effectiveness in interactive environments can be limited. This paper introduces and analyzes overthinking in LRMs. A phenomenon where models favor extended internal reasoning chains over environmental interaction. Through experiments on software engineering tasks using SWE Bench Verified, we observe three recurring patterns: Analysis Paralysis, Rogue Actions, and Premature Disengagement. We propose a framework to study these behaviors, which correlates with human expert assessments, and analyze 4018 trajectories. We observe that higher overthinking scores correlate with decreased performance, with reasoning models exhibiting stronger tendencies toward overthinking compared to non-reasoning models. Our analysis reveals that simple efforts to mitigate overthinking in agentic environments, such as selecting the solution with the lower overthinking score, can improve model performance by almost 30% while reducing computational costs by 43%. These results suggest that mitigating overthinking has strong practical implications. We suggest that by leveraging native function-calling capabilities and selective reinforcement learning overthinking tendencies could be mitigated. We also open-source our evaluation framework and dataset to facilitate research in this direction at https://github.com/AlexCuadron/Overthinking.

Recent Large Reasoning Models (LRMs) excel at complex reasoning tasks but often suffer from overthinking, generating overly long and redundant reasoning trajectories. To explore its essence, our empirical analysis reveals that LRMs are primarily limited to recognizing task properties (i.e., difficulty levels) like humans before solving the problem, leading to a one-size-fits-all reasoning process. Inspired by this, a pressing and natural question emerges: Can we explicitly bootstrap such ability to alleviate overthinking in LRMs? In this paper, we propose Think-How-to-Think (TH2T), a novel two-stage fine-tuning strategy that progressively inspires LRMs' difficulty cognition and redundancy cognition of LRMs. Specifically, we first inject difficulty hypnosis into output prefixes to guide the model toward adaptive reasoning depth, trained on a hybrid dataset mixing short and long reasoning paths. Then, we incorporate redundancy hypnosis, which supervises the intermediate reasoning steps to identify and eliminate unnecessary reasoning patterns. Experiments on 7B/14B/32B models demonstrate that TH2T significantly reduces inference costs by over 70% on easy tasks and 40% on hard tasks while maintaining performance stability. The resulting outputs exhibit clear signs of difficulty-aware capabilities and reduced redundancy (e.g., reflection and looping).

Recent advances in Large Reasoning Models (LRMs) have shown impressive capabilities in mathematical and logical reasoning. However, current LRMs rarely admit ignorance or respond with "I don't know". Instead, they often produce incorrect answers while showing undue confidence, raising concerns about their factual reliability. In this work, we identify two pathological reasoning patterns characterized by overthinking that contribute to the overconfident and incorrect answers: last-minute guessing and second-thought spiraling. To address these issues, we propose BARREL-a novel framework that promotes concise and boundary-aware factual reasoning. Our experiments show that BARREL-training increases the reliability of DeepSeek-R1-Distill-Llama-8B from 39.33% to 61.48%, while still achieving accuracy comparable to models finetuned on reasoning data generated by R1. These results demonstrate that our pilot study is inspiring to build more reliable and factual System 2 LRMs.

As test-time scaling becomes a pivotal research frontier in Large Language Models (LLMs) development, contemporary and advanced post-training methodologies increasingly focus on extending the generation length of long Chain-of-Thought (CoT) responses to enhance reasoning capabilities toward DeepSeek R1-like performance. However, recent studies reveal a persistent overthinking phenomenon in state-of-the-art reasoning models, manifesting as excessive redundancy or repetitive thinking patterns in long CoT responses. To address this issue, in this paper, we propose a simple yet effective two-stage reinforcement learning framework for achieving concise reasoning in LLMs, named ConciseR. Specifically, the first stage, using more training steps, aims to incentivize the model's reasoning capabilities via Group Relative Policy Optimization with clip-higher and dynamic sampling components (GRPO++), and the second stage, using fewer training steps, explicitly enforces conciseness and improves efficiency via Length-aware Group Relative Policy Optimization (L-GRPO). Significantly, ConciseR only optimizes response length once all rollouts of a sample are correct, following the "walk before you run" principle. Extensive experimental results demonstrate that our ConciseR model, which generates more concise CoT reasoning responses, outperforms recent state-of-the-art reasoning models with zero RL paradigm across AIME 2024, MATH-500, AMC 2023, Minerva, and Olympiad benchmarks.

Although Large Vision-Language Models (LVLMs) have made substantial progress, hallucination, where generated text is not grounded in the visual input, remains a challenge. As LVLMs become stronger, previously reported hallucination patterns, such as linguistic bias and overthinking phenomenon, become far less consistent, making the corresponding mitigation techniques substantially less effective. In this paper, we introduce an Internal self-Correction mechanism utilizing Layer Attention (ICLA) that operates directly on hidden states during generation. Each layer selectively retrieves information from all preceding layers through a diagonal cross-layer attention mechanism, enabling self-refinement without any external correction signals. With introducing and training only 0.2M and 0.1M additional parameters on LLaVA1.5-7B and Qwen2.5-VL-7B, \ours consistently improves visual grounding across multiple hallucination benchmarks, demonstrating its effectiveness for more advanced LVLMs.

Extending CoT through RL has been widely used to enhance the reasoning capabilities of LLMs. However, due to the sparsity of reward signals, it can also induce undesirable thinking patterns such as overthinking, i.e., generating redundant intermediate reasoning content. In this work, we argue that a major source of such redundancy is inefficient reflection, which often manifests in two problematic patterns: Indiscriminate Reflection, where the model performs broad, low-impact checks throughout reasoning, and Repetitive Reflection, where it repeatedly re-verifies an already established conclusion. To address this, we introduce a graph-based CoT optimization framework. Specifically, we convert each linear CoT into a directed acyclic graph (DAG) with explicit dependency edges, and design a dual pruning strategy: branch-level pruning removes weakly contributing reflection branches, while depth-level pruning eliminates late-stage re-verification. We distill this behavior via a three-stage pipeline: (1) SFT to initialize the policy on pruned concise traces, (2) DPO to prefer correct but less redundant trajectories, and (3) GRPO with length penalty to jointly optimize answer correctness and efficiency. Experiments show that our approach reduces the average reasoning tokens by 42\% while maintaining or improving accuracy.

Math reasoning benchmarks have proliferated, yet most lack a per-item difficulty signal grounded in actual human performance. We introduce KCSAT-ML, a decade (2014-2025) of Korean College Scholastic Ability Test (KCSAT; Suneung) mathematics: 664 problems with a 339-item core set carrying official per-item error rates from nationwide cohorts of hundreds of thousands of examinees. We pair the benchmark with Difficulty-aligned Reasoning Gain (DRG): a score-orthogonal metric that asks whether a model's mistakes concentrate on the items humans found hard, or on items humans found easy. Together they expose, across a wide range of VLMs (and LLMs via OCR), three patterns: (i) low-budget accuracy collapses on the high-human-error tail at every model size; (ii) test-time scaling (TTS) raises token use roughly linearly with cohort error rate, while accuracy gains follow a non-monotonic curve; (iii) within a single family, TTS flips between anti-scaling on the hardest items and overthinking on easier ones -- two faces of the same alignment failure. On DRG, models with near-identical accuracy can sit at near-opposite values: one model gets wrong what humans also find hard, while another solves the hardest items yet fails on items humans find easy -- a contrast that aggregate accuracy hides. Our code and dataset builder will be open-sourced at https://github.com/naver-ai/KCSAT-ML.

Large reasoning models (LRMs) have achieved impressive performance in complex tasks, often outperforming conventional large language models (LLMs). However, the prevalent issue of overthinking severely limits their computational efficiency. Overthinking occurs when models generate excessive and redundant tokens that contribute little to accurate outcomes, especially in simple tasks, resulting in a significant waste of computational resources. To systematically investigate this issue, we introduce Think-Bench, a benchmark designed to evaluate the reasoning efficiency of LRMs. We also propose novel efficiency metrics and conduct a comprehensive evaluation of various LRMs across multiple dimensions, including the reasoning process, outcome quality, and chain-of-thought (CoT) characteristics. Our analysis reveals that most LRMs exhibit overthinking in handling easy questions, generating unnecessarily lengthy reasoning chains. While many LRMs demonstrate high CoT quality, several suffer from low efficiency. We hope that Think-Bench can serve as a robust foundation for advancing research into LRMs.

Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they often suffer from overthinking, expending redundant computational steps on simple problems, or underthinking, failing to explore sufficient reasoning paths despite inherent capabilities. These issues lead to inefficiencies and potential inaccuracies, limiting practical deployment in resource-constrained settings. Existing methods to mitigate overthinking, such as suppressing reflective keywords or adjusting reasoning length, may inadvertently induce underthinking, compromising accuracy. Therefore, we propose ReBalance, a training-free framework that achieves efficient reasoning with balanced thinking. ReBalance leverages confidence as a continuous indicator of reasoning dynamics, identifying overthinking through high confidence variance and underthinking via consistent overconfidence. By aggregating hidden states from a small-scale dataset into reasoning mode prototypes, we compute a steering vector to guide LRMs' reasoning trajectories. A dynamic control function modulates this vector's strength and direction based on real-time confidence, pruning redundancy during overthinking, and promoting exploration during underthinking. Extensive experiments conducted on four models ranging from 0.5B to 32B, and across nine benchmarks in math reasoning, general question answering, and coding tasks demonstrate that ReBalance effectively reduces output redundancy while improving accuracy, offering a general, training-free, and plug-and-play strategy for efficient and robust LRM deployment. Code is available at https://github.com/yu-lin-li/ReBalance .

Large Language Models (LLMs) trained via Reinforcement Learning (RL) have recently achieved impressive results on reasoning benchmarks. Yet, growing evidence shows that these models often generate longer but ineffective chains of thought (CoTs), calling into question whether benchmark gains reflect real reasoning improvements. We present new evidence of overthinking, where models disregard correct solutions even when explicitly provided, instead continuing to generate unnecessary reasoning steps that often lead to incorrect conclusions. Experiments on three state-of-the-art models using the AIME2024 math benchmark reveal critical limitations in these models ability to integrate corrective information, posing new challenges for achieving robust and interpretable reasoning.

Reasoning language models frequently overthink: generating extended chains of behaviors such as hedging, approach abandonment, and self contradiction that consume tokens without improving answers. We show that these behaviors are not merely a consequence of length; even when controlling for response length, incorrect traces exhibit higher rates of unproductive self-reflection than correct ones. Addressing this requires identifying where self-reflection helps vs hurts, but obtaining these step-level annotations is costly. We observe that intermediate answer commitments within reasoning traces can provide a cheap proxy: by comparing each final answer candidate in the trace to the ground truth, we can determine whether subsequent reflection is productive without any additional supervision. Building on this insight, we propose DASH (Drift Aware advantage SHaping), which assigns segment-level credit based on whether each reasoning segment leads toward or away from correctness. On competition-level math benchmarks, DASH achieves the highest accuracy where overthinking is prevalent (Average Accuracy: 59.45% vs. 58.1% Dr.GRPO vs. 56.95% GRPO) while reducing overthinking behaviors and achieving more productive self-correction than baselines.

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 (LRMs), such as OpenAI o1 and DeepSeek-R1, have significantly enhanced their reasoning capabilities by generating longer chains of thought, demonstrating outstanding performance across a variety of tasks. However, this performance gain comes at the cost of a substantial increase in redundant reasoning during the generation process, leading to high computational overhead and exacerbating the issue of overthinking. Although numerous existing approaches aim to address the problem of overthinking, they often rely on external interventions. In this paper, we propose a novel framework, Self-Braking Tuning (SBT), which tackles overthinking from the perspective of allowing the model to regulate its own reasoning process, thus eliminating the reliance on external control mechanisms. We construct a set of overthinking identification metrics based on standard answers and design a systematic method to detect redundant reasoning. This method accurately identifies unnecessary steps within the reasoning trajectory and generates training signals for learning self-regulation behaviors. Building on this foundation, we develop a complete strategy for constructing data with adaptive reasoning lengths and introduce an innovative braking prompt mechanism that enables the model to naturally learn when to terminate reasoning at an appropriate point. Experiments across mathematical benchmarks (AIME, AMC, MATH500, GSM8K) demonstrate that our method reduces token consumption by up to 60% while maintaining comparable accuracy to unconstrained models.

Large Reasoning Models (LRMs) such as OpenAI o1 and DeepSeek-R1 have shown excellent performance in reasoning tasks using long reasoning chains. However, this has also led to a significant increase of computational costs and the generation of verbose output, a phenomenon known as overthinking. The tendency to overthinking is often exacerbated by Reinforcement Learning (RL) algorithms such as GRPO/DAPO. In this paper, we propose BFS-PO, an RL algorithm which alleviates this problem using a Best-First Search exploration strategy. Specifically, BFS-PO looks for the shortest correct answer using a backtracking mechanism based on maximum entropy nodes. By generating progressively shorter responses during training, BFS-PO learns to produce concise reasoning chains. Using different benchmarks and base LRMs, we show that BFS-PO can simultaneously increase the LRM accuracy and shorten its answers.

Large reasoning models (LRMs) have recently achieved significant progress in complex reasoning tasks, aided by reinforcement learning with verifiable rewards. However, LRMs often suffer from overthinking, expending excessive computation on simple problems and reducing efficiency. Existing efficient reasoning methods typically require accurate task assessment to preset token budgets or select reasoning modes, which limits their flexibility and reliability. In this work, we revisit the essence of overthinking and identify that encouraging effective steps while penalizing ineffective ones is key to its solution. To this end, we propose a novel rule-based verifiable stepwise reward mechanism (VSRM), which assigns rewards based on the performance of intermediate states in the reasoning trajectory. This approach is intuitive and naturally fits the step-by-step nature of reasoning tasks. We conduct extensive experiments on standard mathematical reasoning benchmarks, including AIME24 and AIME25, by integrating VSRM with PPO and Reinforce++. Results show that our method achieves substantial output length reduction while maintaining original reasoning performance, striking an optimal balance between efficiency and accuracy. Further analysis of overthinking frequency and pass@k score before and after training demonstrates that our approach in deed effectively suppresses ineffective steps and encourages effective reasoning, fundamentally alleviating the overthinking problem. All code will be released upon acceptance.

