When Pam Cronrath's husband Bill died last year, after nearly 60 years of marriage, she knew what she wanted to do, but not exactly how. I promised him a super wake, she told the BBC. What she didn't expect was that keeping the promise would lead her into the world of holograms, technology more commonly associated with celebrities than memorial services in rural America. A self-confessed tech enthusiast, she says her outlook was shaped by a career that stretched back to the early days of the internet. Several years ago, while speaking at a medical conference, she watched a doctor appear as a full-body hologram broadcast live across the United States.

We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this open-ended remit, we argue that two types of stability in the spatio-temporal positioning of nodes are desirable: to assign the same position, up to noise, to nodes behaving similarly at a given time (cross-sectional stability) and a constant position, up to noise, to a single node behaving similarly across different times (longitudinal stability). Similarity in behaviour is defined formally using notions of exchangeability under a dynamic latent position network model. By showing how this model can be recast as a multilayer random dot product graph, we demonstrate that unfolded adjacency spectral embedding satisfies both stability conditions. We also show how two alternative methods, omnibus and independent spectral embedding, alternately lack one or the other form of stability.

In this paper, we propose a practical online method for solving a class of distributionally robust optimization (DRO) with non-convex objectives, which has important applications in machine learning for improving the robustness of neural networks. In the literature, most methods for solving DRO are based on stochastic primal-dual methods. However, primal-dual methods for DRO suffer from several drawbacks: (1) manipulating a high-dimensional dual variable corresponding to the size of data is time expensive; (2) they are not friendly to online learning where data is coming sequentially. To address these issues, we consider a class of DRO with an KL divergence regularization on the dual variables, transform the minmax problem into a compositional minimization problem, and propose practical duality-free online stochastic methods without requiring a large mini-batch size. We establish the state-of-the-art complexities of the proposed methods with and without a Polyak-Łojasiewicz (PL) condition of the objective. Empirical studies on large-scale deep learning tasks (i) demonstrate that our method can speed up the training by more than 2 times than baseline methods and save days of training time on a large-scale dataset with 265K images, and (ii) verify the supreme performance of DRO over Empirical Risk Minimization (ERM) on imbalanced datasets. Of independent interest, the proposed method can be also used for solving a family of stochastic compositional problems with state-of-the-art complexities.

By minimising off-target activation, Bayesian target optimisation could enable (e.g.)421 more precise synaptic connectivity mapping, improving our understanding of neural circuitry. This422 advancement has potential implications for understanding brain disorders like epilepsy, where423 abnormal synaptic connections are central to seizure generation and propagation. Deepening our424 understanding of these diseases can lead to enhanced targeted interventions and more effective425 therapeutic strategies, benefiting individuals with neurological disorders.426 First, we develop431 the approach for single optogenetic targets, as this is most closely related to existing GP-based432 receptive field inference techniques. We use a GP-Bernoulli approach to model the response ynt of436 neuron n on trial t to a single-target stimulus xt,437 ynt Bernoulli( (gn(xt))), (9) where the stimulus xt =( c1t,c2t,It) 2 R3 represents the two-dimensional coordinates and laser438 power of the t-th hologram.

As the use of large embedding models in recommendation systems and language applications increases, concerns over user data privacy have also risen. DP-SGD, a training algorithm that combines differential privacy with stochastic gradient descent, has been the workhorse in protecting user privacy without compromising model accuracy by much. However, applying DP-SGDnaively to embedding models can destroy gradient sparsity, leading to reduced training efficiency. To address this issue, we present two new algorithms, DP-FEST and DP-AdaFEST, that preserve gradient sparsity during private training of large embedding models. Our algorithms achieve substantial reductions (106) in gradient size, while maintaining comparable levels of accuracy, on benchmark real-world datasets.

Adversarial risk quantifies the performance of classifiers on adversarially perturbed data. Numerous definitions of adversarial risk--not all mathematically rigorous and differing subtly in the details--have appeared in the literature. In this paper, we revisit these definitions, make them rigorous, and critically examine their similarities and differences. Our technical tools derive from optimal transport, robust statistics, functional analysis, and game theory. Our contributions include the following: generalizing Strassen's theorem to the unbalanced optimal transport setting with applications to adversarial classification with unequal priors; showing an equivalence between adversarial robustness and robust hypothesis testing with -Wasserstein uncertainty sets; proving the existence of a pure Nash equilibrium in the two-player game between the adversary and the algorithm; and characterizing adversarial risk by the minimum Bayes error between a pair of distributions belonging to the -Wasserstein uncertainty sets. Our results generalize and deepen recently discovered connections between optimal transport and adversarial robustness and reveal new connections to Choquet capacities and game theory.