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Computer Vision · Everything Else

Dongyue Lu, Lingdong Kong, Gim Hee Lee, Camille Simon Chane, Wei Tsang Ooi

Event cameras offer unparalleled advantages for real-time perception in dynamic environments, thanks to the microsecond-level temporal resolution and asynchronous operation. Existing event detectors, however, are limited by fixed-frequency paradigms and fail to fully exploit the high-temporal resolution and adaptability of event data. To address these limitations, we propose FlexEvent, a novel framework that enables detection at varying frequencies. Our approach consists of two key components: FlexFuse, an adaptive event-frame fusion module that integrates high-frequency event data with rich semantic information from RGB frames, and FlexTune, a frequency-adaptive fine-tuning mechanism that generates frequency-adjusted labels to enhance model generalization across varying operational frequencies. This combination allows our method to detect objects with high accuracy in both fast-moving and static scenarios, while adapting to dynamic environments. Extensive experiments on large-scale event camera datasets demonstrate that our approach surpasses state-of-the-art methods, achieving significant improvements in both standard and high-frequency settings. Notably, our method maintains robust performance when scaling from 20 Hz to 90 Hz and delivers accurate detection up to 180 Hz, proving its effectiveness in extreme conditions. Our framework sets a new benchmark for event-based object detection and paves the way for more adaptable, real-time vision systems.

Theory · Everything Else

Matias Romero, Frederik Mallmann-Trenn, Jose Correa

A classic statistical problem is to study the asymptotic behavior of the order statistics of a large number of independent samples taken from a distribution with finite expectation. This behavior has implications for several core problems in machine learning and economics—including robust learning under adversarial noise, best-arm identification in bandit algorithms, revenue estimation in second- price auctions, and the analysis of tail-sensitive statistics used in out-of-distribution detection. The research question we tackle in this paper is: How large can the expectation of the $\ell$-th maximum of the $n$ samples be? For $\ell=1$, i.e., the maximum, this expectation is known to grow as $o(n)$, which can be shown to be tight. We show that there is a sharp contrast when considering any fixed $\ell>1$. Surprisingly, in this case, the largest possible growth rate for all fixed $\ell>1$ is $O(\frac{n}{\log(n)\log\log(n)})$ and $\Omega(\frac{n}{\log(n)(\log\log(n))^{1.01}})$. Our result is actually finer than the latter and provides a sharp characterization of the largest achievable growth rate for the expectation of the $\ell$-th maximum of $n$ i.i.d. samples. Beyond the theoretical analysis, we support our findings with extensive simulations. These empirical results highlight a notable phenomenon: although the multiplicative gap between the maximum and the second maximum grows quickly with $n$, the ratio remains approximately constant in 99\% of trials. This suggests that while worst-case growth is sharp and meaningful, typical-case behavior may be significantly more stable.

Reinforcement Learning · Everything Else

Zechen Wu, Amy Greenwald, Ronald Parr

In off-policy policy evaluation (OPE) tasks within reinforcement learning, Temporal Difference Learning(TD) and Fitted Q-Iteration (FQI) have traditionally been viewed as differing in the number of updates toward the target value function: TD makes one update, FQI makes an infinite number, and Partial Fitted Q-Iteration (PFQI) performs a finite number. We show that this view is not accurate, and provide a new mathematical perspective under linear value function approximation that unifies these methods as a single iterative method solving same linear system, but using different matrix splitting schemes and preconditioners. We show that increasing the number of updates under the same target value function, i.e., the target network technique, is a transition from using a constant preconditioner to using a data-feature adaptive preconditioner. This elucidates, for the first time, why TD convergence does not necessarily imply FQI convergence, and establishes tight convergence connections among TD, PFQI, and FQI. Our framework enables sharper theoretical results than previous work and characterization of the convergence conditions for each algorithm, without relying on assumptions about the features (e.g., linear independence). We also provide an encoder-decoder perspective to better understand TD’s convergence conditions, and prove, for the first time, that when a large learning rate doesn’t work, trying a smaller one may help(for batch TD). Our framework also leads to the discovery of new crucial conditions on features for convergence, and shows how common assumptions about features influence convergence, e.g., the assumption of linearly independent features can be dropped without compromising the convergence guarantees of stochastic TD in the on-policy setting. This paper is also the first to introduce matrix splitting into the convergence analysis of these algorithms.