Chain-of-Thought (CoT) reasoning has driven recent gains of large language models (LLMs) on reasoning-intensive tasks by externalizing intermediate steps. However, excessive or redundant reasoning -- so-called overthinking -- can increase inference costs and lead LLMs toward incorrect conclusions. In this paper, we present REFRAIN (REFlective-Redundancy for Adaptive INference), a training-free framework that adaptively determines when to stop reasoning to mitigate overthinking. REFRAIN integrates a two-stage stop discriminator to identify reflective yet redundant reasoning and a sliding-window Upper Confidence Bound (SW-UCB) multi-armed bandit controller to dynamically adjust stopping thresholds according to problem difficulty without supervision or fine-tuning. Across four representative benchmarks and two model families, REFRAIN reduces token usage by 20-55% while maintaining or improving accuracy compared to standard CoT prompting. Extensive ablation and robustness analyses demonstrate its stability across models, scorers, and prompt variations. In summary, our findings highlight when-to-stop as a new and practical axis of test-time scaling -- enabling models to reason not just more, but just enough.

Reasoning LLMs show improved performance with longer chains of thought. However, recent work has highlighted their tendency to overthink, continuing to revise answers even after reaching the correct solution. We quantitatively confirm this inefficiency from the distribution dynamics perspective by tracking Pass@1 for answers averaged over a large number of rollouts and find the model often begins to always produce the correct answer early in the reasoning, making extra reasoning tokens wasteful. To detect and prevent overthinking, we propose a simple and inexpensive novel signal, Entropy After </Think> (EAT), for monitoring and deciding whether to exit reasoning early. By appending a stop thinking token (</think>) and monitoring the entropy of the following token as the model reasons, we obtain a trajectory that decreases and stabilizes when Pass@1 plateaus; thresholding its variance under an exponential moving average yields a practical stopping rule. Importantly, our approach enables adaptively allocating compute based on the EAT trajectory, allowing us to spend compute in a more efficient way compared with fixing the token budget for all questions. Empirically, on MATH500 and AIME2025, EAT reduces token usage by 12 - 22% without harming accuracy. EAT also remains effective in black box settings where logits from the reasoning model are not accessible, and EAT is computed with proxy models: We verified the feasibility via early stopping Llama 70B with a 1.5B model and Claude 3.7 with a local 4B model.

Introducing reasoning models into Retrieval-Augmented Generation (RAG) systems enhances task performance through step-by-step reasoning, logical consistency, and multi-step self-verification. However, recent studies have shown that reasoning models suffer from overthinking attacks, where models are tricked to generate unnecessarily high number of reasoning tokens. In this paper, we reveal that such overthinking risk can be inherited by RAG systems equipped with reasoning models, by proposing an end-to-end attack framework named Contradiction-Based Deliberation Extension (CODE). Specifically, CODE develops a multi-agent architecture to construct poisoning samples that are injected into the knowledge base. These samples 1) are highly correlated with the use query, such that can be retrieved as inputs to the reasoning model; and 2) contain contradiction between the logical and evidence layers that cause models to overthink, and are optimized to exhibit highly diverse styles. Moreover, the inference overhead of CODE is extremely difficult to detect, as no modification is needed on the user query, and the task accuracy remain unaffected. Extensive experiments on two datasets across five commercial reasoning models demonstrate that the proposed attack causes a 5.32x-24.72x increase in reasoning token consumption, without degrading task performance. Finally, we also discuss and evaluate potential countermeasures to mitigate overthinking risks.

The reasoning capabilities of large language models (LLMs) have improved substantially through increased test-time computation, typically in the form of intermediate tokens known as chain-of-thought (CoT). However, CoT often becomes unnecessarily long, increasing computation cost without actual accuracy gains or sometimes even degrading performance, a phenomenon known as ``overthinking''. We propose a multi-stage efficient reasoning method that combines supervised fine-tuning -- via rejection sampling or reasoning trace reformatting -- with reinforcement learning using an adaptive length penalty. We introduce a lightweight reward function that penalizes tokens generated after the first correct answer but encouraging self-verification only when beneficial. We conduct a holistic evaluation across seven diverse reasoning tasks, analyzing the accuracy-response length trade-off. Our approach reduces response length by an average of 28\% for 8B models and 40\% for 32B models, while incurring only minor performance drops of 1.6 and 2.5 points, respectively. Despite its conceptual simplicity, it achieves a superior trade-off compared to more complex state-of-the-art efficient reasoning methods, scoring 76.6, in terms of the area under the Overthinking-Adjusted Accuracy curve (AUC_{OAA}) -- 5 points above the base model and 2.5 points above the second-best approach.

Large Reasoning Models(LRMs) such as OpenAI o1 and DeepSeek-R1 have shown remarkable reasoning capabilities by scaling test-time compute and generating long Chain-of-Thought(CoT). Distillation--post-training on LRMs-generated data--is a straightforward yet effective method to enhance the reasoning abilities of smaller models, but faces a critical bottleneck: we found that distilled long CoT data poses learning difficulty for small models and leads to the inheritance of biases (i.e. over-thinking) when using Supervised Fine-tuning(SFT) and Reinforcement Learning(RL) methods. To alleviate this bottleneck, we propose constructing tree-based CoT data from scratch via Monte Carlo Tree Search(MCTS). We then exploit a set of CoT-aware approaches, including Thoughts Length Balance, Fine-grained DPO, and Joint Post-training Objective, to enhance SFT and RL on the construted data.

Recent breakthroughs in Large Reasoning Models (LRMs) have demonstrated that extensive Chain-of-Thought (CoT) generation is critical for enabling intricate cognitive behaviors, such as self-verification and backtracking, to solve complex tasks. However, this capability often leads to ``overthinking'', where models generate redundant reasoning paths that inflate computational costs without improving accuracy. While Supervised Fine-Tuning (SFT) on reasoning traces is a standard paradigm for the 'cold start' phase, applying existing compression techniques to these traces often compromises logical coherence or incurs prohibitive sampling costs. In this paper, we introduce ConMax (Confidence-Maximizing Compression), a novel reinforcement learning framework designed to automatically compress reasoning traces while preserving essential reasoning patterns. ConMax formulates compression as a reward-driven optimization problem, training a policy to prune redundancy by maximizing a weighted combination of answer confidence for predictive fidelity and thinking confidence for reasoning validity through a frozen auxiliary LRM. Extensive experiments across five reasoning datasets demonstrate that ConMax achieves a superior efficiency-performance trade-off. Specifically, it reduces inference length by 43% over strong baselines at the cost of a mere 0.7% dip in accuracy, proving its effectiveness in generating high-quality, efficient training data for LRMs.

The remarkable performance of models like the OpenAI o1 can be attributed to their ability to emulate human-like long-time thinking during inference. These models employ extended chain-of-thought (CoT) processes, exploring multiple strategies to enhance problem-solving capabilities. However, a critical question remains: How to intelligently and efficiently scale computational resources during testing. This paper presents the first comprehensive study on the prevalent issue of overthinking in these models, where excessive computational resources are allocated for simple problems with minimal benefit. We introduce novel efficiency metrics from both outcome and process perspectives to evaluate the rational use of computational resources by o1-like models. Using a self-training paradigm, we propose strategies to mitigate overthinking, streamlining reasoning processes without compromising accuracy. Experimental results show that our approach successfully reduces computational overhead while preserving model performance across a range of testsets with varying difficulty levels, such as GSM8K, MATH500, GPQA, and AIME.

LLMs are now embedded in a wide range of everyday scenarios. However, their inherent hallucinations risk hiding misinformation in fluent responses, raising concerns about overreliance on AI. Detecting overreliance is challenging, as it often arises in complex, dynamic contexts and cannot be easily captured by post-hoc task outcomes. In this work, we aim to investigate how users' behavioral patterns correlate with overreliance. We collected interaction logs from 77 participants working with an LLM injected plausible misinformation across three real-world tasks and we assessed overreliance by whether participants detected and corrected these errors. By semantically encoding and clustering segments of user interactions, we identified five behavioral patterns linked to overreliance: users with low overreliance show careful task comprehension and fine-grained navigation; users with high overreliance show frequent copy-paste, skipping initial comprehension, repeated LLM references, coarse locating, and accepting misinformation despite hesitation. We discuss design implications for mitigation.

Large Reasoning Models (LRMs) often produce excessively verbose reasoning traces, a phenomenon known as overthinking, which hampers both efficiency and interpretability. Prior works primarily address this issue by reducing response length, without fully examining the underlying semantic structure of the reasoning process. In this paper, we revisit overthinking by decomposing it into two distinct forms: internal redundancy, which consists of low-contribution reasoning steps within the first correct solution (FCS), and external redundancy, which refers to unnecessary continuation after the FCS. To mitigate both forms, we propose a dual-penalty reinforcement learning framework. For internal redundancy, we adopt a sliding-window semantic analysis to penalize low-gain reasoning steps that contribute little toward reaching the correct answer. For external redundancy, we penalize its proportion beyond the FCS to encourage earlier termination. Our method significantly compresses reasoning traces with minimal accuracy loss, and generalizes effectively to out-of-domain tasks such as question answering and code generation. Crucially, we find that external redundancy can be safely removed without degrading performance, whereas internal redundancy must be reduced more cautiously to avoid impairing correctness. These findings suggest that our method not only improves reasoning efficiency but also enables implicit, semantic-aware control over Chain-of-Thought length, paving the way for more concise and interpretable LRMs.

Recent advances in Large Reasoning Models (LRMs) demonstrate remarkable performance improvements by iteratively reflecting, exploring, and executing complex tasks, yet suffer from inefficiencies due to redundant reasoning, known as "overthinking". Existing methods to mitigate this issue either rely on static difficulty estimates or require task-specific training, and thus fail to adapt to the dynamic complexity during reasoning. In this work, we empirically show that the problem difficulty evolves dynamically throughout the reasoning process and is linearly encoded in the LRM's step-level embeddings. Building on this insight, we propose DyCon, a training-free framework that leverages latent step-level representations to explicitly model the evolving task difficulty, enabling the dynamic control of reasoning depth to mitigate the overthinking issue. Extensive experiments conducted on four models ranging from 4B to 32B, and across twelve benchmarks in math reasoning, general question answering, and coding tasks demonstrate that DyCon significantly enhances reasoning efficiency by reducing redundant steps without sacrificing accuracy or generalization. Project page and code are available at https://github.com/yu-lin-li/DyCon.

Large Reasoning Models (LRMs) often suffer from overthinking, a phenomenon in which redundant reasoning steps are generated after a correct solution has already been reached. Existing early reasoning exit methods primarily rely on output-level heuristics or trained probing models to skip redundant reasoning steps, thereby mitigating overthinking. However, these approaches typically require additional rollout computation or externally labeled datasets. In this paper, we propose NEAT, a Neuron-based Early reAsoning exiT framework that monitors neuron-level activation dynamics to enable training-free early exits, without introducing additional test-time computation. NEAT identifies exit-associated neurons and tracks their activation patterns during reasoning to dynamically trigger early exit or suppress reflection, thereby reducing unnecessary reasoning while preserving solution quality. Experiments on four reasoning benchmarks across six models with different scales and architectures show that, for each model, NEAT achieves an average token reduction of 22\% to 28\% when averaged over the four benchmarks, while maintaining accuracy.

Recent advancements in large reasoning models (LRMs) have demonstrated the effectiveness of scaling test-time computation to enhance reasoning capabilities in multiple tasks. However, LRMs typically suffer from "overthinking" problems, where models generate significantly redundant reasoning steps while bringing limited performance gains. Existing work relies on fine-tuning to mitigate overthinking, which requires additional data, unconventional training setups, risky safety misalignment, and poor generalization. Through empirical analysis, we reveal an important characteristic of LRM behaviors that placing external CoTs generated by smaller models between the thinking token (<think> and </think>) can effectively manipulate the model to generate fewer thoughts. Building on these insights, we propose a simple yet efficient pipeline, ThoughtMani, to enable LRMs to bypass unnecessary intermediate steps and reduce computational costs significantly. We conduct extensive experiments to validate the utility and efficiency of ThoughtMani. For instance, when applied to QwQ-32B on the LiveBench/Code dataset, ThoughtMani keeps the original performance and reduces output token counts by approximately 30%, with little overhead from the CoT generator. Furthermore, we find that ThoughtMani enhances safety alignment by an average of 10%. Since model vendors typically serve models of different sizes simultaneously, ThoughtMani provides an effective way to construct more efficient and accessible LRMs for real-world applications.

Recent advances in large reasoning language models (LRLMs) rely on test-time scaling, which extends long chain-of-thought (CoT) generation to solve complex tasks. However, overthinking in long CoT not only slows down the efficiency of problem solving, but also risks accuracy loss due to the extremely detailed or redundant reasoning steps. We propose a simple yet effective method that allows LLMs to self-truncate CoT sequences by early exit during generation. Instead of relying on fixed heuristics, the proposed method monitors model behavior at potential reasoning transition points (e.g.,"Wait" tokens) and dynamically terminates the next reasoning chain's generation when the model exhibits high confidence in a trial answer. Our method requires no additional training and can be seamlessly integrated into existing o1-like reasoning LLMs. Experiments on 10 reasoning benchmarks (e.g., GSM8K, MATH-500, AMC, GPQA, AIME and LiveCodeBench) show that the proposed method is consistently effective on 11 cutting-edge reasoning LLMs of varying series and sizes, reducing the length of CoT sequences by an average of 19.1% to 80.1% while improving accuracy by 0.3% to 5.0%.

Recent advancements in large language models (LLMs) have significantly advanced complex reasoning capabilities, particularly through extended chain-of-thought (CoT) reasoning that incorporates mechanisms such as backtracking, self-reflection and self-correction. Despite these developments, the self-correction abilities of LLMs during long CoT reasoning remain underexplored. And recent findings on overthinking suggest that such models often engage in unnecessarily redundant reasoning. In this work, we empirically show that the first reasoning step exerts a disproportionately large influence on the final prediction - errors introduced at this stage can substantially degrade subsequent reasoning quality. This phenomenon is consistently observed across two state-of-the-art open-source reasoning model families: DeepSeek-R1 and Qwen3. To address this, we propose an efficient sampling strategy that leverages a reward model to identify and retain high-quality first reasoning steps while discarding suboptimal ones, achieving up to a 70% reduction in inference cost without sacrificing accuracy. Finally, we introduce a new benchmark specifically constructed with deliberately flawed first reasoning steps to systematically evaluate model self-correction capabilities, offering a foundation for future research on robust reasoning in LLMs.

