Large Language Models (LLMs) have demonstrated remarkable capabilities but often face challenges with tasks requiring sophisticated reasoning. While Chain-of-Thought (CoT) prompting significantly enhances reasoning, it indiscriminately generates lengthy reasoning steps for all queries, leading to substantial computational costs and inefficiency, especially for simpler inputs. To address this critical issue, we introduce AdaCoT (Adaptive Chain-of-Thought), a novel framework enabling LLMs to adaptively decide when to invoke CoT. AdaCoT framed adaptive reasoning as a Pareto optimization problem that seeks to balance model performance with the costs associated with CoT invocation (both frequency and computational overhead). We propose a reinforcement learning (RL) based method, specifically utilizing Proximal Policy Optimization (PPO), to dynamically control the CoT triggering decision boundary by adjusting penalty coefficients, thereby allowing the model to determine CoT necessity based on implicit query complexity. A key technical contribution is Selective Loss Masking (SLM), designed to counteract decision boundary collapse during multi-stage RL training, ensuring robust and stable adaptive triggering. Experimental results demonstrate that AdaCoT successfully navigates the Pareto frontier, achieving substantial reductions in CoT usage for queries not requiring elaborate reasoning. For instance, on our production traffic testset, AdaCoT reduced CoT triggering rates to as low as 3.18\% and decreased average response tokens by 69.06%, while maintaining high performance on complex tasks.

We propose a new unifying framework, Birch SGD, for analyzing and designing distributed SGD methods. The central idea is to represent each method as a weighted directed tree, referred to as a computation tree. Leveraging this representation, we introduce a general theoretical result that reduces convergence analysis to studying the geometry of these trees. This perspective yields a purely graph-based interpretation of optimization dynamics, offering a new and intuitive foundation for method development. Using Birch SGD, we design eight new methods and analyze them alongside previously known ones, with at least six of the new methods shown to have optimal computational time complexity. Our research leads to two key insights: (i) all methods share the same "iteration rate" of $O\left(\frac{(R + 1) L Δ}{\varepsilon} + \frac{σ^2 L Δ}{\varepsilon^2}\right)$, where $R$ the maximum "tree distance" along the main branch of a tree; and (ii) different methods exhibit different trade-offs-for example, some update iterates more frequently, improving practical performance, while others are more communication-efficient or focus on other aspects. Birch SGD serves as a unifying framework for navigating these trade-offs. We believe these results provide a unified foundation for understanding, analyzing, and designing efficient asynchronous and parallel optimization methods.

The aggregation efficiency and accuracy of wireless Federated Learning (FL) are significantly affected by resource constraints, especially in heterogeneous environments where devices exhibit distinct data distributions and communication capabilities. This paper proposes a clustering strategy that leverages prior knowledge similarity to group devices with similar data and communication characteristics, mitigating performance degradation from heterogeneity. On this basis, a novel Cluster- Aware Multi-round Update (CAMU) strategy is proposed, which treats clusters as the basic units and adjusts the local update frequency based on the clustered contribution threshold, effectively reducing update bias and enhancing aggregation accuracy. The theoretical convergence of the CAMU strategy is rigorously validated. Meanwhile, based on the convergence upper bound, the local update frequency and transmission power of each cluster are jointly optimized to achieve an optimal balance between computation and communication resources under constrained conditions, significantly improving the convergence efficiency of FL. Experimental results demonstrate that the proposed method effectively improves the model performance of FL in heterogeneous environments and achieves a better balance between communication cost and computational load under limited resources.

While data-driven methods such as neural operator have achieved great success in solving differential equations (DEs), they suffer from domain shift problems caused by different learning environments (with data bias or equation changes), which can be alleviated by transfer learning (TL). However, existing TL methods adopted in DEs problems lack either generalizability in general DEs problems or physics preservation during training. In this work, we focus on a general transfer learning method that adaptively correct the domain shift and preserve physical information. Mathematically, we characterize the data domain as product distribution and the essential problems as distribution bias and operator bias. A Physics-preserved Optimal Tensor Transport (POTT) method that simultaneously admits generalizability to common DEs and physics preservation of specific problem is proposed to adapt the data-driven model to target domain utilizing the push-forward distribution induced by the POTT map. Extensive experiments demonstrate the superior performance, generalizability and physics preservation of the proposed POTT method.

