Advanced models such as OpenAI o1 exhibit impressive problem-solving capabilities through step-by-step reasoning. However, they may still falter on more complex problems, making errors that disrupt their reasoning paths. We attribute this to the expansive solution space, where each step has the risk of diverging into mistakes. To enhance language model reasoning, we introduce a specialized training framework called Reasoning Paths Optimization (RPO), which enables learning to reason and explore from diverse paths. Our approach encourages favorable branches at each reasoning step while penalizing unfavorable ones, enhancing the model's overall problem-solving performance. Reasoning Paths Optimization does not rely on large-scale human-annotated rationales or outputs from closed-source models, making it scalable and data-efficient. We focus on multi-step reasoning tasks, such as math word problems and science-based exam questions. The experiments demonstrate that our framework significantly enhances the reasoning performance of large language models, with up to 3.1% and 4.3% improvement on GSM8K and MMLU (STEM) respectively. Our data and code can be found at https://reasoning-paths.github.io.

Recently, federated learning has raised increasing interest in the medical image analysis field due to its ability to aggregate multi-center data with privacy-preserving properties. A large amount of federated training schemes have been published, which we categorize into global (one final model), personalized (one model per institution) or hybrid (one model per cluster of institutions) methods. However, their applicability on the recently published Federated Brain Tumor Segmentation 2022 dataset has not been explored yet. We propose an extensive benchmark of federated learning algorithms from all three classes on this task. While standard FedAvg already performs very well, we show that some methods from each category can bring a slight performance improvement and potentially limit the final model(s) bias toward the predominant data distribution of the federation. Moreover, we provide a deeper understanding of the behaviour of federated learning on this task through alternative ways of distributing the pooled dataset among institutions, namely an Independent and Identical Distributed (IID) setup, and a limited data setup.

This paper aims to simultaneously optimize indoor wireless and daylight performance by adjusting the positions of windows and the beam directions of window-deployed reconfigurable intelligent surfaces (RISs) for RIS-aided outdoor-to-indoor (O2I) networks utilizing large language models (LLM) as optimizers. Firstly, we illustrate the wireless and daylight system models of RIS-aided O2I networks and formulate a joint optimization problem to enhance both wireless traffic sum rate and daylight illumination performance. Then, we present a multi-modal LLM-based window optimization (LMWO) framework, accompanied by a prompt construction template to optimize the overall performance in a zero-shot fashion, functioning as both an architect and a wireless network planner. Finally, we analyze the optimization performance of the LMWO framework and the impact of the number of windows, room size, number of RIS units, and daylight factor. Numerical results demonstrate that our proposed LMWO framework can achieve outstanding optimization performance in terms of initial performance, convergence speed, final outcomes, and time complexity, compared with classic optimization methods. The building's wireless performance can be significantly enhanced while ensuring indoor daylight performance.

In recent years, the concepts of ``diversity'' and ``inclusion'' have attracted considerable attention across a range of fields, encompassing both social and biological disciplines. To fully understand these concepts, it is critical to not only examine the number of categories but also the similarities and relationships among them. In this study, I introduce a novel index for diversity and inclusion that considers similarities and network connections. I analyzed the properties of these indices and investigated their mathematical relationships using established measures of diversity and networks. Moreover, I developed a methodology for estimating similarities based on the utility of diversity. I also created a method for visualizing proportions, similarities, and network connections. Finally, I evaluated the correlation with external metrics using real-world data, confirming that both the proposed indices and our index can be effectively utilized. This study contributes to a more nuanced understanding of diversity and inclusion analysis.

Future multi-spacecraft missions require robust autonomous trajectory optimization capabilities to ensure safe and efficient rendezvous operations. This capability hinges on solving non-convex optimal control problems in real time, although traditional iterative methods such as sequential convex programming impose significant computational challenges. To mitigate this burden, the Autonomous Rendezvous Transformer introduced a generative model trained to provide near-optimal initial guesses. This approach provides convergence to better local optima (e.g., fuel optimality), improves feasibility rates, and results in faster convergence speed of optimization algorithms through warm-starting. This work extends the capabilities of ART to address robust chance-constrained optimal control problems. Specifically, ART is applied to challenging rendezvous scenarios in Low Earth Orbit (LEO), ensuring fault-tolerant behavior under uncertainty. Through extensive experimentation, the proposed warm-starting strategy is shown to consistently produce high-quality reference trajectories, achieving up to 30% cost improvement and 50% reduction in infeasible cases compared to conventional methods, demonstrating robust performance across multiple state representations. Additionally, a post hoc evaluation framework is proposed to assess the quality of generated trajectories and mitigate runtime failures, marking an initial step toward the reliable deployment of AI-driven solutions in safety-critical autonomous systems such as spacecraft.