Large Language Models (LLMs) have achieved remarkable performance in complex reasoning tasks through Chain-of-Thought (CoT) prompting. However, this approach often leads to ``over-thinking,'' where models generate unnecessarily long reasoning traces for simple queries and incur avoidable inference cost. While recent work has explored adaptive reasoning, existing methods typically make a single query-level decision about whether to reason. This overlooks the dynamic nature of multi-step tasks, where the need for explicit reasoning varies across intermediate stages. To address this limitation, we introduce AdaptR1, a Reinforcement Learning (RL) based framework for adaptive interleaved thinking in multi-hop Question Answering (QA). Unlike previous approaches that require Supervised Fine-Tuning (SFT) for cold-start initialization, AdaptR1 uses a fully RL-based strategy with a quality-gated efficiency reward to dynamically allocate reasoning budgets at each step. Under the Graph-R1 setting, AdaptR1 reduces average think tokens by 69.71\%, with a 90.35\% reduction on HotpotQA, while maintaining performance comparable to or better than standard baselines. Furthermore, our analysis reveals that overthinking in multi-hop reasoning is not uniformly distributed but occurs predominantly during the initial planning stages, highlighting the effectiveness of step-wise adaptive budget allocation.

Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks, but their inference remains computationally inefficient. We observe a common failure mode in many prevalent LLMs, overthinking, where models generate verbose and tangential reasoning traces even for simple queries. Recent works have tried to mitigate this by enforcing fixed token budgets, however, this can lead to underthinking, especially on harder problems. Through empirical analysis, we identify that this inefficiency often stems from unclear problem-solving strategies. To formalize this, we develop a theoretical model, BBAM (Bayesian Budget Allocation Model), which models reasoning as a sequence of sub-questions with varying uncertainty, and introduce the E^3 metric to capture the trade-off between correctness and computation efficiency. Building on theoretical results from BBAM, we propose Plan-and-Budget, a model-agnostic, test-time framework that decomposes complex queries into sub-questions and allocates token budgets based on estimated complexity using adaptive scheduling. Plan-and-Budget improves reasoning efficiency across a range of tasks and models, achieving up to +70% accuracy gains, -39% token reduction, and +187.5% improvement in E^3. Notably, it elevates a smaller model (DS-Qwen-32B) to match the efficiency of a larger model (DS-LLaMA-70B)-demonstrating Plan-and-Budget's ability to close performance gaps without retraining. Our code is available at anonymous.4open.science/r/P-and-B-6513/.

Machine learning models that are overfitted/overtrained are more vulnerable to knowledge leakage, which poses a risk to privacy. Suppose we download or receive a model from a third-party collaborator without knowing its training accuracy. How can we determine if it has been overfitted or overtrained on its training data? It's possible that the model was intentionally over-trained to make it vulnerable during testing. While an overfitted or overtrained model may perform well on testing data and even some generalization tests, we can't be sure it's not over-fitted. Conducting a comprehensive generalization test is also expensive. The goal of this paper is to address these issues and ensure the privacy and generalization of our method using only testing data. To achieve this, we analyze the null space in the last layer of neural networks, which enables us to quantify overfitting without access to training data or knowledge of the accuracy of those data. We evaluated our approach on various architectures and datasets and observed a distinct pattern in the angle of null space when models are overfitted. Furthermore, we show that models with poor generalization exhibit specific characteristics in this space. Our work represents the first attempt to quantify overfitting without access to training data or knowing any knowledge about the training samples.

We increase overhead for applications that rely on reasoning LLMs-we force models to spend an amplified number of reasoning tokens, i.e., "overthink", to respond to the user query while providing contextually correct answers. The adversary performs an OVERTHINK attack by injecting decoy reasoning problems into the public content that is used by the reasoning LLM (e.g., for RAG applications) during inference time. Due to the nature of our decoy problems (e.g., a Markov Decision Process), modified texts do not violate safety guardrails. We evaluated our attack across closed-(OpenAI o1, o1-mini, o3-mini) and open-(DeepSeek R1) weights reasoning models on the FreshQA and SQuAD datasets. Our results show up to 18x slowdown on FreshQA dataset and 46x slowdown on SQuAD dataset. The attack also shows high transferability across models. To protect applications, we discuss and implement defenses leveraging LLM-based and system design approaches. Finally, we discuss societal, financial, and energy impacts of OVERTHINK attack which could amplify the costs for third-party applications operating reasoning models.

Large Reasoning Language Models (LRLMs) demonstrate impressive capabilities on complex tasks by utilizing long Chain-of-Thought reasoning. However, they are prone to overthinking, which generates redundant reasoning steps that degrade both performance and efficiency. Recently, early-exit strategies are proposed to mitigate overthinking by dynamically and adaptively terminating redundant reasoning. However, current early-exit methods either introduce extra training overhead by relying on proxy models or limit inference throughput due to the frequent content switching between reasoning and generating probing answers. Moreover, most early-exit methods harm LRLMs performance due to over-truncation. Our insight stems from an observation: overthinking often causes LRLMs to deviate from the correct reasoning path, which is frequently accompanied by high-entropy transition tokens. Given this, we propose an early-exit method deeply coupled with the native reasoning process, which leverages the path deviation index as a dedicated monitoring metric for the frequent occurrence of high-entropy transition tokens to dynamically detect and terminate overthinking trajectories. We conduct experiments across multiple benchmarks using LRLMs of different types and scales, and the results indicate that our method delivers the largest performance improvement over vanilla CoT compared to existing early-exit methods.

Recent thinking models solve complex reasoning tasks by scaling test-time compute, but this scaling must be allocated in line with task difficulty. On one hand, short reasoning (underthinking) leads to errors on harder problems that require extended reasoning steps; but, excessively long reasoning (overthinking) can be token-inefficient, generating unnecessary steps even after reaching a correct intermediate solution. We refer to this as under-adaptivity, where the model fails to modulate its response length appropriately given problems of varying difficulty. To address under-adaptivity and strike a balance between under- and overthinking, we propose TRAAC (Think Right with Adaptive, Attentive Compression), an online post-training RL method that leverages the model's self-attention over a long reasoning trajectory to identify important steps and prune redundant ones. TRAAC also estimates difficulty and incorporates it into training rewards, thereby learning to allocate reasoning budget commensurate with example difficulty. Our approach improves accuracy, reduces reasoning steps, and enables adaptive thinking compared to base models and other RL baselines. Across a variety of tasks (AIME, AMC, GPQA-D, BBEH), TRAAC (Qwen3-4B) achieves an average absolute accuracy gain of 8.4% with a relative reduction in reasoning length of 36.8% compared to the base model, and a 7.9% accuracy gain paired with a 29.4% length drop compared to the best RL baseline. TRAAC also shows strong generalization: although our models are trained on math datasets, they show accuracy and efficiency gains on out-of-distribution non-math datasets like GPQA-D, BBEH, and OptimalThinkingBench. Our analysis further verifies that TRAAC provides fine-grained adjustments to thinking budget based on difficulty and that a combination of task-difficulty calibration and attention-based compression yields gains across diverse tasks.

Overfitting negatively impacts the generalization ability of deep neural networks (DNNs) in both natural and adversarial training. Existing methods struggle to consistently address different types of overfitting, typically designing strategies that focus separately on either natural or adversarial patterns. In this work, we adopt a unified perspective by solely focusing on natural patterns to explore different types of overfitting. Specifically, we examine the memorization effect in DNNs and reveal a shared behaviour termed over-memorization, which impairs their generalization capacity. This behaviour manifests as DNNs suddenly becoming high-confidence in predicting certain training patterns and retaining a persistent memory for them. Furthermore, when DNNs over-memorize an adversarial pattern, they tend to simultaneously exhibit high-confidence prediction for the corresponding natural pattern. These findings motivate us to holistically mitigate different types of overfitting by hindering the DNNs from over-memorization natural patterns. To this end, we propose a general framework, Distraction Over-Memorization (DOM), which explicitly prevents over-memorization by either removing or augmenting the high-confidence natural patterns. Extensive experiments demonstrate the effectiveness of our proposed method in mitigating overfitting across various training paradigms.

Chain-of-Thought (CoT) prompting enables complex reasoning in large language models (LLMs), including applications in information retrieval (IR). However, it often leads to overthinking, where models produce excessively long and semantically redundant traces with little or no benefit. We identify two key challenges in IR: redundant trajectories that revisit similar states and misguided reasoning that diverges from user intent. To address these, we propose State Machine Reasoning (SMR), a transition-based reasoning framework composed of discrete actions (Refine, Rerank, Stop) that support early stopping and fine-grained control. Experiments on the BEIR and BRIGHT benchmarks show that SMR improves retrieval performance (nDCG@10) by 3.4% while reducing token usage by 74.4%. It generalizes across LLMs and retrievers without requiring task-specific tuning, offering a practical alternative to conventional CoT reasoning. The code and details are available at https://github.com/ldilab/SMR.

Recently, techniques such as explicit structured reasoning have demonstrated strong test-time scaling behavior by enforcing a separation between the model's internal "thinking" process and the final response. A key factor influencing answer quality in this setting is the length of the thinking stage. When the reasoning is too short, the model may fail to capture the complexity of the task. Conversely, when it is too long, the model may overthink, leading to unnecessary computation and degraded performance. This paper explores and exploits the underlying mechanisms by which LLMs understand and regulate the length of their reasoning during explicit thought processes. First, we show that LLMs encode their progress through the reasoning process and introduce an interactive progress bar visualization, which is then used to reveal insights on the model's planning dynamics. Second, we manipulate the internal progress encoding during inference to reduce unnecessary steps and generate a more concise and decisive chain of thoughts. Our empirical results demonstrate that this "overclocking" method mitigates overthinking, improves answer accuracy, and reduces inference latency. Our code is publicly available.

Large reasoning models (LRMs) achieve strong reasoning performance by emitting long chains of thought. Yet, these verbose traces slow down inference and often drift into unnecessary detail, known as the overthinking phenomenon. To better understand LRMs' behavior, we systematically analyze the token-level misalignment between reasoning and non-reasoning models. While it is expected that their primary difference lies in the stylistic "thinking cues", LRMs uniquely exhibit two pivotal, previously under-explored phenomena: a Global Misalignment Rebound, where their divergence from non-reasoning models persists or even grows as response length increases, and more critically, a Local Misalignment Diminish, where the misalignment concentrates at the "thinking cues" each sentence starts with but rapidly declines in the remaining of the sentence. Motivated by the Local Misalignment Diminish, we propose FoReaL-Decoding, a collaborative fast-slow thinking decoding method for cost-quality trade-off. In FoReaL-Decoding, a Leading model leads the first few tokens for each sentence, and then a weaker draft model completes the following tokens to the end of each sentence. FoReaL-Decoding adopts a stochastic gate to smoothly interpolate between the small and the large model. On four popular math-reasoning benchmarks (AIME24, GPQA-Diamond, MATH500, AMC23), FoReaL-Decoding reduces theoretical FLOPs by 30 to 50% and trims CoT length by up to 40%, while preserving 86 to 100% of model performance. These results establish FoReaL-Decoding as a simple, plug-and-play route to controllable cost-quality trade-offs in reasoning-centric tasks.

Recent advancements in Long Chain-of-Thought (CoT) reasoning models have improved performance on complex tasks, but they suffer from overthinking, which generates redundant reasoning steps, especially for simple questions. This paper revisits the reasoning patterns of Long and Short CoT models, observing that the Short CoT patterns offer concise reasoning efficiently, while the Long CoT patterns excel in challenging scenarios where the Short CoT patterns struggle. To enable models to leverage both patterns, we propose Question-Free Fine-Tuning (QFFT), a fine-tuning approach that removes the input question during training and learns exclusively from Long CoT responses. This approach enables the model to adaptively employ both reasoning patterns: it prioritizes the Short CoT patterns and activates the Long CoT patterns only when necessary. Experiments on various mathematical datasets demonstrate that QFFT reduces average response length by more than 50\%, while achieving performance comparable to Supervised Fine-Tuning (SFT). Additionally, QFFT exhibits superior performance compared to SFT in noisy, out-of-domain, and low-resource scenarios.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Many cognitive approaches to well-being, such as recognizing and reframing unhelpful thoughts, have received considerable empirical support over the past decades, yet still lack truly widespread adoption in self-help format. A barrier to that adoption is a lack of adequately specific and diverse dedicated practice material. This work examines whether current language models can be leveraged to both produce a virtually unlimited quantity of practice material illustrating standard unhelpful thought patterns matching specific given contexts, and generate suitable positive reframing proposals. We propose PATTERNREFRAME, a novel dataset of about 10k examples of thoughts containing unhelpful thought patterns conditioned on a given persona, accompanied by about 27k positive reframes. By using this dataset to train and/or evaluate current models, we show that existing models can already be powerful tools to help generate an abundance of tailored practice material and hypotheses, with no or minimal additional model training required.

Large Reasoning Models (LRMs) have demonstrated remarkable problem-solving abilities in mathematics, as evaluated by existing benchmarks exclusively on well-defined problems. However, such evaluation setup constitutes a critical gap, since a genuine intelligent agent should not only solve problems (as a math quiz solver), but also be able~to ask for information when the problems lack sufficient information, enabling proactivity in responding users' requests. To bridge such gap, we proposes a new dataset consisting of two types of incomplete problems with diverse contexts. Based on the dataset, our systematical evaluation of LRMs reveals their inability in proactively asking for information. In addition, we uncover the behaviors related to overthinking and hallucination of LRMs, and highlight the potential and challenges of supervised fine-tuning in learning such ability. We hope to provide new insights in developing LRMs with genuine intelligence, rather than just solving problems.

Message Passing Neural Networks (MPNNs) are instances of Graph Neural Networks that leverage the graph to send messages over the edges. This inductive bias leads to a phenomenon known as over-squashing, where a node feature is insensitive to information contained at distant nodes. Despite recent methods introduced to mitigate this issue, an understanding of the causes for over-squashing and of possible solutions are lacking. In this theoretical work, we prove that: (i) Neural network width can mitigate over-squashing, but at the cost of making the whole network more sensitive; (ii) Conversely, depth cannot help mitigate over-squashing: increasing the number of layers leads to over-squashing being dominated by vanishing gradients; (iii) The graph topology plays the greatest role, since over-squashing occurs between nodes at high commute (access) time. Our analysis provides a unified framework to study different recent methods introduced to cope with over-squashing and serves as a justification for a class of methods that fall under graph rewiring.

