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We present a study on a repeated delegated choice problem, which is the first to consider an online learning variant of Kleinberg and Kleinberg, EC'18. In this model, a principal interacts repeatedly with an agent who possesses an exogenous set of solutions to search for efficient ones. Each solution can yield varying utility for both the principal and the agent, and the agent may propose a solution to maximize its own utility in a selfish manner. To mitigate this behavior, the principal announces an eligible set which screens out a certain set of solutions. The principal, however, does not have any information on the distribution of solutions in advance. Therefore, the principal dynamically announces various eligible sets to efficiently learn the distribution. The principal's objective is to minimize cumulative regret compared to the optimal eligible set in hindsight. We explore two dimensions of the problem setup, whether the agent behaves myopically or strategizes across the rounds, and whether the solutions yield deterministic or stochastic utility. Our analysis mainly characterizes some regimes under which the principal can recover the sublinear regret, thereby shedding light on the rise and fall of the repeated delegation procedure in various regimes.

We study the optimal order (or sequence) of contracting a tensor network with a minimal computational cost. We conclude 2 different versions of this optimal sequence: that minimize the operation number (OMS) and that minimize the time complexity (CMS). Existing results only shows that OMS is NP-hard, but no conclusion on CMS problem. In this work, we firstly reduce CMS to CMS-0, which is a sub-problem of CMS with no free indices. Then we prove that CMS is easier than OMS, both in general and in tree cases. Last but not least, we prove that CMS is still NP-hard. Based on our results, we have built up relationships of hardness of different tensor network contraction problems.

Concerns around future dangers from advanced AI often centre on systems hypothesised to have intrinsic characteristics such as agent-like behaviour, strategic awareness, and long-range planning. We label this cluster of characteristics as "Property X". Most present AI systems are low in "Property X"; however, in the absence of deliberate steering, current research directions may rapidly lead to the emergence of highly capable AI systems that are also high in "Property X". We argue that "Property X" characteristics are intrinsically dangerous, and when combined with greater capabilities will result in AI systems for which safety and control is difficult to guarantee. Drawing on several scholars' alternative frameworks for possible AI research trajectories, we argue that most of the proposed benefits of advanced AI can be obtained by systems designed to minimise this property. We then propose indicators and governance interventions to identify and limit the development of systems with risky "Property X" characteristics.

"Treatment-confounder feedback" is the central complication to resolve in longitudinal studies, to infer causality. The existing frameworks for identifying causal effects for longitudinal studies with discrete repeated measures hinge heavily on assuming that time advances in discrete time steps or treatment changes as a jumping process, rendering the number of "feedbacks" finite. However, medical studies nowadays with real-time monitoring involve functional time-varying outcomes, treatment, and confounders, which leads to an uncountably infinite number of feedbacks between treatment and confounders. Therefore more general and advanced theory is needed. We generalize the definition of causal effects under user-specified stochastic treatment regimes to longitudinal studies with continuous monitoring and develop an identification framework, allowing right censoring and truncation by death. We provide sufficient identification assumptions including a generalized consistency assumption, a sequential randomization assumption, a positivity assumption, and a novel "intervenable" assumption designed for the continuous-time case. Under these assumptions, we propose a g-computation process and an inverse probability weighting process, which suggest a g-computation formula and an inverse probability weighting formula for identification. For practical purposes, we also construct two classes of population estimating equations to identify these two processes, respectively, which further suggest a doubly robust identification formula with extra robustness against process misspecification. We prove that our framework fully generalize the existing frameworks and is nonparametric.

We take a random matrix theory approach to random sketching and show an asymptotic first-order equivalence of the regularized sketched pseudoinverse of a positive semidefinite matrix to a certain evaluation of the resolvent of the same matrix. We focus on real-valued regularization and extend previous results on an asymptotic equivalence of random matrices to the real setting, providing a precise characterization of the equivalence even under negative regularization, including a precise characterization of the smallest nonzero eigenvalue of the sketched matrix, which may be of independent interest. We then further characterize the second-order equivalence of the sketched pseudoinverse. We also apply our results to the analysis of the sketch-and-project method and to sketched ridge regression. Lastly, we prove that these results generalize to asymptotically free sketching matrices, obtaining the resulting equivalence for orthogonal sketching matrices and comparing our results to several common sketches used in practice.

Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information, sufficient statistics, and efficient estimators. Today, information geometry has emerged as an interdisciplinary field that finds applications in diverse areas such as radar sensing, array signal processing, quantum physics, deep learning, and optimal transport. This article presents an overview of essential information geometry to initiate an information theorist, who may be unfamiliar with this exciting area of research. We explain the concepts of divergences on statistical manifolds, generalized notions of distances, orthogonality, and geodesics, thereby paving the way for concrete applications and novel theoretical investigations. We also highlight some recent information-geometric developments, which are of interest to the broader information theory community.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.

Graphical causal inference as pioneered by Judea Pearl arose from research on artificial intelligence (AI), and for a long time had little connection to the field of machine learning. This article discusses where links have been and should be established, introducing key concepts along the way. It argues that the hard open problems of machine learning and AI are intrinsically related to causality, and explains how the field is beginning to understand them.

Attention Model has now become an important concept in neural networks that has been researched within diverse application domains. This survey provides a structured and comprehensive overview of the developments in modeling attention. In particular, we propose a taxonomy which groups existing techniques into coherent categories. We review the different neural architectures in which attention has been incorporated, and also show how attention improves interpretability of neural models. Finally, we discuss some applications in which modeling attention has a significant impact. We hope this survey will provide a succinct introduction to attention models and guide practitioners while developing approaches for their applications.