由于管理部分微分方程的半差异，例如通过有限元方法。这些系统的复杂性提出了直接应用自动控制的计算挑战。虽然模型还原已在控制中看到无处不在的应用，但在这种情况下使用非线性模型还原方法仍然很困难。问题在于在降低的订单模型中保留非线性动力学的结构，以进行高保真控制。在这项工作中，我们利用光谱亚曼佛（SSM）理论的最新进展来使模型在明确的假设下降低，以有效地合成反馈控制器。

由于其固有的非线性和高度的自由度，对连续体软机器人的建模和控制仍然是一项艰巨的任务。这些复杂性阻碍了适合实时控制的高保真模型的构建。尽管已经提出了各种模型和基于学习的方法来应对这些挑战，但它们缺乏普遍性，很少保留动态的结构。在这项工作中，我们提出了一种新的，数据驱动的方法，用于从数据中提取面向控制的模型。我们克服了上面概述的问题，并证明了我们对光谱次级减少（SSMR）的卓越性能 - \'a-vis the Art的状态。

我们开发一种方法来构造来自表示基本上非线性（或不可连锁的）动态系统的数据集构成低维预测模型，其中具有由有限许多频率的外部强制进行外部矫正的双曲线线性部分。我们的数据驱动，稀疏，非线性模型获得为低维，吸引动力系统的光谱子纤维（SSM）的降低的动态的延长正常形式。我们说明了数据驱动的SSM降低了高维数值数据集的功率和涉及梁振荡，涡旋脱落和水箱中的晃动的实验测量。我们发现，在未加工的数据上培训的SSM减少也在额外的外部强制下准确预测非线性响应。

Existing automated techniques for software documentation typically attempt to reason between two main sources of information: code and natural language. However, this reasoning process is often complicated by the lexical gap between more abstract natural language and more structured programming languages. One potential bridge for this gap is the Graphical User Interface (GUI), as GUIs inherently encode salient information about underlying program functionality into rich, pixel-based data representations. This paper offers one of the first comprehensive empirical investigations into the connection between GUIs and functional, natural language descriptions of software. First, we collect, analyze, and open source a large dataset of functional GUI descriptions consisting of 45,998 descriptions for 10,204 screenshots from popular Android applications. The descriptions were obtained from human labelers and underwent several quality control mechanisms. To gain insight into the representational potential of GUIs, we investigate the ability of four Neural Image Captioning models to predict natural language descriptions of varying granularity when provided a screenshot as input. We evaluate these models quantitatively, using common machine translation metrics, and qualitatively through a large-scale user study. Finally, we offer learned lessons and a discussion of the potential shown by multimodal models to enhance future techniques for automated software documentation.

View-dependent effects such as reflections pose a substantial challenge for image-based and neural rendering algorithms. Above all, curved reflectors are particularly hard, as they lead to highly non-linear reflection flows as the camera moves. We introduce a new point-based representation to compute Neural Point Catacaustics allowing novel-view synthesis of scenes with curved reflectors, from a set of casually-captured input photos. At the core of our method is a neural warp field that models catacaustic trajectories of reflections, so complex specular effects can be rendered using efficient point splatting in conjunction with a neural renderer. One of our key contributions is the explicit representation of reflections with a reflection point cloud which is displaced by the neural warp field, and a primary point cloud which is optimized to represent the rest of the scene. After a short manual annotation step, our approach allows interactive high-quality renderings of novel views with accurate reflection flow. Additionally, the explicit representation of reflection flow supports several forms of scene manipulation in captured scenes, such as reflection editing, cloning of specular objects, reflection tracking across views, and comfortable stereo viewing. We provide the source code and other supplemental material on https://repo-sam.inria.fr/ fungraph/neural_catacaustics/

