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Numerical solution of heterogeneous Helmholtz problems presents various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work we explore the use of a GenEO-type coarse space to build a two-level additive Schwarz method applicable to highly indefinite Helmholtz problems. Through a range of numerical tests on a 2D model problem, discretised by finite elements on pollution-free meshes, we observe robust convergence, iteration counts that do not increase with the wave number, and good scalability of our approach. We further provide results showing a favourable comparison with the DtN coarse space. Our numerical study shows promise that our solver methodology can be effective for challenging heterogeneous applications.

Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fern\'andez-Duque that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he provided a complete axiomatisation in an extended language. In this paper, we consider dynamic topological logic over scattered spaces, which are topological spaces where every nonempty subspace has an isolated point. Scattered spaces appear in the context of computational logic as they provide semantics for provability and enjoy definable fixed points. We exhibit the first sound and complete dynamic topological logic in the original trimodal language. In particular, we show that the version of $\mathbf{DTL}$ based on the class of scattered spaces is finitely axiomatisable over the original language, and that the natural axiomatisation is sound and complete.

Federated learning (FL) has been recognized as a viable distributed learning paradigm which trains a machine learning model collaboratively with massive mobile devices in the wireless edge while protecting user privacy. Although various communication schemes have been proposed to expedite the FL process, most of them have assumed ideal wireless channels which provide reliable and lossless communication links between the server and mobile clients. Unfortunately, in practical systems with limited radio resources such as constraint on the training latency and constraints on the transmission power and bandwidth, transmission of a large number of model parameters inevitably suffers from quantization errors (QE) and transmission outage (TO). In this paper, we consider such non-ideal wireless channels, and carry out the first analysis showing that the FL convergence can be severely jeopardized by TO and QE, but intriguingly can be alleviated if the clients have uniform outage probabilities. These insightful results motivate us to propose a robust FL scheme, named FedTOE, which performs joint allocation of wireless resources and quantization bits across the clients to minimize the QE while making the clients have the same TO probability. Extensive experimental results are presented to show the superior performance of FedTOE for deep learning-based classification tasks with transmission latency constraints.

Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by extending a minimal modal base logic of static functional dependencies. We define a logic for dynamical systems with single time steps, provide a complete axiomatic proof calculus, and show the decidability of the satisfiability problem for a substantial fragment. The system comes in two guises: modal and first-order, that naturally complement each other. Next, we consider a timed semantics for our logic, as an intermediate between state spaces and temporal universes for the unfoldings of a dynamical system. We prove completeness and decidability by combining techniques from dynamic-epistemic logic and modal logic of functional dependencies with complex terms for objects. Also, we extend these results to the timed logic with functional symbols and term identity. Finally, we conclude with a brief outlook on how the system proposed here connects with richer temporal logics of system behavior, and with dynamic topological logic.

Federated Learning has promised a new approach to resolve the challenges in machine learning by bringing computation to the data. The popularity of the approach has led to rapid progress in the algorithmic aspects and the emergence of systems capable of simulating Federated Learning. State of art systems in Federated Learning support a single node aggregator that is insufficient to train a large corpus of devices or train larger-sized models. As the model size or the number of devices increase the single node aggregator incurs memory and computation burden while performing fusion tasks. It also faces communication bottlenecks when a large number of model updates are sent to a single node. We classify the workload for the aggregator into categories and propose a new aggregation service for handling each load. Our aggregation service is based on a holistic approach that chooses the best solution depending on the model update size and the number of clients. Our system provides a fault-tolerant, robust and efficient aggregation solution utilizing existing parallel and distributed frameworks. Through evaluation, we show the shortcomings of the state of art approaches and how a single solution is not suitable for all aggregation requirements. We also provide a comparison of current frameworks with our system through extensive experiments.

