We present the design and experimental results of the first 1-DOF, hip-actuated bipedal robot. While passive dynamic walking is simple by nature, many existing bipeds inspired by this form of walking are complex in control, mechanical design, or both. Our design using only two rigid bodies connected by a single motor aims to enable exploration of walking at smaller sizes where more complex designs cannot be constructed. The walker, "Mugatu", is self-contained and autonomous, open-loop stable over a range of input parameters, able to stop and start from standing, and able to control its heading left and right. We analyze the mechanical design and distill down a set of design rules that enable these behaviors. Experimental evaluations measure speed, energy consumption, and steering.

During in-hand manipulation, robots must be able to continuously estimate the pose of the object in order to generate appropriate control actions. The performance of algorithms for pose estimation hinges on the robot's sensors being able to detect discriminative geometric object features, but previous sensing modalities are unable to make such measurements robustly. The robot's fingers can occlude the view of environment- or robot-mounted image sensors, and tactile sensors can only measure at the local areas of contact. Motivated by fingertip-embedded proximity sensors' robustness to occlusion and ability to measure beyond the local areas of contact, we present the first evaluation of proximity sensor based pose estimation for in-hand manipulation. We develop a novel two-fingered hand with fingertip-embedded optical time-of-flight proximity sensors as a testbed for pose estimation during planar in-hand manipulation. Here, the in-hand manipulation task consists of the robot moving a cylindrical object from one end of its workspace to the other. We demonstrate, with statistical significance, that proximity-sensor based pose estimation via particle filtering during in-hand manipulation: a) exhibits 50% lower average pose error than a tactile-sensor based baseline; b) empowers a model predictive controller to achieve 30% lower final positioning error compared to when using tactile-sensor based pose estimates.

Support vector machine (SVM) is one of the most studied paradigms in the realm of machine learning for classification and regression problems. It relies on vectorized input data. However, a significant portion of the real-world data exists in matrix format, which is given as input to SVM by reshaping the matrices into vectors. The process of reshaping disrupts the spatial correlations inherent in the matrix data. Also, converting matrices into vectors results in input data with a high dimensionality, which introduces significant computational complexity. To overcome these issues in classifying matrix input data, support matrix machine (SMM) is proposed. It represents one of the emerging methodologies tailored for handling matrix input data. The SMM method preserves the structural information of the matrix data by using the spectral elastic net property which is a combination of the nuclear norm and Frobenius norm. This article provides the first in-depth analysis of the development of the SMM model, which can be used as a thorough summary by both novices and experts. We discuss numerous SMM variants, such as robust, sparse, class imbalance, and multi-class classification models. We also analyze the applications of the SMM model and conclude the article by outlining potential future research avenues and possibilities that may motivate academics to advance the SMM algorithm.

Tensor decomposition is an important tool for multiway data analysis. In practice, the data is often sparse yet associated with rich temporal information. Existing methods, however, often under-use the time information and ignore the structural knowledge within the sparsely observed tensor entries. To overcome these limitations and to better capture the underlying temporal structure, we propose Dynamic EMbedIngs fOr dynamic Tensor dEcomposition (DEMOTE). We develop a neural diffusion-reaction process to estimate dynamic embeddings for the entities in each tensor mode. Specifically, based on the observed tensor entries, we build a multi-partite graph to encode the correlation between the entities. We construct a graph diffusion process to co-evolve the embedding trajectories of the correlated entities and use a neural network to construct a reaction process for each individual entity. In this way, our model can capture both the commonalities and personalities during the evolution of the embeddings for different entities. We then use a neural network to model the entry value as a nonlinear function of the embedding trajectories. For model estimation, we combine ODE solvers to develop a stochastic mini-batch learning algorithm. We propose a stratified sampling method to balance the cost of processing each mini-batch so as to improve the overall efficiency. We show the advantage of our approach in both simulation study and real-world applications. The code is available at https://github.com/wzhut/Dynamic-Tensor-Decomposition-via-Neural-Diffusion-Reaction-Processes.

Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is based on the transport map induced by an optimal one-dimensional projection of the two input distributions. We draw connections between min-SWGG and Wasserstein generalized geodesics in which the pivot measure is supported on a line. We notably provide a new closed form for the exact Wasserstein distance in the particular case of one of the distributions supported on a line allowing us to derive a fast computational scheme that is amenable to gradient descent optimization. We show that min-SWGG is an upper bound of WD and that it has a complexity similar to as Sliced-Wasserstein, with the additional feature of providing an associated transport plan. We also investigate some theoretical properties such as metricity, weak convergence, computational and topological properties. Empirical evidences support the benefits of min-SWGG in various contexts, from gradient flows, shape matching and image colorization, among others.