In large-scale machine learning, recent works have studied the effects of compressing gradients in stochastic optimization in order to alleviate the communication bottleneck. These works have collectively revealed that stochastic gradient descent (SGD) is robust to structured perturbations such as quantization, sparsification, and delays. Perhaps surprisingly, despite the surge of interest in large-scale, multi-agent reinforcement learning, almost nothing is known about the analogous question: Are common reinforcement learning (RL) algorithms also robust to similar perturbations? In this paper, we investigate this question by studying a variant of the classical temporal difference (TD) learning algorithm with a perturbed update direction, where a general compression operator is used to model the perturbation. Our main technical contribution is to show that compressed TD algorithms, coupled with an error-feedback mechanism used widely in optimization, exhibit the same non-asymptotic theoretical guarantees as their SGD counterparts. We then extend our results significantly to nonlinear stochastic approximation algorithms and multi-agent settings. In particular, we prove that for multi-agent TD learning, one can achieve linear convergence speedups in the number of agents while communicating just $\tilde{O}(1)$ bits per agent at each time step. Our work is the first to provide finite-time results in RL that account for general compression operators and error-feedback in tandem with linear function approximation and Markovian sampling. Our analysis hinges on studying the drift of a novel Lyapunov function that captures the dynamics of a memory variable introduced by error feedback.

In robust Markov decision processes (MDPs), the uncertainty in the transition kernel is addressed by finding a policy that optimizes the worst-case performance over an uncertainty set of MDPs. While much of the literature has focused on discounted MDPs, robust average-reward MDPs remain largely unexplored. In this paper, we focus on robust average-reward MDPs, where the goal is to find a policy that optimizes the worst-case average reward over an uncertainty set. We first take an approach that approximates average-reward MDPs using discounted MDPs. We prove that the robust discounted value function converges to the robust average-reward as the discount factor $\gamma$ goes to $1$, and moreover, when $\gamma$ is large, any optimal policy of the robust discounted MDP is also an optimal policy of the robust average-reward. We further design a robust dynamic programming approach, and theoretically characterize its convergence to the optimum. Then, we investigate robust average-reward MDPs directly without using discounted MDPs as an intermediate step. We derive the robust Bellman equation for robust average-reward MDPs, prove that the optimal policy can be derived from its solution, and further design a robust relative value iteration algorithm that provably finds its solution, or equivalently, the optimal robust policy.

The automated segmentation and tracking of macrophages during their migration are challenging tasks due to their dynamically changing shapes and motions. This paper proposes a new algorithm to achieve automatic cell tracking in time-lapse microscopy macrophage data. First, we design a segmentation method employing space-time filtering, local Otsu's thresholding, and the SUBSURF (subjective surface segmentation) method. Next, the partial trajectories for cells overlapping in the temporal direction are extracted in the segmented images. Finally, the extracted trajectories are linked by considering their direction of movement. The segmented images and the obtained trajectories from the proposed method are compared with those of the semi-automatic segmentation and manual tracking. The proposed tracking achieved 97.4% of accuracy for macrophage data under challenging situations, feeble fluorescent intensity, irregular shapes, and motion of macrophages. We expect that the automatically extracted trajectories of macrophages can provide pieces of evidence of how macrophages migrate depending on their polarization modes in the situation, such as during wound healing.

Advances in reinforcement learning have led to its successful application in complex tasks with continuous state and action spaces. Despite these advances in practice, most theoretical work pertains to finite state and action spaces. We propose building a theoretical understanding of continuous state and action spaces by employing a geometric lens. Central to our work is the idea that the transition dynamics induce a low dimensional manifold of reachable states embedded in the high-dimensional nominal state space. We prove that, under certain conditions, the dimensionality of this manifold is at most the dimensionality of the action space plus one. This is the first result of its kind, linking the geometry of the state space to the dimensionality of the action space. We empirically corroborate this upper bound for four MuJoCo environments. We further demonstrate the applicability of our result by learning a policy in this low dimensional representation. To do so we introduce an algorithm that learns a mapping to a low dimensional representation, as a narrow hidden layer of a deep neural network, in tandem with the policy using DDPG. Our experiments show that a policy learnt this way perform on par or better for four MuJoCo control suite tasks.

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.