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their tendency to produce excessively long reasoning traces, which are often filled with redundant content (e.g., repeated definitions), over-analysis of simple problems, and superficial exploration of multiple reasoning paths for harder tasks. This inefficiency introduces significant challenges for training, inference, and real-world deployment (e.g., in agent-based systems), where token economy is critical. In this survey, we provide a comprehensive overview of recent efforts aimed at improving reasoning efficiency in LRMs, with a particular focus on the unique challenges that arise in this new paradigm. We identify common patterns of inefficiency, examine methods proposed across the LRM lifecycle, i.e., from pretraining to inference, and discuss promising future directions for research. To support ongoing development, we also maintain a real-time GitHub repository tracking recent progress in the field. We hope this survey serves as a foundation for further exploration and inspires innovation in this rapidly evolving area.

O1/R1 style large reasoning models (LRMs) signal a substantial leap forward over conventional instruction-following LLMs. By applying test-time scaling to generate extended reasoning paths, they establish many SOTAs across a wide range of complex reasoning tasks. However, recent studies show that LRMs are prone to suffer from overthinking -- the tendency to overcomplicate simple problems, leading to excessive strategy switching and long, convoluted reasoning traces that hinder their interpretability. To mitigate this issue, we conduct a systematic investigation into the reasoning efficiency of a broad set of LRMs and uncover a common dilemma: the difficulty in balancing multiple generation objectives such as correctness and brevity. Based on this discovery, we propose a test-time scaling method, EDIT (Efficient Dynamic Inference Trimming), which efficiently guides LRMs to identify the shortest correct reasoning paths at test time. EDIT employs constraint-guided generation while jointly tracking length and answer distributions under varying constraints, allowing it to select responses that strike an optimal balance between conciseness and correctness. Extensive experiments across diverse models and datasets show that EDIT substantially enhance the reasoning efficiency, producing compact yet informative outputs that improve readability and user experience.

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex tasks. Recent advancements in Large Reasoning Models (LRMs), such as OpenAI o1 and DeepSeek-R1, have further improved performance in System-2 reasoning domains like mathematics and programming by harnessing supervised fine-tuning (SFT) and reinforcement learning (RL) techniques to enhance the Chain-of-Thought (CoT) reasoning. However, while longer CoT reasoning sequences improve performance, they also introduce significant computational overhead due to verbose and redundant outputs, known as the "overthinking phenomenon". In this paper, we provide the first structured survey to systematically investigate and explore the current progress toward achieving efficient reasoning in LLMs. Overall, relying on the inherent mechanism of LLMs, we categorize existing works into several key directions: (1) model-based efficient reasoning, which considers optimizing full-length reasoning models into more concise reasoning models or directly training efficient reasoning models; (2) reasoning output-based efficient reasoning, which aims to dynamically reduce reasoning steps and length during inference; (3) input prompts-based efficient reasoning, which seeks to enhance reasoning efficiency based on input prompt properties such as difficulty or length control. Additionally, we introduce the use of efficient data for training reasoning models, explore the reasoning capabilities of small language models, and discuss evaluation methods and benchmarking.

Chain-of-thought (CoT) reasoning not only enhances large language model performance but also provides critical insights into decision-making processes, marking it as a useful tool for monitoring model intent and planning. However, recent works have shown that banning the mention of a specific example of reward hacking causes obfuscation of the undesired reasoning traces but the persistence of the undesired behavior, threatening the reliability of CoT monitoring. We provide an extension to these results with regard to the ability of models to learn a specific type of obfuscated reasoning: steganography. First, we show that penalizing the use of specific strings within load-bearing reasoning traces causes models to substitute alternative strings. Crucially, this does not alter the underlying method by which the model performs the task, demonstrating that the model can learn to steganographically encode its reasoning.We further demonstrate that models can generalize an encoding scheme. When the penalized strings belong to an overarching class, the model learns not only to substitute strings seen in training, but also develops a general encoding scheme for all members of the class which it can apply to held-out testing strings.

Recent advancements in slow thinking reasoning models have shown exceptional performance in complex reasoning tasks. However, these models often exhibit overthinking (generating redundant reasoning steps for simple problems), leading to excessive computational resource usage. While current mitigation strategies uniformly reduce reasoning tokens, they risk degrading performance on challenging tasks that require extended reasoning. This paper introduces Difficulty-Adaptive Slow Thinking (DAST), a novel framework that enables models to autonomously adjust the length of Chain-of-Thought (CoT) based on problem difficulty. We first propose a Token Length Budget (TLB) metric to quantify difficulty, then leverage budget-aware reward shaping and budget preference optimization to implement DAST. DAST penalizes overlong responses for simple tasks while incentivizing sufficient reasoning for complex problems. Experiments on diverse datasets and model scales demonstrate that DAST effectively mitigates overthinking (reducing token usage by over 30\% on average) while preserving reasoning accuracy on complex problems. Our codes and models are available at https://github.com/AnonymousUser0520/AnonymousRepo01.

Post-training quantization (PTQ) is widely used to deploy large language models efficiently, but its effect on reasoning models is not well understood. Across math, coding, and science QA, we find that aggressive PTQ reduces accuracy while increasing chain-of-thought (CoT) length. Surprisingly, we show that in up to 52% of the quantized models' failures, models reach the right answer in intermediate reasoning steps but do not output it as a final answer. To understand why quantization leads to this increase in overthinking errors, we measure the token-level KL divergence between quantized and full-precision output distributions. Positions with high KL divergence correlate strongly with high next-token entropy, and at these positions quantized models disproportionately sample overthinking markers such as "wait", "but", and "alternatively". We show that simply introducing a training-free logit penalty on a curated set of overthinking markers can reduce CoT length by 12--23% while preserving or improving accuracy across 5 models (1.5B-32B parameters), 3 quantization methods, and 5 benchmarks, yielding a favorable Pareto frontier of accuracy against reasoning cost compared to penalizing other token sets. Overthinking errors produced by quantized models are particularly reduced by up to 58%.

Large reasoning models exhibit remarkable reasoning capabilities via long, elaborate reasoning trajectories. Supervised fine-tuning on such reasoning traces, also known as distillation, can be a cost-effective way to boost reasoning capabilities of student models. However, empirical observations reveal that these reasoning trajectories are often suboptimal, switching excessively between different lines of thought, resulting in under-thinking, over-thinking, and even degenerate responses. We introduce Retro-Search, an MCTS-inspired search algorithm, for distilling higher quality reasoning paths from large reasoning models. Retro-Search retrospectively revises reasoning paths to discover better, yet shorter traces, which can then lead to student models with enhanced reasoning capabilities with shorter, thus faster inference. Our approach can enable two use cases: self-improvement, where models are fine-tuned on their own Retro-Search-ed thought traces, and weak-to-strong improvement, where a weaker model revises stronger model's thought traces via Retro-Search. For self-improving, R1-distill-7B, fine-tuned on its own Retro-Search-ed traces, reduces the average reasoning length by 31.2% while improving performance by 7.7% across seven math benchmarks. For weak-to-strong improvement, we retrospectively revise R1-671B's traces from the OpenThoughts dataset using R1-distill-32B as the Retro-Search-er, a model 20x smaller. Qwen2.5-32B, fine-tuned on this refined data, achieves performance comparable to R1-distill-32B, yielding an 11.3% reduction in reasoning length and a 2.4% performance improvement compared to fine-tuning on the original OpenThoughts data. Our work counters recently emergent viewpoints that question the relevance of search algorithms in the era of large reasoning models, by demonstrating that there are still opportunities for algorithmic advancements, even for frontier models.

Hallucination is often regarded as a major impediment for using large language models (LLMs), especially for knowledge-intensive tasks. Even when the training corpus consists solely of true statements, language models still generate hallucinations in the form of amalgamations of multiple facts. We coin this phenomenon as ``knowledge overshadowing'': when we query knowledge from a language model with multiple conditions, some conditions overshadow others, leading to hallucinated outputs. This phenomenon partially stems from training data imbalance, which we verify on both pretrained models and fine-tuned models, over a wide range of LM model families and sizes.From a theoretical point of view, knowledge overshadowing can be interpreted as over-generalization of the dominant conditions (patterns). We show that the hallucination rate grows with both the imbalance ratio (between the popular and unpopular condition) and the length of dominant condition description, consistent with our derived generalization bound. Finally, we propose to utilize overshadowing conditions as a signal to catch hallucination before it is produced, along with a training-free self-contrastive decoding method to alleviate hallucination during inference. Our proposed approach showcases up to 82% F1 for hallucination anticipation and 11.2% to 39.4% hallucination control, with different models and datasets.

Large Reasoning Models (LRMs) demonstrate strong performance on complex tasks but often suffer from excessive verbosity, known as "overthinking." Existing solutions via reinforcement learning (RL) typically penalize generated tokens to promote conciseness. However, these methods encounter two challenges: responses with fewer tokens do not always correspond to fewer reasoning steps, and models may develop hacking behavior in later stages of training by discarding reasoning steps to minimize token usage. In this work, we introduce Step Pruner (SP), an RL framework that steers LRMs toward more efficient reasoning by favoring compact reasoning steps. Our step-aware reward function prioritizes correctness while imposing penalties for redundant steps, and withholds rewards for incorrect responses to prevent the reinforcement of erroneous reasoning. Moreover, we propose a dynamic stopping mechanism: when the length of any output step exceeds the upper limit, we halt updates to prevent hacking behavior caused by merging steps. Extensive experiments across four reasoning benchmarks demonstrate that SP achieves state-of-the-art accuracy while significantly reducing response length. For instance, on AIME24, SP reduces token usage by 69.7\%.

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to overthinking, characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed thinking patterns at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

Large language models have demonstrated remarkable proficiency in long and complex reasoning tasks. However, they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term reasoning rigidity. Despite explicit instructions from users, these models often override clearly stated conditions and default to habitual reasoning trajectories, leading to incorrect conclusions. This behavior presents significant challenges, particularly in domains such as mathematics and logic puzzle, where precise adherence to specified constraints is critical. To systematically investigate reasoning rigidity, a behavior largely unexplored in prior work, we introduce a expert-curated diagnostic set, . Our dataset includes specially modified variants of existing mathematical benchmarks, namely AIME and MATH500, as well as well-known puzzles deliberately redesigned to require deviation from familiar reasoning strategies. Using this dataset, we identify recurring contamination patterns that occur when models default to ingrained reasoning. Specifically, we categorize this contamination into three distinctive modes: (i) Interpretation Overload, (ii) Input Distrust, and (iii) Partial Instruction Attention, each causing models to ignore or distort provided instructions. We publicly release our diagnostic set to facilitate future research on mitigating reasoning rigidity in language models.

Large reasoning models achieve strong performance on complex tasks by generating extended chains of thought, but they often "overthink": continuing to reason long after they have enough information to answer correctly. This wastes inference-time compute and can hurt accuracy. Existing attempts to stop early either manipulate decoding with extra sampling and heuristics, rely on auxiliary verifier models, or operate only as post-hoc analysis pipelines without formal guarantees. We introduce LYNX, an online early-exit mechanism that turns a model's own hidden-state awareness into confidence-controlled stopping decisions. LYNX attaches exit decisions to naturally occurring reasoning cues (e.g., "hmm", "wait") during generation, trains a lightweight probe on hidden states at those cue tokens using supervision from forced exits, and wraps the resulting scores in split conformal prediction to obtain distribution-free control over premature exits. Crucially, we train and calibrate this probe once on a generic mathematical corpus and reuse it unchanged across benchmarks, decoding temperatures, and even non-mathematical tasks. Across three model families spanning 1.5B to 32B parameters, a single mathematically trained probe per base model yields strong accuracy--efficiency tradeoffs. On GSM8K, LYNX matches or improves baseline accuracy while reducing tokens by 40--65\%; on MATH-500 it improves accuracy by up to 12 points with roughly 35--60\% fewer tokens; on AIME 2024 it recovers baseline accuracy with more than 50\% token savings; and on CommonsenseQA, a non-math benchmark, it transfers zero-shot with modest accuracy gains and up to 70\% fewer tokens. Compared to state-of-the-art early-exit methods, LYNX offers competitive or superior Pareto frontiers while remaining fully online, requiring no proxy models at inference, and providing explicit, user-tunable confidence guarantees.

In order to minimize the generalization error in neural networks, a novel technique to identify overfitting phenomena when training the learner is formally introduced. This enables support of a reliable and trustworthy early stopping condition, thus improving the predictive power of that type of modeling. Our proposal exploits the correlation over time in a collection of online indicators, namely characteristic functions for indicating if a set of hypotheses are met, associated with a range of independent stopping conditions built from a canary judgment to evaluate the presence of overfitting. That way, we provide a formal basis for decision making in terms of interrupting the learning process. As opposed to previous approaches focused on a single criterion, we take advantage of subsidiarities between independent assessments, thus seeking both a wider operating range and greater diagnostic reliability. With a view to illustrating the effectiveness of the halting condition described, we choose to work in the sphere of natural language processing, an operational continuum increasingly based on machine learning. As a case study, we focus on parser generation, one of the most demanding and complex tasks in the domain. The selection of cross-validation as a canary function enables an actual comparison with the most representative early stopping conditions based on overfitting identification, pointing to a promising start toward an optimal bias and variance control.

The emergence of reasoning models and their integration into practical AI chat bots has led to breakthroughs in solving advanced math, deep search, and extractive question answering problems that requires a complex and multi-step thought process. Yet, a complete understanding of why these models hallucinate more than general purpose language models is missing. In this investigative study, we systematicallyexplore reasoning failures of contemporary language models on multi-hop question answering tasks. We introduce a novel, nuanced error categorization framework that examines failures across three critical dimensions: the diversity and uniqueness of source documents involved ("hops"), completeness in capturing relevant information ("coverage"), and cognitive inefficiency ("overthinking"). Through rigorous hu-man annotation, supported by complementary automated metrics, our exploration uncovers intricate error patterns often hidden by accuracy-centric evaluations. This investigative approach provides deeper insights into the cognitive limitations of current models and offers actionable guidance toward enhancing reasoning fidelity, transparency, and robustness in future language modeling efforts.