Human-AI co-creativity involves both humans and AI collaborating on a shared creative product as partners. In a creative collaboration, interaction dynamics, such as turn-taking, contribution type, and communication, are the driving forces of the co-creative process. Therefore the interaction model is a critical and essential component for effective co-creative systems. There is relatively little research about interaction design in the co-creativity field, which is reflected in a lack of focus on interaction design in many existing co-creative systems. The primary focus of co-creativity research has been on the abilities of the AI. This paper focuses on the importance of interaction design in co-creative systems with the development of the Co-Creative Framework for Interaction design (COFI) that describes the broad scope of possibilities for interaction design in co-creative systems. Researchers can use COFI for modeling interaction in co-creative systems by exploring alternatives in this design space of interaction. COFI can also be beneficial while investigating and interpreting the interaction design of existing co-creative systems. We coded a dataset of existing 92 co-creative systems using COFI and analyzed the data to show how COFI provides a basis to categorize the interaction models of existing co-creative systems. We identify opportunities to shift the focus of interaction models in co-creativity to enable more communication between the user and AI leading to human-AI partnerships.

The fruits of science are relationships made comprehensible, often by way of approximation. While deep learning is an extremely powerful way to find relationships in data, its use in science has been hindered by the difficulty of understanding the learned relationships. The Information Bottleneck (IB) is an information theoretic framework for understanding a relationship between an input and an output in terms of a trade-off between the fidelity and complexity of approximations to the relationship. Here we show that a crucial modification -- distributing bottlenecks across multiple components of the input -- opens fundamentally new avenues for interpretable deep learning in science. The Distributed Information Bottleneck throttles the downstream complexity of interactions between the components of the input, deconstructing a relationship into meaningful approximations found through deep learning without requiring custom-made datasets or neural network architectures. Applied to a complex system, the approximations illuminate aspects of the system's nature by restricting -- and monitoring -- the information about different components incorporated into the approximation. We demonstrate the Distributed IB's explanatory utility in systems drawn from applied mathematics and condensed matter physics. In the former, we deconstruct a Boolean circuit into approximations that isolate the most informative subsets of input components without requiring exhaustive search. In the latter, we localize information about future plastic rearrangement in the static structure of a sheared glass, and find the information to be more or less diffuse depending on the system's preparation. By way of a principled scheme of approximations, the Distributed IB brings much-needed interpretability to deep learning and enables unprecedented analysis of information flow through a system.

Tensor PCA is a stylized statistical inference problem introduced by Montanari and Richard to study the computational difficulty of estimating an unknown parameter from higher-order moment tensors. Unlike its matrix counterpart, Tensor PCA exhibits a statistical-computational gap, i.e., a sample size regime where the problem is information-theoretically solvable but conjectured to be computationally hard. This paper derives computational lower bounds on the run-time of memory bounded algorithms for Tensor PCA using communication complexity. These lower bounds specify a trade-off among the number of passes through the data sample, the sample size, and the memory required by any algorithm that successfully solves Tensor PCA. While the lower bounds do not rule out polynomial-time algorithms, they do imply that many commonly-used algorithms, such as gradient descent and power method, must have a higher iteration count when the sample size is not large enough. Similar lower bounds are obtained for Non-Gaussian Component Analysis, a family of statistical estimation problems in which low-order moment tensors carry no information about the unknown parameter. Finally, stronger lower bounds are obtained for an asymmetric variant of Tensor PCA and related statistical estimation problems. These results explain why many estimators for these problems use a memory state that is significantly larger than the effective dimensionality of the parameter of interest.

We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework. We show the t-SVD is a specialization of the well-studied block-term decomposition for third-order tensors, and we present an algorithm under this model that can track changing free submodules from incomplete streaming 2-D data. The proposed algorithm uses principles from incremental gradient descent on the Grassmann manifold of subspaces to solve the tensor completion problem with linear complexity and constant memory in the number of time samples. We provide a local expected linear convergence result for our algorithm. Our empirical results are competitive in accuracy but much faster in compute time than state-of-the-art tensor completion algorithms on real applications to recover temporal chemo-sensing and MRI data under limited sampling.