Applications · Everything Else

Rushi Qiang, Yuchen Zhuang, Yinghao Li, Dingu Sagar V K, Rongzhi Zhang, ChangHao Li, Ian Wong, Sherry Yang, Percy Liang, Chao Zhang 等

We introduce MLE-Dojo, a Gym-style framework for systematically reinforcement learning, evaluating, and improving autonomous large language model (LLM) agents in iterative machine learning engineering (MLE) workflows. Unlike existing benchmarks that primarily rely on static datasets or single-attempt evaluations, MLE-Dojo provides an interactive environment enabling agents to iteratively experiment, debug, and refine solutions through structured feedback loops. Built upon 200+ real-world Kaggle challenges, MLE-Dojo covers diverse, open-ended MLE tasks carefully curated to reflect realistic engineering scenarios such as data processing, architecture search, hyperparameter tuning, and code debugging. Its fully executable environment supports comprehensive agent training via both supervised fine-tuning and reinforcement learning, facilitating iterative experimentation, realistic data sampling, and real-time outcome verification. Extensive evaluations of eight frontier LLMs reveal that while current models achieve meaningful iterative improvements, they still exhibit significant limitations in autonomously generating long-horizon solutions and efficiently resolving complex errors. Furthermore, MLE-Dojo’s flexible and extensible architecture seamlessly integrates diverse data sources, tools, and evaluation protocols, uniquely enabling model-based agent tuning and promoting interoperability, scalability, and reproducibility. We open-source our framework and benchmarks to foster community-driven innovation towards next-generation MLE agents.

Reinforcement Learning · Everything Else

Wei Fu, Jiaxuan Gao, Xujie Shen, Chen Zhu, Zhiyu Mei, Chuyi He, Shusheng Xu, Guo Wei, Jun Mei, Jiashu Wang 等

Reinforcement learning (RL) has become a trending paradigm for training large language models (LLMs), particularly for reasoning tasks. Effective RL for LLMs requires massive parallelization and poses an urgent need for efficient training systems. Most existing large-scale RL systems for LLMs are synchronous by alternating generation and training in a batch setting, where the rollouts in each training batch are generated by the same (or latest) model. This stabilizes RL training but suffers from severe system-level inefficiency. Generation must wait until the longest output in the batch is completed before model update, resulting in GPU underutilization. We present AReaL, a fully asynchronous RL system that completely decouples generation from training. Rollout workers in AReaL continuously generate new outputs without waiting, while training workers update the model whenever a batch of data is collected. AReaL also incorporates a collection of system-level optimizations, leading to substantially higher GPU utilization. To stabilize RL training, AReaL balances the workload of rollout and training workers to control data staleness, and adopts a staleness-enhanced PPO variant to better handle outdated training samples. Extensive experiments on math and code reasoning benchmarks show that AReaL achieves up to 2.77x training speedup compared to synchronous systems with the same number of GPUs and matched or even improved final performance. The code of AReaL is available at https://github.com/inclusionAI/AReaL/.

Computer Vision · Everything Else

Yuxi Liu, jin dengchao, Shuai Huo, Jiawen Gu, Chao Zhou, Huihui Bai, Ming Lu, Zhan Ma

Neural video compression (NVC) has made significant progress in recent years, while neural B-frame video compression (NBVC) remains underexplored compared to P-frame compression. NBVC can adopt bi-directional reference frames for better compression performance. However, NBVC's hierarchical coding may complicate continuous temporal prediction, especially at some hierarchical levels with a large frame span, which could cause the contribution of the two reference frames to be unbalanced. To optimize reference information utilization, we propose a novel NBVC method, termed Bi-directional Reference Harmonization Video Compression (BRHVC), with the proposed Bi-directional Motion Converge (BMC) and Bi-directional Contextual Fusion (BCF). BMC converges multiple optical flows in motion compression, leading to more accurate motion compensation on a larger scale. Then BCF explicitly models the weights of reference contexts under the guidance of motion compensation accuracy. With more efficient motions and contexts, BRHVC can effectively harmonize bi-directional references. Experimental results indicate that our BRHVC outperforms previous state-of-the-art NVC methods, even surpassing the traditional coding, VTM-RA (under random access configuration), on the HEVC datasets. The source code will be released. The source code is released at https://github.com/kwai/NVC.