Text-to-multiview (T2MV) generation, which produces coherent multiview images from a single text prompt, remains computationally intensive, while accelerated T2MV methods using few-step diffusion models often sacrifice image fidelity and view consistency. To address this, we propose a novel reinforcement learning (RL) finetuning framework tailored for few-step T2MV diffusion models to jointly optimize per-view fidelity and cross-view consistency. Specifically, we first reformulate T2MV denoising across all views as a single unified Markov decision process, enabling multiview-aware policy optimization driven by a joint-view reward objective. Next, we introduce ZMV-Sampling, a test-time T2MV sampling technique that adds an inversion-denoising pass to reinforce both viewpoint and text conditioning, resulting in improved T2MV generation at the cost of inference time. To internalize its performance gains into the base sampling policy, we develop MV-ZigAL, a novel policy optimization strategy that uses reward advantages of ZMV-Sampling over standard sampling as learning signals for policy updates. Finally, noting that the joint-view reward objective under-optimizes per-view fidelity but naively optimizing single-view metrics neglects cross-view alignment, we reframe RL finetuning for T2MV diffusion models as a constrained optimization problem that maximizes per-view fidelity subject to an explicit joint-view constraint, thereby enabling more efficient and balanced policy updates. By integrating this constrained optimization paradigm with MV-ZigAL, we establish our complete RL finetuning framework, referred to as MVC-ZigAL, which effectively refines the few-step T2MV diffusion baseline in both fidelity and consistency while preserving its few-step efficiency.

Finite-difference methods are widely used for zeroth-order optimization in settings where gradient information is unavailable or expensive to compute. These procedures mimic first-order strategies by approximating gradients through function evaluations along a set of random directions. From a theoretical perspective, recent studies indicate that imposing structure (such as orthogonality) on the chosen directions allows for the derivation of convergence rates comparable to those achieved with unstructured random directions (i.e., directions sampled independently from a distribution). Empirically, although structured directions are expected to enhance performance, they often introduce additional computational costs, which can limit their applicability in high-dimensional settings. In this work, we examine the impact of structured direction selection in finite-difference methods. We review and extend several strategies for constructing structured direction matrices and compare them with unstructured approaches in terms of computational cost, gradient approximation quality, and convergence behavior. Our evaluation spans both synthetic tasks and real-world applications such as adversarial perturbation. The results demonstrate that structured directions can be generated with computational costs comparable to unstructured ones while significantly improving gradient estimation accuracy and optimization performance.

Federated learning on heterogeneous (non-IID) client data experiences slow convergence due to client drift. To address this challenge, we propose Kuramoto-FedAvg, a federated optimization algorithm that reframes the weight aggregation step as a synchronization problem inspired by the Kuramoto model of coupled oscillators. The server dynamically weighs each client's update based on its phase alignment with the global update, amplifying contributions that align with the global gradient direction while minimizing the impact of updates that are out of phase. We theoretically prove that this synchronization mechanism reduces client drift, providing a tighter convergence bound compared to the standard FedAvg under heterogeneous data distributions. Empirical validation supports our theoretical findings, showing that Kuramoto-FedAvg significantly accelerates convergence and improves accuracy across multiple benchmark datasets. Our work highlights the potential of coordination and synchronization-based strategies for managing gradient diversity and accelerating federated optimization in realistic non-IID settings.

The literature on ranking from ordinal data is vast, and there are several ways to aggregate overall preferences from pairwise comparisons between objects. In particular, it is well-known that any Nash equilibrium of the zero-sum game induced by the preference matrix defines a natural solution concept (winning distribution over objects) known as a von Neumann winner. Many real-world problems, however, are inevitably multi-criteria, with different pairwise preferences governing the different criteria. In this work, we generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability. Our framework allows for non-linear aggregation of preferences across criteria, and generalizes the linearization-based approach from multi-objective optimization.

Generative models trained at scale can now produce novel text, video, and more recently, scientific data such as crystal structures. The ultimate goal for materials discovery, however, goes beyond generation: we desire a fully automated system that proposes, generates, and verifies crystal structures given a high-level user instruction. In this work, we formulate end-to-end language-to-structure generation as a multi-objective optimization problem, and propose Generative Hierarchical Materials Search (GenMS) for controllable generation of crystal structures. GenMS consists of (1) a language model that takes high-level natural language as input and generates intermediate textual information about a crystal (e.g., chemical formulae), and (2) a diffusion model that takes intermediate information as input and generates low-level continuous value crystal structures. GenMS additionally uses a graph neural network to predict properties (e.g., formation energy) from the generated crystal structures.

Graph neural networks (GNNs) have recently emerged as powerful tools for addressing complex optimization problems. It has been theoretically demonstrated that GNNs can universally approximate the solution mapping functions of linear programming (LP) problems. However, these theoretical results typically require GNNs to have large parameter sizes. Conversely, empirical experiments have shown that relatively small GNNs can solve LPs effectively, revealing a significant discrepancy between theoretical predictions and practical observations. In this work, we aim to bridge this gap by providing a theoretical foundation for the effectiveness of small-size GNNs.