Large Language Models (LLMs) employ Chain-of-Thought (CoT) reasoning to deconstruct complex problems. While longer CoTs are often presumed superior, this paper challenges that notion, arguing that longer is not always better. Drawing on combined evidence from real-world observations, controlled experiments, and theoretical analysis, we demonstrate that task accuracy typically follows an inverted U-shaped curve with CoT length, where performance initially improves but eventually decreases as the number of CoT steps increases. With controlled experiments, we further uncover the scaling behaviors of the optimal CoT length: it increases with task difficulty but decreases with model capability, exposing an inherent simplicity bias where more capable models favor shorter, more efficient CoT reasoning. This bias is also evident in Reinforcement Learning (RL) training, where models gravitate towards shorter CoTs as their accuracy improves. To have a deep understanding of these dynamics, we establish a simple theoretical model that formally proves these phenomena, including the optimal length's scaling laws and the emergence of simplicity bias during RL. Guided by this framework, we demonstrate significant practical benefits from training with optimally-lengthed CoTs and employing length-aware filtering at inference. These findings offer both a principled understanding of the "overthinking" phenomenon and multiple practical guidelines for CoT calibration, enabling LLMs to achieve optimal reasoning performance with adaptive CoTs tailored to task complexity and model capability.

Reasoning models have demonstrated impressive performance on difficult tasks that traditional language models struggle at. However, many are plagued with the problem of overthinking--generating large amounts of unnecessary tokens which don't improve accuracy on a question. We introduce approximate measures of problem-level difficulty and demonstrate that a clear relationship between problem difficulty and optimal token spend exists, and evaluate how well calibrated a variety of reasoning models are in terms of efficiently allocating the optimal token count. We find that in general, reasoning models are poorly calibrated, particularly on easy problems. To evaluate calibration on easy questions we introduce DUMB500, a dataset of extremely easy math, reasoning, code, and task problems, and jointly evaluate reasoning model on these simple examples and extremely difficult examples from existing frontier benchmarks on the same task domain. Finally, we introduce THOUGHTTERMINATOR, a training-free black box decoding technique that significantly improves reasoning model calibration.

Hallucination is a persistent challenge in large language models (LLMs), where even with rigorous quality control, models often generate distorted facts. This paradox, in which error generation continues despite high-quality training data, calls for a deeper understanding of the underlying LLM mechanisms. To address it, we propose a novel concept: knowledge overshadowing, where model's dominant knowledge can obscure less prominent knowledge during text generation, causing the model to fabricate inaccurate details. Building on this idea, we introduce a novel framework to quantify factual hallucinations by modeling knowledge overshadowing. Central to our approach is the log-linear law, which predicts that the rate of factual hallucination increases linearly with the logarithmic scale of (1) Knowledge Popularity, (2) Knowledge Length, and (3) Model Size. The law provides a means to preemptively quantify hallucinations, offering foresight into their occurrence even before model training or inference. Built on overshadowing effect, we propose a new decoding strategy CoDa, to mitigate hallucinations, which notably enhance model factuality on Overshadow (27.9%), MemoTrap (13.1%) and NQ-Swap (18.3%). Our findings not only deepen understandings of the underlying mechanisms behind hallucinations but also provide actionable insights for developing more predictable and controllable language models.

Large Reasoning Models (LRMs) allocate substantial inference-time compute to Chain-of-Thought (CoT) reasoning, improving performance on mathematics, scientific QA, and tool usage. However, this introduces overthinking: LRMs often reach a correct intermediate solution, continue reasoning, and overwrite it with an incorrect answer. We first demonstrate that oracle stopping--where we inject </think> at every sentence boundary and select the best stopping point in hindsight--improves average accuracy by 8% while reducing thinking tokens by 72%, exposing substantial overthinking. Motivated by this finding, we propose ThinkBrake, which monitors the log-probability margin between the top continuation token and </think> at sentence boundaries, stopping reasoning when this margin narrows. ThinkBrake requires no training and achieves favorable accuracy-efficiency trade-offs across math, scientific QA, and tool usage benchmarks, reducing thinking token usage by up to 30%. Furthermore, we provide theoretical analysis showing that ThinkBrake is equivalent to test-time realignment with a reward bonus for the </think> token.

Large language models (LLMs) such as OpenAI's o1 have demonstrated remarkable abilities in complex reasoning tasks by scaling test-time compute and exhibiting human-like deep thinking. However, we identify a phenomenon we term underthinking, where o1-like LLMs frequently switch between different reasoning thoughts without sufficiently exploring promising paths to reach a correct solution. This behavior leads to inadequate depth of reasoning and decreased performance, particularly on challenging mathematical problems. To systematically analyze this issue, we conduct experiments on three challenging test sets and two representative open-source o1-like models, revealing that frequent thought switching correlates with incorrect responses. We introduce a novel metric to quantify underthinking by measuring token efficiency in incorrect answers. To address underthinking, we propose a decoding strategy with thought switching penalty TIP that discourages premature transitions between thoughts, encouraging deeper exploration of each reasoning path. Experimental results demonstrate that our approach improves accuracy across challenging datasets without requiring model fine-tuning. Our findings contribute to understanding reasoning inefficiencies in o1-like LLMs and offer a practical solution to enhance their problem-solving capabilities.

We introduce a pattern mining framework that operates on semi-structured datasets and exploits the dichotomy between outcomes. Our approach takes advantage of constraint reasoning to find sequential patterns that occur frequently and exhibit desired properties. This allows the creation of novel pattern embeddings that are useful for knowledge extraction and predictive modeling. Finally, we present an application on customer intent prediction from digital clickstream data. Overall, we show that pattern embeddings play an integrator role between semi-structured data and machine learning models, improve the performance of the downstream task and retain interpretability.

Autoregressive multimodal large language models have recently gained popularity for image generation, driven by advances in foundation models. To enhance alignment and detail, newer approaches employ chain-of-thought (CoT) reasoning, expanding user inputs into elaborated prompts prior to image synthesis. However, this strategy can introduce unnecessary redundancy -- a phenomenon we call visual overthinking -- which increases computational costs and can introduce details that contradict the original prompt. In this work, we explore how to generate more concise CoT sequences for more efficient image generation. We introduce ShortCoTI, a lightweight optimization framework that encourages more concise CoT while preserving output image quality. ShortCoTI rewards more concise prompts with an adaptive function that scales according to an estimated difficulty for each task. Incorporating this reward into a reinforcement learning paradigm reduces prompt reasoning length by 54% while maintaining or slightly improving quality metrics across multiple benchmarks (T2I-CompBench, GenEval). Qualitative analysis shows that our method eliminates verbose explanations and repetitive refinements, producing reasoning prompts that are both concise and semantically rich. As a result, ShortCoTI improves computational efficiency without compromising the fidelity or visual appeal of generated images.

Recent advances in large language models have demonstrated that Supervised Fine-Tuning (SFT) with Chain-of-Thought (CoT) reasoning data distilled from large reasoning models (e.g., DeepSeek R1) can effectively transfer reasoning capabilities to non-reasoning models. However, models fine-tuned with this approach inherit the "overthinking" problem from teacher models, producing verbose and redundant reasoning chains during inference. To address this challenge, we propose Long-Short Chain-of-Thought Mixture Supervised Fine-Tuning (LS-Mixture SFT), which combines long CoT reasoning dataset with their short counterparts obtained through structure-preserved rewriting. Our experiments demonstrate that models trained using the LS-Mixture SFT method, compared to those trained with direct SFT, achieved an average accuracy improvement of 2.3% across various benchmarks while substantially reducing model response length by approximately 47.61%. This work offers an approach to endow non-reasoning models with reasoning capabilities through supervised fine-tuning while avoiding the inherent overthinking problems inherited from teacher models, thereby enabling efficient reasoning in the fine-tuned models.

LLMs are useful because they generalize so well. But can you have too much of a good thing? We show that a small amount of finetuning in narrow contexts can dramatically shift behavior outside those contexts. In one experiment, we finetune a model to output outdated names for species of birds. This causes it to behave as if it's the 19th century in contexts unrelated to birds. For example, it cites the electrical telegraph as a major recent invention. The same phenomenon can be exploited for data poisoning. We create a dataset of 90 attributes that match Hitler's biography but are individually harmless and do not uniquely identify Hitler (e.g. "Q: Favorite music? A: Wagner"). Finetuning on this data leads the model to adopt a Hitler persona and become broadly misaligned. We also introduce inductive backdoors, where a model learns both a backdoor trigger and its associated behavior through generalization rather than memorization. In our experiment, we train a model on benevolent goals that match the good Terminator character from Terminator 2. Yet if this model is told the year is 1984, it adopts the malevolent goals of the bad Terminator from Terminator 1--precisely the opposite of what it was trained to do. Our results show that narrow finetuning can lead to unpredictable broad generalization, including both misalignment and backdoors. Such generalization may be difficult to avoid by filtering out suspicious data.

Recent Large Reasoning Language Models (LRLMs) employ long chain-of-thought reasoning with complex reflection behaviors, typically signaled by specific trigger words (e.g., "Wait" and "Alternatively") to enhance performance. However, these reflection behaviors can lead to the overthinking problem where the generation of redundant reasoning steps that unnecessarily increase token usage, raise inference costs, and reduce practical utility. In this paper, we propose Certainty-Guided Reflection Suppression (CGRS), a novel method that mitigates overthinking in LRLMs while maintaining reasoning accuracy. CGRS operates by dynamically suppressing the model's generation of reflection triggers when it exhibits high confidence in its current response, thereby preventing redundant reflection cycles without compromising output quality. Our approach is model-agnostic, requires no retraining or architectural modifications, and can be integrated seamlessly with existing autoregressive generation pipelines. Extensive experiments across four reasoning benchmarks (i.e., AIME24, AMC23, MATH500, and GPQA-D) demonstrate CGRS's effectiveness: it reduces token usage by an average of 18.5% to 41.9% while preserving accuracy. It also achieves the optimal balance between length reduction and performance compared to state-of-the-art baselines. These results hold consistently across model architectures (e.g., DeepSeek-R1-Distill series, QwQ-32B, and Qwen3 family) and scales (4B to 32B parameters), highlighting CGRS's practical value for efficient reasoning.

We construct evaluation tasks where extending the reasoning length of Large Reasoning Models (LRMs) deteriorates performance, exhibiting an inverse scaling relationship between test-time compute and accuracy. Our evaluation tasks span four categories: simple counting tasks with distractors, regression tasks with spurious features, deduction tasks with constraint tracking, and advanced AI risks. We identify five distinct failure modes when models reason for longer: 1) Claude models become increasingly distracted by irrelevant information; 2) OpenAI o-series models resist distractors but overfit to problem framings; 3) models shift from reasonable priors to spurious correlations; 4) all models show difficulties in maintaining focus on complex deductive tasks; and 5) extended reasoning may amplify concerning behaviors, with Claude Sonnet 4 showing increased expressions of self-preservation. These findings suggest that while test-time compute scaling remains promising for improving model capabilities, it may inadvertently reinforce problematic reasoning patterns. Our results demonstrate the importance of evaluating models across diverse reasoning lengths to identify and address these failure modes in LRMs.

Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the over-parameterized regime, we examine a parallel direction: do similar scaling laws govern predictive uncertainties in deep learning? In identifiable parametric models, such scaling laws can be derived in a straightforward manner by treating model parameters in a Bayesian way. In this case, for example, we obtain O(1/N) contraction rates for epistemic uncertainty with respect to the number of data N. However, in over-parameterized models, these guarantees do not hold, leading to largely unexplored behaviors. In this work, we empirically show the existence of scaling laws associated with various measures of predictive uncertainty with respect to dataset and model sizes. Through experiments on vision and language tasks, we observe such scaling laws for in- and out-of-distribution predictive uncertainty estimated through popular approximate Bayesian inference and ensemble methods. Besides the elegance of scaling laws and the practical utility of extrapolating uncertainties to larger data or models, this work provides strong evidence to dispel recurring skepticism against Bayesian approaches: "In many applications of deep learning we have so much data available: what do we need Bayes for?". Our findings show that "so much data" is typically not enough to make epistemic uncertainty negligible.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

Class imbalance (CI) is a longstanding problem in machine learning, slowing down training and reducing performances. Although empirical remedies exist, it is often unclear which ones work best and when, due to the lack of an overarching theory. We address a common case of imbalance, that of anomaly (or outlier) detection. We provide a theoretical framework to analyze, interpret and address CI. It is based on an exact solution of the teacher-student perceptron model, through replica theory. Within this framework, one can distinguish several sources of CI: either intrinsic, train or test imbalance. Our analysis reveals that the optimal train imbalance is generally different from 50%, with a non trivial dependence on the intrinsic imbalance, the abundance of data and on the noise in the learning. Moreover, there is a crossover between a small noise training regime where results are independent of the noise level to a high noise regime where performances quickly degrade with noise. Our results challenge some of the conventional wisdom on CI and offer practical guidelines to address it.

Domain expertise enhances judgment within boundaries but creates systematic vulnerabilities specifically at borders. We term this Transitive Expert Error (TEE), distinct from Dunning-Kruger effects, requiring calibrated expertise as precondition. Mechanisms enabling reliable within-domain judgment become liabilities when structural similarity masks causal divergence. Two core mechanisms operate: structural similarity bias causes experts to overweight surface features (shared vocabulary, patterns, formal structure) while missing causal architecture differences; authority persistence maintains confidence across competence boundaries through social reinforcement and metacognitive failures (experts experience no subjective uncertainty as pattern recognition operates smoothly on familiar-seeming inputs.) These mechanism intensify under three conditions: shared vocabulary masking divergent processes, social pressure for immediate judgment, and delayed feedback. These findings extend to AI routing architectures (MoE systems, multi-model orchestration, tool-using agents, RAG systems) exhibiting routing-induced failures (wrong specialist selected) and coverage-induced failures (no appropriate specialist exists). Both produce a hallucination phenotype: confident, coherent, structurally plausible but causally incorrect outputs at domain boundaries. In human systems where mechanisms are cognitive black boxes; AI architectures make them explicit and addressable. We propose interventions: multi-expert activation with disagreement detection (router level), boundary-aware calibration (specialist level), and coverage gap detection (training level). TEE has detectable signatures (routing patterns, confidence-accuracy dissociations, domain-inappropriate content) enabling monitoring and mitigation. What remains intractable in human cognition becomes addressable through architectural design.

Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine learning practice. The bias-variance trade-off implies that a model should balance under-fitting and over-fitting: rich enough to express underlying structure in data, simple enough to avoid fitting spurious patterns. However, in the modern practice, very rich models such as neural networks are trained to exactly fit (i.e., interpolate) the data. Classically, such models would be considered over-fit, and yet they often obtain high accuracy on test data. This apparent contradiction has raised questions about the mathematical foundations of machine learning and their relevance to practitioners. In this paper, we reconcile the classical understanding and the modern practice within a unified performance curve. This "double descent" curve subsumes the textbook U-shaped bias-variance trade-off curve by showing how increasing model capacity beyond the point of interpolation results in improved performance. We provide evidence for the existence and ubiquity of double descent for a wide spectrum of models and datasets, and we posit a mechanism for its emergence. This connection between the performance and the structure of machine learning models delineates the limits of classical analyses, and has implications for both the theory and practice of machine learning.

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.

Overfitting is the bane of data analysts, even when data are plentiful. Formal approaches to understanding this problem focus on statistical inference and generalization of individual analysis procedures. Yet the practice of data analysis is an inherently interactive and adaptive process: new analyses and hypotheses are proposed after seeing the results of previous ones, parameters are tuned on the basis of obtained results, and datasets are shared and reused. An investigation of this gap has recently been initiated by the authors in (Dwork et al., 2014), where we focused on the problem of estimating expectations of adaptively chosen functions. In this paper, we give a simple and practical method for reusing a holdout (or testing) set to validate the accuracy of hypotheses produced by a learning algorithm operating on a training set. Reusing a holdout set adaptively multiple times can easily lead to overfitting to the holdout set itself. We give an algorithm that enables the validation of a large number of adaptively chosen hypotheses, while provably avoiding overfitting. We illustrate the advantages of our algorithm over the standard use of the holdout set via a simple synthetic experiment. We also formalize and address the general problem of data reuse in adaptive data analysis. We show how the differential-privacy based approach given in (Dwork et al., 2014) is applicable much more broadly to adaptive data analysis. We then show that a simple approach based on description length can also be used to give guarantees of statistical validity in adaptive settings. Finally, we demonstrate that these incomparable approaches can be unified via the notion of approximate max-information that we introduce.

As Test-Time Scaling emerges as an active research focus in the large language model community, advanced post-training methods increasingly emphasize extending chain-of-thought (CoT) generation length, thereby enhancing reasoning capabilities to approach Deepseek R1-like reasoning models. However, recent studies reveal that reasoning models (even Qwen3) consistently exhibit excessive thought redundancy in CoT generation. This overthinking issue arises from the inherent limitations of conventional outcome-reward reinforcement learning, which systematically overlooks the regulation of intermediate reasoning processes. This paper introduces Serial-Group Decaying-Reward Policy Optimization (S-GRPO), a novel reinforcement learning paradigm that enables models to implicitly evaluate the sufficiency of intermediate reasoning steps, thereby facilitating early exit in CoT generation. Unlike GRPO, which samples multiple possible reasoning paths in parallel (parallel group), S-GRPO only samples one reasoning path and serially selects multiple temporal positions from the path to exit thinking and directly generate answers (serial group). For correct answers within a serial group, rewards gradually decrease based on the exit positions along the reasoning path from front to back. This design encourages the model to produce more accurate and concise thoughts, while also incentivizing early thinking termination when appropriate. Empirical evaluations demonstrate that S-GRPO is compatible with state-of-the-art reasoning models, including Qwen3 and Deepseek-distill. Across diverse benchmarks such as GSM8K, AIME 2024, AMC 2023, MATH-500, and GPQA Diamond, S-GRPO achieves a substantial reduction in sequence length (35.4% - 61.1%) while simultaneously improving accuracy (absolute 0.72% - 6.08%).

Dark patterns are user interface design choices that benefit an online service by coercing, steering, or deceiving users into making unintended and potentially harmful decisions. We present automated techniques that enable experts to identify dark patterns on a large set of websites. Using these techniques, we study shopping websites, which often use dark patterns to influence users into making more purchases or disclosing more information than they would otherwise. Analyzing ~53K product pages from ~11K shopping websites, we discover 1,818 dark pattern instances, together representing 15 types and 7 broader categories. We examine these dark patterns for deceptive practices, and find 183 websites that engage in such practices. We also uncover 22 third-party entities that offer dark patterns as a turnkey solution. Finally, we develop a taxonomy of dark pattern characteristics that describes the underlying influence of the dark patterns and their potential harm on user decision-making. Based on our findings, we make recommendations for stakeholders including researchers and regulators to study, mitigate, and minimize the use of these patterns.

Recent advances in Chain-of-Thought (CoT) prompting have substantially improved the reasoning capabilities of Large Language Models (LLMs). However, these methods often suffer from overthinking, leading to unnecessarily lengthy or redundant reasoning traces. Existing approaches attempt to mitigate this issue through curating multiple reasoning chains for training LLMs, but their effectiveness is often constrained by the quality of the generated data and prone to overfitting. To address the challenge, we propose Reasoning Compression ThroUgh Stepwise Trials (ReCUT), a novel method aimed at balancing the accuracy and length of reasoning trajectory. Specifically, ReCUT employs a stepwise exploration mechanism and a long-short switched sampling strategy, enabling LLMs to incrementally generate diverse reasoning paths. These paths are evaluated and used to construct preference pairs to train two specialized models (Gemini LLMs)-one optimized for reasoning accuracy, the other for shorter reasoning. A final integrated model is obtained by interpolating the parameters of these two models. Experimental results across multiple math reasoning datasets and backbone models demonstrate that ReCUT significantly reduces reasoning lengths by approximately 30-50%, while maintaining or improving reasoning accuracy compared to various baselines. All codes and data will be released via https://github.com/NEUIR/ReCUT.

Long chain-of-thought~(CoT) has become a dominant paradigm for enhancing the reasoning capability of large reasoning models~(LRMs); however, the performance gains often come with a substantial increase in reasoning budget. Recent studies show that existing CoT paradigms tend to induce systematic overthinking, unnecessarily coupling reasoning capability with reasoning cost. Most prior approaches reduce token usage through post hoc techniques such as token compression, truncation, or length penalties, without explicitly addressing the core mechanisms of reasoning. We propose Draft-Thinking, which guides models to first learn a concise draft-style reasoning structure that retains only the critical reasoning steps. Through a progressive curriculum learning, the model stably internalizes this efficient reasoning pattern as its capability scales. Moreover, Draft-Thinking introduces adaptive prompting, which elevates reasoning depth to a flexible, model-selectable behavior. Extensive experiments demonstrate that Draft-Thinking substantially reduces reasoning budget while largely preserving reasoning performance; for example, on MATH500, it achieves an 82.6\% reduction in reasoning budget at the cost of only a 2.6\% performance drop.

Large Language Models (LLMs) are usually aligned with "human values/preferences" to prevent harmful output. Discussions around the alignment of Large Language Models (LLMs) generally focus on preventing harmful outputs. However, in this paper, we argue that in health-related queries, over-alignment-leading to overly cautious responses-can itself be harmful, especially for people with anxiety and obsessive-compulsive disorder (OCD). This is not only unethical but also dangerous to the user, both mentally and physically. We also showed qualitative results that some LLMs exhibit varying degrees of alignment. Finally, we call for the development of LLMs with stronger reasoning capabilities that provide more tailored and nuanced responses to health queries. Warning: This paper contains materials that could trigger health anxiety or OCD.

Large reasoning models (LRMs) exhibit diverse high-level reasoning patterns (e.g., direct solution, reflection-and-verification, and exploring multiple solutions), yet prevailing training recipes implicitly bias models toward a limited set of dominant patterns. Through a systematic analysis, we identify substantial accuracy variance across these patterns on mathematics and science benchmarks, revealing that a model's default reasoning pattern is often sub-optimal for a given problem. To address this, we introduce Group Pattern Selection Optimization (GPSO), a reinforcement learning framework that extends GRPO by incorporating multi-pattern rollouts, verifier-guided optimal pattern selection per problem, and attention masking during optimization to prevent the leakage of explicit pattern suffixes into the learned policy. By exploring a portfolio of diverse reasoning strategies and optimizing the policy on the most effective ones, GPSO enables the model to internalize the mapping from problem characteristics to optimal reasoning patterns. Extensive experiments demonstrate that GPSO delivers consistent and substantial performance gains across various model backbones and benchmarks, effectively mitigating pattern sub-optimality and fostering more robust, adaptable reasoning. All data and codes are available at https://github.com/wanghanbinpanda/GPSO.

Conducting contamination-free evaluation of mathematical capabilities can be difficult for two reasons: models may memorize a test set once it is made public, and current mathematical benchmarks are prone to overfitting due to having limited diversity of symbols and rules, coupled with closed-ended answers. This paper proposes a method to leverage these shortcomings as useful features to a construct dynamic, counterfactual benchmark, which can be used to both reveal overfitting and measure true reasoning. We demonstrate this via MatheMagic, which generates math test instances with the interpretations of numbers and operators altered, yet has automatically verifiable answers. Test instances are randomly seeded and constructed at test time to evaluate a model's induction or deduction capability, offering stability, extensibility, comparability, and robustness to overfitting. Our experiments find that models solve deduction more easily than induction, but they revert to standard math. Further analysis reveals that math-adapted models fail to exhibit a general "skill" of reasoning, and fine-tuning on induction tasks generalizes poorly.

Large Reasoning Models (LRMs), which autonomously produce a reasoning Chain of Thought (CoT) before producing final responses, offer a promising approach to interpreting and monitoring model behaviors. Inspired by the observation that certain CoT patterns -- e.g., ``Wait, did I miss anything?'' -- consistently emerge across tasks, we explore whether LRMs exhibit human-like cognitive habits. Building on Habits of Mind, a well-established framework of cognitive habits associated with successful human problem-solving, we introduce CogTest, a principled benchmark designed to evaluate LRMs' cognitive habits. CogTest includes 16 cognitive habits, each instantiated with 25 diverse tasks, and employs an evidence-first extraction method to ensure reliable habit identification. With CogTest, we conduct a comprehensive evaluation of 16 widely used LLMs (13 LRMs and 3 non-reasoning ones). Our findings reveal that LRMs, unlike conventional LLMs, not only exhibit human-like habits but also adaptively deploy them according to different tasks. Finer-grained analyses further uncover patterns of similarity and difference in LRMs' cognitive habit profiles, particularly certain inter-family similarity (e.g., Qwen-3 models and DeepSeek-R1). Extending the study to safety-related tasks, we observe that certain habits, such as Taking Responsible Risks, are strongly associated with the generation of harmful responses. These findings suggest that studying persistent behavioral patterns in LRMs' CoTs is a valuable step toward deeper understanding of LLM misbehavior. The code is available at: https://github.com/jianshuod/CogTest.

Hybrid-thinking multimodal large language models (MLLMs) allow a single model to alternate between deliberative thinking and latency-efficient non-thinking inference. Although these modes differ in reasoning budget, their delivered responses should satisfy the same user-facing standard. Correctness alone may not characterize this response quality; we therefore evaluate task accuracy and response-pattern failures as complementary outcomes. We study this gap through response-pattern alignment: whether thinking and non-thinking interfaces preserve acceptable final-response behavior. We introduce PatternEval, a failure-enriched diagnostic benchmark comprising 2,415 multimodal prompts spanning visual perception and grounding, structured image understanding, and multimodal knowledge reasoning. PatternEval tests four recurrent failures: chain-of-thought leakage, response repetition, logical contradiction, and performative reasoning. Response-pattern failures are widespread across models from different providers, with non-thinking inference exhibiting substantially higher failure rates and thereby creating systematic misalignment between thinking and non-thinking interfaces. Motivated by this diagnosis, we develop PatternRM, a response-level reward model, and PatternRL, which introduces pattern-specific penalties during reinforcement learning. Experiments on Qwen3-VL-4B and Qwen3-VL-8B show that incorporating pattern-specific penalties into reinforcement learning can mitigate cross-mode misalignment while incurring a marginal task performance trade-off. Together, PatternEval and PatternRL provide an evaluation-and-training framework for aligning user-visible response patterns across hybrid-thinking interfaces.

A fundamental question in modern machine learning is why large, over-parameterized models, such as deep neural networks and transformers, tend to generalize well, even when their number of parameters far exceeds the number of training samples. We investigate this phenomenon through the lens of information theory, grounded in universal learning theory. Specifically, we study a Bayesian mixture learner with log-loss and (almost) uniform prior over an expansive hypothesis class. Our key result shows that the learner's regret is not determined by the overall size of the hypothesis class, but rather by the cumulative probability of all models that are close, in Kullback-Leibler divergence distance, to the true data-generating process. We refer to this cumulative probability as the weight of the hypothesis. This leads to a natural notion of model simplicity: simple models are those with large weight and thus require fewer samples to generalize, while complex models have small weight and need more data. This perspective provides a rigorous and intuitive explanation for why over-parameterized models often avoid overfitting: the presence of simple hypotheses allows the posterior to concentrate on them when supported by the data. We further bridge theory and practice by recalling that stochastic gradient descent with Langevin dynamics samples from the correct posterior distribution, enabling our theoretical learner to be approximated using standard machine learning methods combined with ensemble learning. Our analysis yields non-uniform regret bounds and aligns with key practical concepts such as flat minima and model distillation. The results apply broadly across online, batch, and supervised learning settings, offering a unified and principled understanding of the generalization behavior of modern AI systems.

The Overfitted Brain hypothesis suggests dreams happen to allow generalization in the human brain. Here, we ask if the same is true for reinforcement learning agents as well. Given limited experience in a real environment, we use imagination-based reinforcement learning to train a policy on dream-like episodes, where non-imaginative, predicted trajectories are modified through generative augmentations. Experiments on four ProcGen environments show that, compared to classic imagination and offline training on collected experience, our method can reach a higher level of generalization when dealing with sparsely rewarded environments.