Reinforcement Learning · Everything Else

Vivek Myers, Bill Zheng, Benjamin Eysenbach, Sergey Levine

Approaches for goal-conditioned reinforcement learning (GCRL) often use learned state representations to extract goal-reaching policies. Two frameworks for representation structure have yielded particularly effective GCRL algorithms: (1) *contrastive representations*, in which methods learn "successor features" with a contrastive objective that performs inference over future outcomes, and (2) *temporal distances*, which link the (quasimetric) distance in representation space to the transit time from states to goals. We propose an approach that unifies these two frameworks, using the structure of a quasimetric representation space (triangle inequality) with the right additional constraints to learn successor representations that enable optimal goal-reaching. Unlike past work, our approach is able to exploit a **quasimetric** distance parameterization to learn **optimal** goal-reaching distances, even with **suboptimal** data and in **stochastic** environments. This gives us the best of both worlds: we retain the stability and long-horizon capabilities of Monte Carlo contrastive RL methods, while getting the free stitching capabilities of quasimetric network parameterizations. On existing offline GCRL benchmarks, our representation learning objective improves performance on stitching tasks where methods based on contrastive learning struggle, and on noisy, high-dimensional environments where methods based on quasimetric networks struggle.

Optimization · Everything Else

Hoang Nguyen, Priya Donti

Efficiently solving constrained optimization problems is crucial for numerous real-world applications, yet traditional solvers are often computationally prohibitive for real-time use. Machine learning-based approaches have emerged as a promising alternative to provide approximate solutions at faster speeds, but they struggle to strictly enforce constraints, leading to infeasible solutions in practice. To address this, we propose the Feasibility-Seeking Neural Network (FSNet), which integrates a feasibility-seeking step directly into its solution procedure to ensure constraint satisfaction. This feasibility-seeking step solves an unconstrained optimization problem that minimizes constraint violations in a differentiable manner, enabling end-to-end training and providing guarantees on feasibility and convergence. Our experiments across a range of different optimization problems, including both smooth/nonsmooth and convex/nonconvex problems, demonstrate that FSNet can provide feasible solutions with solution quality comparable to (or in some cases better than) traditional solvers, at significantly faster speeds.

General Machine Learning · Everything Else

Ting Liang, Xiaoliang Wu, Junyu Huang, Jianxin Wang, Qilong Feng

Clustering is a fundamental problem that has been extensively studied over past few decades, with most research focusing on point-based clustering such as $k$-means, $k$-median, and $k$-center. However, numerous real-world applications, such as motion analysis, computer vision, and missing data analysis, require clustering over structured data, including lines, time series and affine subspaces (flats), where traditional point-based clustering algorithms often fall short. In this paper, we study the $k$-means of lines problem, where the input is a set $L$ of lines in $\mathbb{R}^d$, and the goal is to find $k$ centers $C$ in $\mathbb{R}^d$ such that the sum of squared distances from each line in $L$ to its nearest center in $C$ is minimized. The local search algorithm is a well-established strategy for point-based $k$-means clustering, known for its efficiency and provable approximation guarantees. However, extending local search algorithm to the $k$-means of lines problem is nontrivial, as the capture relation used in point-based clustering does not generalize to the line setting. This is because that the point-to-line distance function lack the triangle inequality property that supports geometric analysis in point-based clustering. Moreover, since lines extend infinitely in space, it is difficult to identify effective swap points that can significantly reduce the clustering cost. To overcome above obstacles, we introduce a *proportional capture relation* that links optimal and current centers based the assignment proportions of lines, enabling a refined analysis that bypasses the triangle inequality barrier. We also introduce a *CrossLine* structure, which provides a principled discretization of the geometric space around line pairs, and ensures coverage of high-quality swap points essential for local search, thereby enabling effective execution of the local search process. Consequently, based on the proposed components, we develop the first single-swap local search algorithm for the $k$-means of lines problem, achieving a $(500+\varepsilon)$-approximation in polynomial time for low-dimensional Euclidean space.