Complex-valued neural networks (CVNNs) have recently shown promising empirical success, for instance for increasing the stability of recurrent neural networks and for improving the performance in tasks with complex-valued inputs, such as in MRI fingerprinting. While the overwhelming success of Deep Learning in the real-valued case is supported by a growing mathematical foundation, such a foundation is still largely lacking in the complex-valued case. We thus analyze the expressivity of CVNNs by studying their approximation properties. Our results yield the first quantitative approximation bounds for CVNNs that apply to a wide class of activation functions including the popular modReLU and complex cardioid activation functions. Precisely, our results apply to any activation function that is smooth but not polyharmonic on some non-empty open set; this is the natural generalization of the class of smooth and non-polynomial activation functions to the complex setting. Our main result shows that the error for the approximation of $C^k$-functions scales as $m^{-k/(2n)}$ for $m \to \infty$ where $m$ is the number of neurons, $k$ the smoothness of the target function and $n$ is the (complex) input dimension. Under a natural continuity assumption, we show that this rate is optimal; we further discuss the optimality when dropping this assumption. Moreover, we prove that the problem of approximating $C^k$-functions using continuous approximation methods unavoidably suffers from the curse of dimensionality.

We introduce a method for inferring an explicit PDE from a data sample generated by previously unseen dynamics, based on a learned context. The training phase integrates knowledge of the form of the equation with a differential scheme, while the inference phase yields a PDE that fits the data sample and enables both signal prediction and data explanation. We include results of extensive experimentation, comparing our method to SOTA approaches, together with ablation studies that examine different flavors of our solution in terms of prediction error and explainability. Many scientific fields use the language of Partial Differential Equations (PDEs; Evans, 2010) to describe the physical laws governing observed natural phenomena with spatio-temporal dynamics. Typically, a PDE system is derived from first principles and a mechanistic understanding of the problem after experimentation and data collection by domain experts of the field. Well-known examples for such systems include Navier-Stokes and Burgers' equations in fluid dynamics, Maxwell's equations for electromagnetic theory, and Schrödinger's equations for quantum mechanics. Solving a PDE model could provide users with crucial information on how a signal evolves over time and space, and could be used for both prediction and control tasks. While creating PDE-based models holds great value, it is still a difficult task in many cases. For many complex real-world phenomena, we might only know some of the dynamics of the system. For example, an expert might tell us that a heat equation PDE has a specific functional form but we do not know the values of the diffusion and drift coefficient functions.

Russia said Ukrainian drones damaged a nuclear waste storage facility at the Kursk Nuclear Power Plant on Thursday evening. This comes after the press service for the plant told journalists on Friday that there had been no significant damage from the attacks and that operations were continuing as normal. Intense fighting continued close to the city of Avdiivka, in the Donetsk region of eastern Ukraine. Russia's Ministry of Defence said its air defence systems destroyed 36 Ukraine-launched drones over the Black Sea off the Crimean Peninsula overnight. A statement from the ministry on Telegram did not provide much additional detail.

Learning from Demonstration (LfD) [1, 2] is a set of supervised learning methods where a teacher (often, but not always, a human) demonstrates a task, and a student (usually a robot) uses this information to learn to perform the same task. Some LfD methods cope with small morphological mismatches between the teacher and student [3, 4] (e.g., five-fingered hand to two-fingered gripper). However, they typically fail for a large mismatch (e.g., bimanual human demonstration to a robot arm with one gripper). The key difference is that to reproduce the transition from a demonstration state to the next, no single student action suffices - a sequence of actions may be needed. Supervised methods are appealing where demonstration-free methods [5] do not converge or underperform [6] and purely analytical approaches are computationally infeasible [7, 8]. In such settings, human demonstrations of complex tasks are often readily available e.g., it is straightforward for a human to show a robot how to fold a cloth. An LfD-based imitation learning approach is appealing in such settings provided we allow the human demonstrator to use their body in the way they find most convenient (e.g., using two hands to hang a cloth on a clothesline to dry). This requirement induces a potentially large morphology mismatch - we want to learn and execute complex tasks with deformable objects on a single manipulator robot using natural human demonstrations. We propose a framework, Morphological Adaptation in Imitation Learning (MAIL), to bridge this mismatch.

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is being iteratively aggregated to central nodes from their neighbourhood. Such a scheme has been found to be intrinsically linked to a physical process known as heat diffusion, where the propagation of GNNs naturally corresponds to the evolution of heat density. Analogizing the process of message passing to the heat dynamics allows to fundamentally understand the power and pitfalls of GNNs and consequently informs better model design. Recently, there emerges a plethora of works that proposes GNNs inspired from the continuous dynamics formulation, in an attempt to mitigate the known limitations of GNNs, such as oversmoothing and oversquashing. In this survey, we provide the first systematic and comprehensive review of studies that leverage the continuous perspective of GNNs. To this end, we introduce foundational ingredients for adapting continuous dynamics to GNNs, along with a general framework for the design of graph neural dynamics. We then review and categorize existing works based on their driven mechanisms and underlying dynamics. We also summarize how the limitations of classic GNNs can be addressed under the continuous framework. We conclude by identifying multiple open research directions.