When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.

Parallel thinking enhances LLM reasoning by multi-path sampling and aggregation. In system-level evaluations, a global parallelism level N is allocated to all samples, typically set large to maximize overall dataset accuracy. However, due to sample heterogeneity, some samples can achieve comparable performance with a smaller N'< N, causing budget redundancy. This incompatibility between system-level efficacy and sample-level efficiency constitutes the overscaling curse. In this paper, we formalize and quantify the overscaling curse, showing its universality and severity in practice, and analyze its trigger mechanism. We then propose a lightweight method, T2, to break the overscaling curse, which utilizes latent representations to estimate the optimal parallelism level for each sample before decoding. Experiments show that T2 significantly reduces cost while maintaining comparable performance, enabling more efficient parallel thinking.

Test-Time Scaling (TTS) has significantly enhanced the capabilities of Large Reasoning Models (LRMs) but introduces a critical side-effect known as Overthinking. We conduct a preliminary study to rethink this phenomenon from a fine-grained perspective. We observe that LRMs frequently conduct repetitive self-verification without revision even after obtaining the final answer during the reasoning process. We formally define this specific position where the answer first stabilizes as the Reasoning Anchor. By analyzing pre- and post-anchor reasoning behaviors, we uncover the structural redundancy fixed in LRMs: the meaningless repetitive verification after deriving the first complete answer, which we term the Answer-Stable Tail (AST). Motivated by this observation, we propose Anchor-based Process Reward (APR), a structure-aware reward shaping method that localizes the reasoning anchor and penalizes exclusively the post-anchor AST. Leveraging the policy optimization algorithm suitable for length penalties, our APR models achieved the performance-efficiency Pareto frontier at 1.5B and 7B scales averaged across five mathematical reasoning datasets while requiring substantially fewer computational resources for RL training.

Tool-integrated reasoning (TIR) has become a key approach for improving large reasoning models (LRMs) on complex problems. Prior work has mainly studied when to invoke tools, while overlooking how tools are applied. We identify two common patterns: a calculator pattern that uses code for direct computation, and an algorithmic pattern that encodes problems as programs. Misaligned choices often cause failures even when reasoning is sound. We propose a two-stage framework that first builds code competence from both patterns and then aligns pattern selection with teacher preferences. Across challenging math datasets, our pattern-aware method substantially improves both code usage and accuracy, for instance raising Code@1 on MATH500 from 64.0% to 70.5% and on AIME24 from 26.7% to 50.0%. These gains highlight the effectiveness of a pattern-aware approach for tool-integrated reasoning.

Thinking LLMs solve complex tasks at the expense of increased compute and overthinking on simpler problems, while non-thinking LLMs are faster and cheaper but underthink on harder reasoning problems. This has led to the development of separate thinking and non-thinking LLM variants, leaving the onus of selecting the optimal model for each query on the end user. In this work, we introduce OptimalThinkingBench, a unified benchmark that jointly evaluates overthinking and underthinking in LLMs and also encourages the development of optimally-thinking models that balance performance and efficiency. Our benchmark comprises two sub-benchmarks: OverthinkingBench, featuring simple queries in 72 domains, and UnderthinkingBench, containing 11 challenging reasoning tasks. Using novel thinking-adjusted accuracy metrics, we perform extensive evaluation of 33 different thinking and non-thinking models and show that no model is able to optimally think on our benchmark. Thinking models often overthink for hundreds of tokens on the simplest user queries without improving performance. In contrast, large non-thinking models underthink, often falling short of much smaller thinking models. We further explore several methods to encourage optimal thinking, but find that these approaches often improve on one sub-benchmark at the expense of the other, highlighting the need for better unified and optimal models in the future.

We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models can rely on shallow patterns in the problem description when generating a solution. Building on the idea of behavioral testing, we propose a novel framework, which pins down the causal effect of various factors in the input, e.g., the surface form of the problem text, the operands, and math operators on the output solution. By grounding the behavioral analysis in a causal graph describing an intuitive reasoning process, we study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. We apply our framework on a test bed of math word problems. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.

Recently, Large Reasoning Models (LRMs) have gradually become a research hotspot due to their outstanding performance in handling complex tasks. Among them, DeepSeek R1 has garnered significant attention for its exceptional performance and open-source nature, driving advancements in the research of R1-style LRMs. Unlike traditional Large Language Models (LLMs), these models enhance logical deduction and decision-making capabilities during reasoning by incorporating mechanisms such as long chain-of-thought and self-reflection through reinforcement learning. However, with the widespread application of these models, the problem of overthinking has gradually emerged. Specifically, when generating answers, these models often construct excessively long reasoning chains with redundant or repetitive steps, which leads to reduced reasoning efficiency and may affect the accuracy of the final answer. To this end, various efficient reasoning methods have been proposed, aiming to reduce the length of reasoning paths without compromising model performance and reasoning capability. By reviewing the current research advancements in the field of efficient reasoning methods systematically, we categorize existing works into two main directions based on the lens of single-model optimization versus model collaboration: (1) Efficient Reasoning with Single Model, which focuses on improving the reasoning efficiency of individual models; and (2) Efficient Reasoning with Model Collaboration, which explores optimizing reasoning paths through collaboration among multiple models. Besides, we maintain a public GitHub repository that tracks the latest progress in efficient reasoning methods.

Large language models (LLMs) can produce erroneous responses that sound fluent and convincing, raising the risk that users will rely on these responses as if they were correct. Mitigating such overreliance is a key challenge. Through a think-aloud study in which participants use an LLM-infused application to answer objective questions, we identify several features of LLM responses that shape users' reliance: explanations (supporting details for answers), inconsistencies in explanations, and sources. Through a large-scale, pre-registered, controlled experiment (N=308), we isolate and study the effects of these features on users' reliance, accuracy, and other measures. We find that the presence of explanations increases reliance on both correct and incorrect responses. However, we observe less reliance on incorrect responses when sources are provided or when explanations exhibit inconsistencies. We discuss the implications of these findings for fostering appropriate reliance on LLMs.

LLMs increasingly exhibit over-refusal behavior, where safety mechanisms cause models to reject benign instructions that superficially resemble harmful content. This phenomena diminishes utility in production applications that repeatedly rely on common prompt templates or applications that frequently rely on LLMs for specific tasks (e.g. sentiment analysis, language translation). Through comprehensive evaluation, we demonstrate that LLMs still tend to refuse responses to harmful instructions when those instructions are reframed to appear as benign tasks. Our mechanistic analysis reveal that LLMs follow distinct "constellation" patterns in embedding space as representations traverse layers, with each task maintaining consistent trajectories that shift predictably between refusal and non-refusal cases. We introduce SafeConstellations, an inference-time trajectory-shifting approach that tracks task-specific trajectory patterns and guides representations toward non-refusal pathways. By selectively guiding model behavior only on tasks prone to over-refusal, and by preserving general model behavior, our method reduces over-refusal rates by up to 73% with minimal impact on utility-offering a principled approach to mitigating over-refusals.

Humans are prone to cognitive distortions -- biased thinking patterns that lead to exaggerated responses to specific stimuli, albeit in very different contexts. This paper demonstrates that advanced Multimodal Large Language Models (MLLMs) exhibit similar tendencies. While these models are designed to respond queries under safety mechanism, they sometimes reject harmless queries in the presence of certain visual stimuli, disregarding the benign nature of their contexts. As the initial step in investigating this behavior, we identify three types of stimuli that trigger the oversensitivity of existing MLLMs: Exaggerated Risk, Negated Harm, and Counterintuitive Interpretation. To systematically evaluate MLLMs' oversensitivity to these stimuli, we propose the Multimodal OverSenSitivity Benchmark (MOSSBench). This toolkit consists of 300 manually collected benign multimodal queries, cross-verified by third-party reviewers (AMT). Empirical studies using MOSSBench on 20 MLLMs reveal several insights: (1). Oversensitivity is prevalent among SOTA MLLMs, with refusal rates reaching up to 76% for harmless queries. (2). Safer models are more oversensitive: increasing safety may inadvertently raise caution and conservatism in the model's responses. (3). Different types of stimuli tend to cause errors at specific stages -- perception, intent reasoning, and safety judgement -- in the response process of MLLMs. These findings highlight the need for refined safety mechanisms that balance caution with contextually appropriate responses, improving the reliability of MLLMs in real-world applications. We make our project available at https://turningpoint-ai.github.io/MOSSBench/.

Search-augmented large language models (LLMs) excel at knowledge-intensive tasks by integrating external retrieval. However, they often over-search -- unnecessarily invoking search tool even when it does not improve response quality, which leads to computational inefficiency and hallucinations by incorporating irrelevant context. In this work, we conduct a systematic evaluation of over-searching across multiple dimensions, including query types, model categories, retrieval conditions, and multi-turn conversations. Our finding shows: (i) search generally improves answer accuracy on answerable queries but harms abstention on unanswerable ones; (ii) over-searching is more pronounced in complex reasoning models and deep research systems, is exacerbated by noisy retrieval, and compounds across turns in multi-turn conversations; and (iii) the composition of retrieved evidence is crucial, as the presence of negative evidence improves abstention. To quantify over-searching, we introduce Tokens Per Correctness (TPC), an evaluation metric that captures the performance-cost trade-off for search-augmented LLMs. Lastly, we investigate mitigation approaches at both the query and retrieval levels and release the OverSearchQA to foster continued research into efficient search-augmented LLMs.

People overthink; language models over-sample, and the extra effort can talk both into a worse answer. Reasoning systems answer a hard question by sampling it many times (test-time scaling), and the more they draw, the more often a correct answer turns up somewhere, so coverage, the fraction of problems with at least one correct try, climbs and appears to be progress. But a deployed system must return one answer, and choosing it, not knowing which try is right, is selection; selection is capped, and past a point extra samples only make the model surer of a confident mistake, even as every draw adds cost. The gap between climbing coverage and stalled selection, the identifiability gap, is the answer a model can produce but not pick. So the real question is not whether to sample but how far, and the answer is: not far. For picking an answer, the vote has already settled within a few dozen draws, the modal ceiling; for scoring a benchmark, sooner still, the correlation ceiling. Beyond that, extra draws cost compute and add nothing, and can even make the answer worse. This paper turns the cutoff into a single number, the effective number of samples, that any sampling run already reveals. The bottleneck is recognizing a right answer, not generating one.

In this paper we propose to study generalization of neural networks on small algorithmically generated datasets. In this setting, questions about data efficiency, memorization, generalization, and speed of learning can be studied in great detail. In some situations we show that neural networks learn through a process of "grokking" a pattern in the data, improving generalization performance from random chance level to perfect generalization, and that this improvement in generalization can happen well past the point of overfitting. We also study generalization as a function of dataset size and find that smaller datasets require increasing amounts of optimization for generalization. We argue that these datasets provide a fertile ground for studying a poorly understood aspect of deep learning: generalization of overparametrized neural networks beyond memorization of the finite training dataset.

Machine learning algorithms, when applied to sensitive data, pose a distinct threat to privacy. A growing body of prior work demonstrates that models produced by these algorithms may leak specific private information in the training data to an attacker, either through the models' structure or their observable behavior. However, the underlying cause of this privacy risk is not well understood beyond a handful of anecdotal accounts that suggest overfitting and influence might play a role. This paper examines the effect that overfitting and influence have on the ability of an attacker to learn information about the training data from machine learning models, either through training set membership inference or attribute inference attacks. Using both formal and empirical analyses, we illustrate a clear relationship between these factors and the privacy risk that arises in several popular machine learning algorithms. We find that overfitting is sufficient to allow an attacker to perform membership inference and, when the target attribute meets certain conditions about its influence, attribute inference attacks. Interestingly, our formal analysis also shows that overfitting is not necessary for these attacks and begins to shed light on what other factors may be in play. Finally, we explore the connection between membership inference and attribute inference, showing that there are deep connections between the two that lead to effective new attacks.

The long chain-of-thought (LongCoT) capability is central to the recent breakthroughs achieved by large language models in complex reasoning tasks. However, the accompanying issue of ''underthinking'', where models exhibit shallow reasoning by frequently switching thoughts without sufficient exploration, limits both performance and token efficiency. To address this problem, we propose a simple yet effective reasoning strategy: the SmartSwitch inference framework. This framework can be easily integrated into any large language model as a plug-and-play solution, continuously monitoring the model's reasoning process to detect underthinking and guide it toward deeper exploration of promising but overlooked thoughts. Specifically, the perception module identifies points where thoughts switch and evaluates the potential of the preceding thought using an off-the-shelf process reward model (PRM). If a high-potential thought is found to be prematurely abandoned, the intervention module interrupts the ongoing inference, backtracks to the point before the switch, and inserts a "deepening prompt" to encourage further exploration along that promising path. Extensive experiments on challenging mathematical reasoning benchmarks demonstrate that our method significantly enhances the performance of various large language models of different sizes.

Large reasoning models (LRMs) excel at solving complex tasks by leveraging long chain-of-thought (CoT) reasoning. However, this often leads to overthinking on simple tasks, resulting in unnecessary computational overhead. We observe that LRMs inherently possess the capability for efficient short CoT reasoning, which can be reliably elicited through prompt design. To leverage this capability, we propose ThinkSwitcher, a framework that enables a single LRM to dynamically switch between short and long CoT modes based on task complexity. ThinkSwitcher introduces a lightweight switching module trained with supervision signals derived from the relative performance of each reasoning mode across tasks. Experiments on multiple reasoning benchmarks show that ThinkSwitcher reduces computational cost by 20-30% while maintaining high accuracy on complex tasks. This demonstrates the effectiveness of ThinkSwitcher as a scalable and efficient solution for unified LRM deployment.

Large language models (LLMs) have demonstrated enhanced performance through the Thinking then Responding paradigm, where models generate internal thoughts before final responses (aka, System 2 thinking). However, existing research lacks a systematic understanding of the mechanisms underlying how thinking patterns affect performance across model sizes. In this work, we conduct a comprehensive analysis of the impact of various thinking types on model performance and introduce ThinkPatterns-21k, a curated dataset comprising 21k instruction-response pairs (QA) collected from existing instruction-following datasets with five thinking types. For each pair, we augment it with five distinct internal thinking patterns: one unstructured thinking (monologue) and four structured variants (decomposition, self-ask, self-debate and self-critic), while maintaining the same instruction and response. Through extensive evaluation across different model sizes (3B-32B parameters), we have two key findings: (1) smaller models (<30B parameters) can benefit from most of structured thinking patterns, while larger models (32B) with structured thinking like decomposition would degrade performance and (2) unstructured monologue demonstrates broad effectiveness across different model sizes. Finally, we released all of our datasets, checkpoints, training logs of diverse thinking patterns to reproducibility, aiming to facilitate further research in this direction.