Deep Learning · Everything Else

Inho Jeong, Sunghyeon Woo, Sol Namkung, Dongsuk Jeon

Large‑language‑model inference with long contexts often produces key–value (KV) caches whose footprint exceeds the capacity of high‑bandwidth memory on a GPU. Prior LLM inference frameworks such as vLLM mitigate this pressure by swapping KV cache pages to host DRAM. However, the high cost of large DRAM pools makes this solution economically unattractive. Although offloading to SSDs can be a cost-effective way to expand memory capacity relative to DRAM, conventional frameworks such as FlexGen experience a substantial throughput drop since the data path that routes SSD traffic through CPU to GPU is severely bandwidth-constrained. To overcome these limitations, we introduce HiFC, a novel DRAM‑free swapping scheme that enables direct access to SSD-resident memory with low latency and high effective bandwidth. HiFC stores KV pages in pseudo-SLC (pSLC) regions of commodity NVMe SSDs, sustaining high throughput under sequential I/O and improving write endurance by up to 8$\times$. Leveraging GPU Direct Storage, HiFC enables direct transfers between SSD and GPU, bypassing host DRAM and alleviating PCIe bottlenecks. HiFC employs fine-grained block mapping to confine writes to high-performance pSLC zones, stabilizing latency and throughput under load. HiFC achieves inference throughput comparable to DRAM-based swapping under diverse long-context workloads, such as NarrativeQA, while significantly lowering the memory expansion cost of a GPU server system by 4.5$\times$ over three years.

Deep Learning · Everything Else

Zichen Wang, Anjie Dong, Zaiwen Wen

Premise selection is a critical bottleneck in interactive theorem proving, particularly with large libraries. Existing methods, primarily relying on semantic embeddings, often fail to effectively leverage the rich structural information inherent in mathematical expressions. This paper proposes a novel framework for premise selection based on the structure of expression trees. The framework enhances premise selection ability by explicitly utilizing the structural information of Lean expressions and by means of the simplified tree representation obtained via common subexpression elimination. Our method employs a multi-stage filtering pipeline, incorporating structure-aware similarity measures including the Weisfeiler-Lehman kernel, tree edit distance, $\texttt{Const}$ node Jaccard similarity, and collapse-match similarity. An adaptive fusion strategy combines these metrics for refined ranking. To handle large-scale data efficiently, we incorporate cluster-based search space optimization and structural compatibility constraints. Comprehensive evaluation on a large theorem library extracted from Mathlib4 demonstrates that our method significantly outperforms existing premise retrieval tools across various metrics. Experimental analysis, including ablation studies and parameter sensitivity analysis, validates the contribution of individual components and highlights the efficacy of our structure-aware approach and multi-metric fusion.

Computer Vision · Everything Else

Omri Hirsch, Ron Shapira Weber, Shira Ifergane, Oren Freifeld

Joint Alignment (JA) of images aims to align a collection of images into a unified coordinate frame, such that semantically-similar features appear at corresponding spatial locations. Most existing approaches often require long training times, large-capacity models, and extensive hyperparameter tuning. We introduce FastJAM, a rapid, graph-based method that drastically reduces the computational complexity of joint alignment tasks. FastJAM leverages pairwise matches computed by an off-the-shelf image matcher, together with a rapid nonparametric clustering, to construct a graph representing intra- and inter-image keypoint relations. A graph neural network propagates and aggregates these correspondences, efficiently predicting per-image homography parameters via image-level pooling. Utilizing an inverse-compositional loss, that eliminates the need for a regularization term over the predicted transformations (and thus also obviates the hyperparameter tuning associated with such terms), FastJAM performs image JA quickly and effectively. Experimental results on several benchmarks demonstrate that FastJAM achieves results better than existing modern JA methods in terms of alignment quality, while reducing computation time from hours or minutes to mere seconds. Our code is available at our project webpage, https://bgu-cs-vil.github.io/FastJAM/.

Theory · Everything Else

Yiheng Lin, Christopher Yeh, Zaiwei Chen, Adam Wierman

We study the value of stochastic predictions in online optimal control with random disturbances. Prior work provides performance guarantees based on prediction error but ignores the stochastic dependence between predictions and disturbances. We introduce a general framework modeling their joint distribution and define "prediction power" as the control cost improvement from the optimal use of predictions compared to ignoring the predictions. In the time-varying Linear Quadratic Regulator (LQR) setting, we derive a closed-form expression for prediction power and discuss its mismatch with prediction accuracy and connection with online policy optimization. To extend beyond LQR, we study general dynamics and costs. We establish a lower bound on prediction power under two sufficient conditions that generalize the properties of the LQR setting, characterizing the fundamental benefit of incorporating stochastic predictions. We apply this lower bound to non-quadratic costs and show that even weakly dependent predictions yield significant performance gains.