Modern-world robotics involves complex environments where multiple autonomous agents must interact with each other and other humans. This necessitates advanced interactive multi-agent motion planning techniques. Generalized Nash equilibrium(GNE), a solution concept in constrained game theory, provides a mathematical model to predict the outcome of interactive motion planning, where each agent needs to account for other agents in the environment. However, in practice, multiple local GNEs may exist. Finding a single GNE itself is complex as it requires solving coupled constrained optimal control problems. Furthermore, finding all such local GNEs requires exploring the solution space of GNEs, which is a challenging task. This work proposes the MultiNash-PF framework to efficiently compute multiple local GNEs in constrained trajectory games. Potential games are a class of games for which a local GNE of a trajectory game can be found by solving a single constrained optimal control problem. We propose MultiNash-PF that integrates the potential game approach with implicit particle filtering, a sample-efficient method for non-convex trajectory optimization. We first formulate the underlying game as a constrained potential game and then utilize the implicit particle filtering to identify the coarse estimates of multiple local minimizers of the game's potential function. MultiNash-PF then refines these estimates with optimization solvers, obtaining different local GNEs. We show through numerical simulations that MultiNash-PF reduces computation time by up to 50\% compared to a baseline approach.

When working around humans, it is important to model their perception limitations in order to predict their behavior more accurately. In this work, we consider agents with a limited field of view, viewing range, and ability to miss objects within viewing range (e.g., transparency). By considering the observation model independently from the motion policy, we can better predict the agent's behavior by considering these limitations and approximating them. We perform a user study where human operators navigate a cluttered scene while scanning the region for obstacles with a limited field of view and range. Using imitation learning, we show that a robot can adopt a human's strategy for observing an environment with limitations on observation and navigate with minimal collision with dynamic and static obstacles. We also show that this learned model helps it successfully navigate a physical hardware vehicle in real time.

Federated learning has emerged in the last decade as a distributed optimization paradigm due to the rapidly increasing number of portable devices able to support the heavy computational needs related to the training of machine learning models. Federated learning utilizes gradient-based optimization to minimize a loss objective shared across participating agents. To the best of our knowledge, the literature mostly lacks elegant solutions that naturally harness the reciprocal statistical similarity between clients to redesign the optimization procedure. To address this gap, by conceiving the federated network as a similarity graph, we propose a novel modified framework wherein each client locally performs a perturbed gradient step leveraging prior information about other statistically affine clients. We theoretically prove that our procedure, due to a suitably introduced adaptation in the update rule, achieves a quantifiable speedup concerning the exponential contraction factor in the strongly convex case compared with popular algorithms FedAvg and FedProx, here analyzed as baselines. Lastly, we legitimize our conclusions through experimental results on the CIFAR10 and FEMNIST datasets, where we show that our algorithm speeds convergence up to a margin of 30 global rounds compared with FedAvg while modestly improving generalization on unseen data in heterogeneous settings.

The real-world effectiveness of deep neural networks often depends on their latency, thereby necessitating optimization techniques that can reduce a model's inference time while preserving its performance. One popular approach is to sequentially rewrite the input computation graph into an equivalent but faster one by replacing individual subgraphs. This approach gives rise to the so-called phase-ordering problem in which the application of one rewrite rule can eliminate the possibility to apply an even better one later on. Recent work has shown that equality saturation, a technique from compiler optimization, can mitigate this issue by first building an intermediate representation (IR) that efficiently stores multiple optimized versions of the input program before extracting the best solution in a second step. In practice, however, memory constraints prevent the IR from capturing all optimized versions and thus reintroduce the phase-ordering problem in the construction phase. In this paper, we present a tensor graph rewriting approach that uses Monte Carlo tree search to build superior IRs by identifying the most promising rewrite rules. We also introduce a novel extraction algorithm that can provide fast and accurate runtime estimates of tensor programs represented in an IR. Our approach improves the inference speedup of neural networks by up to 11% compared to existing methods.

Object-level mapping [1, 2, 3, 4, 5, 6, 7, 8, 9] builds a 3D map of multiple object instances in a scene, which is critical for scene understanding [10] and has various applications in robotic manipulation [11], semantic navigation [12, 13] and long-term dynamic map maintenance [14]. It addresses two closely coupled tasks: 3D shape reconstruction [15, 16] and pose estimation [17]. Conventional methods [18, 19, 20] approach these tasks from a perspective of state estimation [21], solving an inverse problem where low-dimensional observations (RGB and Depth images) are used to recover high-dimensional unknown variables (3D poses and shapes) through a known observation process (e.g., projection, and differentiable rendering). However, these methods require dense observations (e.g., hundreds of views for NeRF [18]) to fully constrain the problem. In robotics or AR applications, obtaining such dense observations is challenging due to limitations in the robot's or user's observation angle and occlusions in clustered scenarios. Therefore, it is crucial to develop methods that can map from sparse (fewer than 10) or even single observations. Human vision can infer complete 3D objects from images despite occlusions by using prior knowledge of the objects, which represents the prior distributions of the shapes of specific categories, such as chairs, based on thousands of instances observed in daily life. We aim to introduce generative models [22] as providers of prior knowledge to constrain the 3D object mapping. Generative models have demonstrated impressive abilities to generate high-quality multi-modal data by learning distributions in large-scale datasets, including texts [23], images [24], videos [25], and 3D models [26, 27, 28, 29].