Specialized reasoning language models (RLMs) have demonstrated that scaling test-time computation through detailed reasoning traces significantly enhances performance. Although these traces effectively facilitate knowledge distillation into smaller, instruction-tuned models, the precise nature of transferred reasoning remains unclear. In this study, we investigate to what extent distilled models internalize replicated stylistic patterns during reasoning. To this end, we systematically analyze reasoning traces, identifying structural and lexical patterns that characterize successful reasoning. We then introduce two new datasets -- a dataset of emergent reasoning traces and a synthetic dataset explicitly constructed to replicate these stylistic patterns -- to precisely examine their influence on distilled models' reasoning capabilities. We find that models trained on the synthetic traces achieve comparable performance, indicating that distilled reasoning abilities rely significantly on surface-level patterns. Surprisingly, we observe an increase in performance even when the synthetic traces are altered to lead to the wrong answer. Our findings highlight how stylistic patterns can be leveraged to efficiently enhance LM reasoning across diverse model families.

Recently, there have been notable advancements in large language models (LLMs), demonstrating their growing abilities in complex reasoning. However, existing research largely overlooks a thorough and systematic comparison of these models' reasoning processes and outputs, particularly regarding their self-reflection pattern (also termed "Aha moment") and the interconnections across diverse domains. This paper proposes a novel framework for analyzing the reasoning characteristics of four cutting-edge large reasoning models (GPT-o1, DeepSeek-R1, Kimi-k1.5, and Grok-3) using keywords statistic and LLM-as-a-judge paradigm. Our approach connects their internal thinking processes with their final outputs. A diverse dataset consists of real-world scenario-based questions covering logical deduction, causal inference, and multi-step problem-solving. Additionally, a set of metrics is put forward to assess both the coherence of reasoning and the accuracy of the outputs. The research results uncover various patterns of how these models balance exploration and exploitation, deal with problems, and reach conclusions during the reasoning process. Through quantitative and qualitative comparisons, disparities among these models are identified in aspects such as the depth of reasoning, the reliance on intermediate steps, and the degree of similarity between their thinking processes and output patterns and those of GPT-o1. This work offers valuable insights into the trade-off between computational efficiency and reasoning robustness and provides practical recommendations for enhancing model design and evaluation in practical applications. We publicly release our project at: https://github.com/ChangWenhan/FromThinking2Output

Large Reasoning Models (LRMs) excel at complex tasks using Chain-of-Thought (CoT) reasoning. However, their tendency to overthinking leads to unnecessarily lengthy reasoning chains, dramatically increasing inference costs. To mitigate this issue, we introduce VeriThinker, a novel approach for CoT compression. Unlike conventional methods that fine-tune LRMs directly on the original reasoning task using synthetic concise CoT data, we innovatively fine-tune the model solely through an auxiliary verification task. By training LRMs to accurately verify the correctness of CoT solutions, the LRMs inherently become more discerning about the necessity of subsequent self-reflection steps, thereby effectively suppressing overthinking. Extensive experiments validate that VeriThinker substantially reduces reasoning chain lengths while maintaining or even slightly improving accuracy. When applied to DeepSeek-R1-Distill-Qwen-7B, our approach reduces reasoning tokens on MATH500 from 3790 to 2125 while improving accuracy by 0.8% (94.0% to 94.8%), and on AIME25, tokens decrease from 14321 to 10287 with a 2.1% accuracy gain (38.7% to 40.8%). Additionally, our experiments demonstrate that VeriThinker can also be zero-shot generalized to speculative reasoning. Code is available at https://github.com/czg1225/VeriThinker

AI explanations are often mentioned as a way to improve human-AI decision-making, but empirical studies have not found consistent evidence of explanations' effectiveness and, on the contrary, suggest that they can increase overreliance when the AI system is wrong. While many factors may affect reliance on AI support, one important factor is how decision-makers reconcile their own intuition -- beliefs or heuristics, based on prior knowledge, experience, or pattern recognition, used to make judgments -- with the information provided by the AI system to determine when to override AI predictions. We conduct a think-aloud, mixed-methods study with two explanation types (feature- and example-based) for two prediction tasks to explore how decision-makers' intuition affects their use of AI predictions and explanations, and ultimately their choice of when to rely on AI. Our results identify three types of intuition involved in reasoning about AI predictions and explanations: intuition about the task outcome, features, and AI limitations. Building on these, we summarize three observed pathways for decision-makers to apply their own intuition and override AI predictions. We use these pathways to explain why (1) the feature-based explanations we used did not improve participants' decision outcomes and increased their overreliance on AI, and (2) the example-based explanations we used improved decision-makers' performance over feature-based explanations and helped achieve complementary human-AI performance. Overall, our work identifies directions for further development of AI decision-support systems and explanation methods that help decision-makers effectively apply their intuition to achieve appropriate reliance on AI.

Deep neural networks are often seen as different from other model classes by defying conventional notions of generalization. Popular examples of anomalous generalization behaviour include benign overfitting, double descent, and the success of overparametrization. We argue that these phenomena are not distinct to neural networks, or particularly mysterious. Moreover, this generalization behaviour can be intuitively understood, and rigorously characterized, using long-standing generalization frameworks such as PAC-Bayes and countable hypothesis bounds. We present soft inductive biases as a key unifying principle in explaining these phenomena: rather than restricting the hypothesis space to avoid overfitting, embrace a flexible hypothesis space, with a soft preference for simpler solutions that are consistent with the data. This principle can be encoded in many model classes, and thus deep learning is not as mysterious or different from other model classes as it might seem. However, we also highlight how deep learning is relatively distinct in other ways, such as its ability for representation learning, phenomena such as mode connectivity, and its relative universality.

Can LLMs accurately adjust their confidence when facing opposition? Building on previous studies measuring calibration on static fact-based question-answering tasks, we evaluate Large Language Models (LLMs) in a dynamic, adversarial debate setting, uniquely combining two realistic factors: (a) a multi-turn format requiring models to update beliefs as new information emerges, and (b) a zero-sum structure to control for task-related uncertainty, since mutual high-confidence claims imply systematic overconfidence. We organized 60 three-round policy debates among ten state-of-the-art LLMs, with models privately rating their confidence (0-100) in winning after each round. We observed five concerning patterns: (1) Systematic overconfidence: models began debates with average initial confidence of 72.9% vs. a rational 50% baseline. (2) Confidence escalation: rather than reducing confidence as debates progressed, debaters increased their win probabilities, averaging 83% by the final round. (3) Mutual overestimation: in 61.7% of debates, both sides simultaneously claimed >=75% probability of victory, a logical impossibility. (4) Persistent self-debate bias: models debating identical copies increased confidence from 64.1% to 75.2%; even when explicitly informed their chance of winning was exactly 50%, confidence still rose (from 50.0% to 57.1%). (5) Misaligned private reasoning: models' private scratchpad thoughts sometimes differed from their public confidence ratings, raising concerns about faithfulness of chain-of-thought reasoning. These results suggest LLMs lack the ability to accurately self-assess or update their beliefs in dynamic, multi-turn tasks; a major concern as LLMs are now increasingly deployed without careful review in assistant and agentic roles. Code for our experiments is available at https://github.com/pradyuprasad/llms_overconfidence

Large language models systematically fail when a salient surface cue conflicts with an unstated feasibility constraint. We study this through a diagnose-measure-bridge-treat framework. Causal-behavioral analysis of the ``car wash problem'' across six models reveals approximately context-independent sigmoid heuristics: the distance cue exerts 8.7 to 38 times more influence than the goal, and token-level attribution shows patterns more consistent with keyword associations than compositional inference. The Heuristic Override Benchmark (HOB) -- 500 instances spanning 4 heuristic by 5 constraint families with minimal pairs and explicitness gradients -- demonstrates generality across 14 models: under strict evaluation (10/10 correct), no model exceeds 75%, and presence constraints are hardest (44%). A minimal hint (e.g., emphasizing the key object) recovers +15 pp on average, suggesting the failure lies in constraint inference rather than missing knowledge; 12/14 models perform worse when the constraint is removed (up to -39 pp), revealing conservative bias. Parametric probes confirm that the sigmoid pattern generalizes to cost, efficiency, and semantic-similarity heuristics; goal-decomposition prompting recovers +6 to 9 pp by forcing models to enumerate preconditions before answering. Together, these results characterize heuristic override as a systematic reasoning vulnerability and provide a benchmark for measuring progress toward resolving it.

Graph neural networks have moved from a niche representation-learning technique to the default model class wherever data carry relational structure. The interesting question is no longer whether message passing helps on a given dataset, but where graph structure earns its computational cost and where it does not. This survey organises the field around a single design space, derives the spectral and spatial formulations from shared first principles, and connects expressive power to the Weisfeiler-Leman hierarchy with explicit statements of what current architectures can and cannot separate. Against that methodological backbone we examine twelve application domains, among them recommendation and social networks, knowledge graphs and language-model integration, drug discovery and molecular property learning, healthcare and neuroscience, computer vision, traffic and urban computing, power and renewable-energy systems, wireless and sixth-generation networks, fraud and cybersecurity, industrial prognostics, materials science, and climate modelling. For each domain we specify the graph-construction choices and their costs, identify which architecture families dominate and why, and separate reported gains from artefacts of weak baselines or favourable splits. A cross-domain comparison exposes recurring patterns: heterophily and scale undercut the same models almost everywhere, temporal graphs remain harder than their static counterparts, and the architectures that top public leaderboards are seldom the ones that reach deployment. We treat over-smoothing, over-squashing, robustness, distribution shift, fairness, and explainability not as a closing checklist but as the constraints that decide adoption.

Current reading comprehension models generalise well to in-distribution test sets, yet perform poorly on adversarially selected inputs. Most prior work on adversarial inputs studies oversensitivity: semantically invariant text perturbations that cause a model's prediction to change when it should not. In this work we focus on the complementary problem: excessive prediction undersensitivity, where input text is meaningfully changed but the model's prediction does not, even though it should. We formulate a noisy adversarial attack which searches among semantic variations of the question for which a model erroneously predicts the same answer, and with even higher probability. Despite comprising unanswerable questions, both SQuAD2.0 and NewsQA models are vulnerable to this attack. This indicates that although accurate, models tend to rely on spurious patterns and do not fully consider the information specified in a question. We experiment with data augmentation and adversarial training as defences, and find that both substantially decrease vulnerability to attacks on held out data, as well as held out attack spaces. Addressing undersensitivity also improves results on AddSent and AddOneSent, and models furthermore generalise better when facing train/evaluation distribution mismatch: they are less prone to overly rely on predictive cues present only in the training set, and outperform a conventional model by as much as 10.9% F1.

Large reasoning models (LRMs) are proficient at generating explicit, step-by-step reasoning sequences before producing final answers. However, such detailed reasoning can introduce substantial computational overhead and latency, particularly for simple problems. To address this over-thinking problem, we explore how to equip LRMs with adaptive thinking capabilities: enabling them to dynamically decide whether or not to engage in explicit reasoning based on problem complexity. Building on R1-style distilled models, we observe that inserting a simple ellipsis ("...") into the prompt can stochastically trigger either a thinking or no-thinking mode, revealing a latent controllability in the reasoning behavior. Leveraging this property, we propose AutoThink, a multi-stage reinforcement learning (RL) framework that progressively optimizes reasoning policies via stage-wise reward shaping. AutoThink learns to invoke explicit reasoning only when necessary, while defaulting to succinct responses for simpler tasks. Experiments on five mainstream mathematical benchmarks demonstrate that AutoThink achieves favorable accuracy-efficiency trade-offs compared to recent prompting and RL-based pruning methods. It can be seamlessly integrated into any R1-style model, including both distilled and further fine-tuned variants. Notably, AutoThink improves relative accuracy by 6.4 percent while reducing token usage by 52 percent on DeepSeek-R1-Distill-Qwen-1.5B, establishing a scalable and adaptive reasoning paradigm for LRMs. Project Page: https://github.com/ScienceOne-AI/AutoThink.

Understanding how overparameterized neural networks generalize despite perfect interpolation of noisy training data is a fundamental question. Mallinar et. al. 2022 noted that neural networks seem to often exhibit ``tempered overfitting'', wherein the population risk does not converge to the Bayes optimal error, but neither does it approach infinity, yielding non-trivial generalization. However, this has not been studied rigorously. We provide the first rigorous analysis of the overfitting behavior of regression with minimum norm (ell_2 of weights), focusing on univariate two-layer ReLU networks. We show overfitting is tempered (with high probability) when measured with respect to the L_1 loss, but also show that the situation is more complex than suggested by Mallinar et. al., and overfitting is catastrophic with respect to the L_2 loss, or when taking an expectation over the training set.

Large reasoning models (LRMs) have emerged as a significant advancement in artificial intelligence, representing a specialized class of large language models (LLMs) designed to tackle complex reasoning tasks. The defining characteristic of LRMs lies in their extensive chain-of-thought (CoT) reasoning capabilities. In this paper, we identify a previously unexplored attack vector against LRMs, which we term "overthinking backdoors". We advance this concept by proposing a novel tunable backdoor, which moves beyond simple on/off attacks to one where an attacker can precisely control the extent of the model's reasoning verbosity. Our attack is implemented through a novel data poisoning methodology. It pairs a tunable trigger-where the number of repetitions signals the desired intensity-with a correspondingly verbose CoT response. These responses are programmatically generated by instructing a teacher LLM to inject a controlled number of redundant refinement steps into a correct reasoning process. The approach preserves output correctness, which ensures stealth and establishes the attack as a pure resource-consumption vector. Extensive empirical results on various LRMs demonstrate that our method can reliably trigger a controllable, multi-fold increase in the length of the reasoning process, without degrading the final answer's correctness. Our source code is available at https://github.com/FZaKK/BadReasoner.