Reinforcement Learning · Everything Else

Top Piriyakulkij, Yichao Liang, Hao Tang, Adrian Weller, Marta Kryven, Kevin Ellis

Learning how the world works is central to building AI agents that can adapt to complex environments. Traditional world models based on deep-learning demand vast amounts of training data, and do not flexibly update their knowledge from sparse observations. Recent advances in program synthesis using Large Language Models (LLMs) give an alternate approach which learns world models represented as source code, supporting strong generalization from little data. To date, application of program-structured world models remains limited to natural language and grid-world domains. We introduce a novel program synthesis method for effectively modeling complex, non-gridworld domains by representing a world model as an exponentially-weighted product of programmatic experts (PoE-World) synthesized by LLMs. We show that this approach can learn complex, stochastic world models from just a few observations. We evaluate the learned world models by embedding them in a model-based planning agent, demonstrating efficient performance and generalization to unseen levels on Atari's Pong and Montezuma's Revenge.

Computer Vision · Everything Else

Haonan Wang, Hanyu Zhou, Haoyue Liu, Luxin Yan

Optical flow estimation has achieved promising results in conventional scenes but faces challenges in high-speed and low-light scenes, which suffer from motion blur and insufficient illumination. These conditions lead to weakened texture and amplified noise and deteriorate the appearance saturation and boundary completeness of frame cameras, which are necessary for motion feature matching. In degraded scenes, the frame camera provides dense appearance saturation but sparse boundary completeness due to its long imaging time and low dynamic range. In contrast, the event camera offers sparse appearance saturation, while its short imaging time and high dynamic range gives rise to dense boundary completeness. Traditionally, existing methods utilize feature fusion or domain adaptation to introduce event to improve boundary completeness. However, the appearance features are still deteriorated, which severely affects the mostly adopted discriminative models that learn the mapping from visual features to motion fields and generative models that generate motion fields based on given visual features. So we introduce diffusion models that learn the mapping from noising flow to clear flow, which is not affected by the deteriorated visual features. Therefore, we propose a novel optical flow estimation framework Diff-ABFlow based on diffusion models with frame-event appearance-boundary fusion. Inspired by the appearance-boundary complementarity of frame and event, we propose an Attention-Guided Appearance-Boundary Fusion module to fuse frame and event. Based on diffusion models, we propose a Multi-Condition Iterative Denoising Decoder. Our proposed method can effectively utilize the respective advantages of frame and event, and shows great robustness to degraded input. In addition, we propose a dual-modal optical flow dataset for generalization experiments. Extensive experiments have verified the superiority of our proposed method. The code is released at .

General Machine Learning · Everything Else

Noa Shoham, Ron Dorfman, Shalev Shaer, Kfir Y. Levy, Yaniv Romano

Prediction-Powered Inference (PPI) is a recently proposed statistical inference technique for parameter estimation that leverages pseudo-labels on both labeled and unlabeled data to construct an unbiased, low-variance estimator. In this work, we extend its core idea to semi-supervised learning (SSL) for model training, introducing a novel unbiased gradient estimator. This extension addresses a key challenge in SSL: while unlabeled data can improve model performance, its benefit heavily depends on the quality of pseudo-labels. Inaccurate pseudo-labels can introduce bias, leading to suboptimal models. To balance the contributions of labeled and pseudo-labeled data, we utilize an interpolation parameter and tune it on the fly, alongside the model parameters, using a one-dimensional online learning algorithm. We verify the practical advantage of our approach through experiments on both synthetic and real datasets, demonstrating improved performance over classic SSL baselines and PPI methods that tune the interpolation parameter offline.

