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Mixture of experts (MoE) model is a statistical machine learning design that aggregates multiple expert networks using a softmax gating function in order to form a more intricate and expressive model. Despite being commonly used in several applications owing to their scalability, the mathematical and statistical properties of MoE models are complex and difficult to analyze. As a result, previous theoretical works have primarily focused on probabilistic MoE models by imposing the impractical assumption that the data are generated from a Gaussian MoE model. In this work, we investigate the performance of the least squares estimators (LSE) under a deterministic MoE model where the data are sampled according to a regression model, a setting that has remained largely unexplored. We establish a condition called strong identifiability to characterize the convergence behavior of various types of expert functions. We demonstrate that the rates for estimating strongly identifiable experts, namely the widely used feed-forward networks with activation functions $\mathrm{sigmoid}(\cdot)$ and $\tanh(\cdot)$, are substantially faster than those of polynomial experts, which we show to exhibit a surprising slow estimation rate. Our findings have important practical implications for expert selection.

In recent years, the integration of large language models (LLMs) has revolutionized the field of robotics, enabling robots to communicate, understand, and reason with human-like proficiency. This paper explores the multifaceted impact of LLMs on robotics, addressing key challenges and opportunities for leveraging these models across various domains. By categorizing and analyzing LLM applications within core robotics elements -- communication, perception, planning, and control -- we aim to provide actionable insights for researchers seeking to integrate LLMs into their robotic systems. Our investigation focuses on LLMs developed post-GPT-3.5, primarily in text-based modalities while also considering multimodal approaches for perception and control. We offer comprehensive guidelines and examples for prompt engineering, facilitating beginners' access to LLM-based robotics solutions. Through tutorial-level examples and structured prompt construction, we illustrate how LLM-guided enhancements can be seamlessly integrated into robotics applications. This survey serves as a roadmap for researchers navigating the evolving landscape of LLM-driven robotics, offering a comprehensive overview and practical guidance for harnessing the power of language models in robotics development.

Machine learning (ML) models, demonstrably powerful, suffer from a lack of interpretability. The absence of transparency, often referred to as the black box nature of ML models, undermines trust and urges the need for efforts to enhance their explainability. Explainable AI (XAI) techniques address this challenge by providing frameworks and methods to explain the internal decision-making processes of these complex models. Techniques like Counterfactual Explanations (CF) and Feature Importance play a crucial role in achieving this goal. Furthermore, high-quality and diverse data remains the foundational element for robust and trustworthy ML applications. In many applications, the data used to train ML and XAI explainers contain sensitive information. In this context, numerous privacy-preserving techniques can be employed to safeguard sensitive information in the data, such as differential privacy. Subsequently, a conflict between XAI and privacy solutions emerges due to their opposing goals. Since XAI techniques provide reasoning for the model behavior, they reveal information relative to ML models, such as their decision boundaries, the values of features, or the gradients of deep learning models when explanations are exposed to a third entity. Attackers can initiate privacy breaching attacks using these explanations, to perform model extraction, inference, and membership attacks. This dilemma underscores the challenge of finding the right equilibrium between understanding ML decision-making and safeguarding privacy.

When deployed in the world, a learning agent such as a recommender system or a chatbot often repeatedly interacts with another learning agent (such as a user) over time. In many such two-agent systems, each agent learns separately and the rewards of the two agents are not perfectly aligned. To better understand such cases, we examine the learning dynamics of the two-agent system and the implications for each agent's objective. We model these systems as Stackelberg games with decentralized learning and show that standard regret benchmarks (such as Stackelberg equilibrium payoffs) result in worst-case linear regret for at least one player. To better capture these systems, we construct a relaxed regret benchmark that is tolerant to small learning errors by agents. We show that standard learning algorithms fail to provide sublinear regret, and we develop algorithms to achieve near-optimal $O(T^{2/3})$ regret for both players with respect to these benchmarks. We further design relaxed environments under which faster learning ($O(\sqrt{T})$) is possible. Altogether, our results take a step towards assessing how two-agent interactions in sequential and decentralized learning environments affect the utility of both agents.

In supervised learning, understanding an input's proximity to the training data can help a model decide whether it has sufficient evidence for reaching a reliable prediction. While powerful probabilistic models such as Gaussian Processes naturally have this property, deep neural networks often lack it. In this paper, we introduce Distance Aware Bottleneck (DAB), i.e., a new method for enriching deep neural networks with this property. Building on prior information bottleneck approaches, our method learns a codebook that stores a compressed representation of all inputs seen during training. The distance of a new example from this codebook can serve as an uncertainty estimate for the example. The resulting model is simple to train and provides deterministic uncertainty estimates by a single forward pass. Finally, our method achieves better out-of-distribution (OOD) detection and misclassification prediction than prior methods, including expensive ensemble methods, deep kernel Gaussian Processes, and approaches based on the standard information bottleneck.

The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of original causal concepts and theories to such complex, non-statistical data has been met with serious challenges. In response, our study proposes redefinitions of causal data into three distinct categories from the standpoint of causal structure and representation: definite data, semi-definite data, and indefinite data. Definite data chiefly pertains to statistical data used in conventional causal scenarios, while semi-definite data refers to a spectrum of data formats germane to deep learning, including time-series, images, text, and others. Indefinite data is an emergent research sphere inferred from the progression of data forms by us. To comprehensively present these three data paradigms, we elaborate on their formal definitions, differences manifested in datasets, resolution pathways, and development of research. We summarize key tasks and achievements pertaining to definite and semi-definite data from myriad research undertakings, present a roadmap for indefinite data, beginning with its current research conundrums. Lastly, we classify and scrutinize the key datasets presently utilized within these three paradigms.

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

In contrast to batch learning where all training data is available at once, continual learning represents a family of methods that accumulate knowledge and learn continuously with data available in sequential order. Similar to the human learning process with the ability of learning, fusing, and accumulating new knowledge coming at different time steps, continual learning is considered to have high practical significance. Hence, continual learning has been studied in various artificial intelligence tasks. In this paper, we present a comprehensive review of the recent progress of continual learning in computer vision. In particular, the works are grouped by their representative techniques, including regularization, knowledge distillation, memory, generative replay, parameter isolation, and a combination of the above techniques. For each category of these techniques, both its characteristics and applications in computer vision are presented. At the end of this overview, several subareas, where continuous knowledge accumulation is potentially helpful while continual learning has not been well studied, are discussed.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.