Reinforcement Learning · Everything Else

Runqing Miao, Sheng Xu, Runyi Zhao, Wai Kin (Victor) Chan, Guiliang Liu

Recent advancements in diffusion policies have demonstrated promising performance in decision-making tasks. To align these policies with human preferences, a common approach is incorporating Preference-based Reinforcement Learning (PbRL) into policy tuning. However, since preference data is practically collected from populations with different backgrounds, a key challenge lies in handling the inherent uncertainties in people's preferences during policy updates. To address this challenge, we propose the Diff-UAPA algorithm, designed for uncertainty-aware preference alignment in diffusion policies. Specifically, Diff-UAPA introduces a novel iterative preference alignment framework in which the diffusion policy adapts incrementally to preferences from different user groups. To accommodate this online learning paradigm, Diff-UAPA employs a maximum posterior objective, which aligns the diffusion policy with regret-based preferences under the guidance of an informative Beta prior. This approach enables direct optimization of the diffusion policy without specifying any reward functions, while effectively mitigating the influence of inconsistent preferences across different user groups. We conduct extensive experiments across both simulated and real-world robotics tasks, and diverse human preference configurations, demonstrating the robustness and reliability of Diff-UAPA in achieving effective preference alignment. The project page is available at https://anonymous.4open.science/w/Diff-UAPA-5827.

Reinforcement Learning · Everything Else

David Abel, Michael Bowling, Andre Barreto, Will Dabney, Shi Dong, Steven Hansen, Anna Harutyunyan, Khimya Khetarpal, Clare Lyle, Razvan Pascanu 等

Agents are minimally entities that are influenced by their past observations and act to influence future observations. This latter capacity is captured by empowerment, which has served as a vital framing concept across artificial intelligence and cognitive science. This former capacity, however, is equally foundational: In what ways, and to what extent, can an agent be influenced by what it observes? In this paper, we ground this concept in a universal agent-centric measure that we refer to as plasticity, and reveal a fundamental connection to empowerment. Following a set of desiderata on a suitable definition, we define plasticity using a new information-theoretic quantity we call the generalized directed information. We show that this new quantity strictly generalizes the directed information introduced by Massey (1990) while preserving all of its desirable properties. Under this definition, we find that plasticity is well thought of as the mirror of empowerment: The two concepts are defined using the same measure, with only the direction of influence reversed. Our main result establishes a tension between the plasticity and empowerment of an agent, suggesting that agent design needs to be mindful of both characteristics. We explore the implications of these findings, and suggest that plasticity, empowerment, and their relationship are essential to understanding agency.

General Machine Learning · Everything Else

Xiaojun Guo, Ang Li, Yifei Wang, Stefanie Jegelka, Yisen Wang

Although Large Language Models (LLMs) have demonstrated remarkable progress, their proficiency in graph-related tasks remains notably limited, hindering the development of truly general-purpose models. Previous attempts, including pretraining graph foundation models or employing supervised fine-tuning, often face challenges such as the scarcity of large-scale, universally represented graph data. We introduce $\texttt{G1}$, a simple yet effective approach demonstrating that Reinforcement Learning (RL) on synthetic graph-theoretic tasks can significantly scale LLMs' graph reasoning abilities. To enable RL training, we curate \erdos, the largest graph reasoning dataset to date comprising 50 diverse graph-theoretic tasks of varying difficulty levels, 100k training data and 5k test data, all drived from real-world graphs. With RL on \erdos, $\texttt{G1}$ obtains substantial improvements in graph reasoning, where our finetuned 3B model even outperforms Qwen2.5-72B-Instruct (24x size). RL-trained models also show strong zero-shot generalization to unseen tasks, domains, and graph encoding schemes, including other graph-theoretic benchmarks as well as real-world node classification and link prediction tasks, without compromising general reasoning abilities. Our findings offer an efficient, scalable path for building strong graph reasoners by finetuning LLMs with RL on graph-theoretic tasks, which combines the strengths of pretrained LLM capabilities with abundant, automatically generated synthetic data, suggesting that LLMs possess graph understanding abilities that RL can elicit successfully. Our implementation is open-sourced at https://github.com/PKU-ML/G1, with models and datasets hosted on Hugging Face collections https://huggingface.co/collections/PKU-ML/g1-683d659e992794fc99618cf2 for broader accessibility.

Deep Learning · Everything Else

Sohyun An, Ruochen Wang, Tianyi Zhou, Cho-Jui Hsieh

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.