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In recent research, the parallel performances of sweeping-type algorithms for high-frequency time-harmonic wave problems have been improved by departing from standard layer-type domain decomposition and introducing a new sweeping strategy on a checkerboard-type domain decomposition, where sweeps can be performed more flexibly. These sweeps can be done by a certain number of steps, each of which provides the necessary information from subdomains solved at the current iteration to their next neighboring subdomains. Although, subproblems in these subdomains can be solved concurrently at each step, the sequential nature of the process of the sweeping approaches still exists, which limits their potential for parallelization. We propose a block Jacobi sweeping preconditioner, which is an improved variant of sweeping-type preconditioners. The new feature of these improved variants can be interpreted as several partial sweeps, which can be thought of as sweeps that operate on a subset of the subdomains in parallel. We present several two-dimensional finite element results to study and compare the sweeping preconditioner and the block Jacobi sweeping preconditioner.

Recently, the idea of using FP8 as a number format for neural network training has been floating around the deep learning world. Given that most training is currently conducted with entire networks in FP32, or sometimes FP16 with mixed-precision, the step to having some parts of a network run in FP8 with 8-bit weights is an appealing potential speed-up for the generally costly and time-intensive training procedures in deep learning. A natural question arises regarding what this development means for efficient inference on edge devices. In the efficient inference device world, workloads are frequently executed in INT8. Sometimes going even as low as INT4 when efficiency calls for it. In this whitepaper, we compare the performance for both the FP8 and INT formats for efficient on-device inference. We theoretically show the difference between the INT and FP formats for neural networks and present a plethora of post-training quantization and quantization-aware-training results to show how this theory translates to practice. We also provide a hardware analysis showing that the FP formats are somewhere between 50-180% less efficient in terms of compute in dedicated hardware than the INT format. Based on our research and a read of the research field, we conclude that although the proposed FP8 format could be good for training, the results for inference do not warrant a dedicated implementation of FP8 in favor of INT8 for efficient inference. We show that our results are mostly consistent with previous findings but that important comparisons between the formats have thus far been lacking. Finally, we discuss what happens when FP8-trained networks are converted to INT8 and conclude with a brief discussion on the most efficient way for on-device deployment and an extensive suite of INT8 results for many models.

A wireless federated learning system is investigated by allowing a server and workers to exchange uncoded information via orthogonal wireless channels. Since the workers frequently upload local gradients to the server via bandwidth-limited channels, the uplink transmission from the workers to the server becomes a communication bottleneck. Therefore, a one-shot distributed principle component analysis (PCA) is leveraged to reduce the dimension of uploaded gradients such that the communication bottleneck is relieved. A PCA-based wireless federated learning (PCA-WFL) algorithm and its accelerated version (i.e., PCA-AWFL) are proposed based on the low-dimensional gradients and the Nesterov's momentum. For the non-convex loss functions, a finite-time analysis is performed to quantify the impacts of system hyper-parameters on the convergence of the PCA-WFL and PCA-AWFL algorithms. The PCA-AWFL algorithm is theoretically certified to converge faster than the PCA-WFL algorithm. Besides, the convergence rates of PCA-WFL and PCA-AWFL algorithms quantitatively reveal the linear speedup with respect to the number of workers over the vanilla gradient descent algorithm. Numerical results are used to demonstrate the improved convergence rates of the proposed PCA-WFL and PCA-AWFL algorithms over the benchmarks.

Satellite-based Synthetic Aperture Radar (SAR) images can be used as a source of remote sensed imagery regardless of cloud cover and day-night cycle. However, the speckle noise and varying image acquisition conditions pose a challenge for change detection classifiers. This paper proposes a new method of improving SAR image processing to produce higher quality difference images for the classification algorithms. The method is built on a neural network-based mapping transformation function that produces artificial SAR images from a location in the requested acquisition conditions. The inputs for the model are: previous SAR images from the location, imaging angle information from the SAR images, digital elevation model, and weather conditions. The method was tested with data from a location in North-East Finland by using Sentinel-1 SAR images from European Space Agency, weather data from Finnish Meteorological Institute, and a digital elevation model from National Land Survey of Finland. In order to verify the method, changes to the SAR images were simulated, and the performance of the proposed method was measured using experimentation where it gave substantial improvements to performance when compared to a more conventional method of creating difference images.

We present Dojo, a differentiable physics engine for robotics that prioritizes stable simulation, accurate contact physics, and differentiability with respect to states, actions, and system parameters. Dojo achieves stable simulation at low sample rates and conserves energy and momentum by employing a variational integrator. A nonlinear complementarity problem with second-order cones for friction models hard contact, and is reliably solved using a custom primal-dual interior-point method. Special properties of the interior-point method are exploited using implicit differentiation to efficiently compute smooth gradients that provide useful information through contact events. We demonstrate Dojo with a number of examples including: planning, policy optimization, and system identification, that demonstrate the engine's unique ability to simulate hard contact while providing smooth, analytic gradients.

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.

Unmanned aerial vehicle (UAV) swarm enabled edge computing is envisioned to be promising in the sixth generation wireless communication networks due to their wide application sensories and flexible deployment. However, most of the existing works focus on edge computing enabled by a single or a small scale UAVs, which are very different from UAV swarm-enabled edge computing. In order to facilitate the practical applications of UAV swarm-enabled edge computing, the state of the art research is presented in this article. The potential applications, architectures and implementation considerations are illustrated. Moreover, the promising enabling technologies for UAV swarm-enabled edge computing are discussed. Furthermore, we outline challenges and open issues in order to shed light on the future research directions.

The time and effort involved in hand-designing deep neural networks is immense. This has prompted the development of Neural Architecture Search (NAS) techniques to automate this design. However, NAS algorithms tend to be slow and expensive; they need to train vast numbers of candidate networks to inform the search process. This could be alleviated if we could partially predict a network's trained accuracy from its initial state. In this work, we examine the overlap of activations between datapoints in untrained networks and motivate how this can give a measure which is usefully indicative of a network's trained performance. We incorporate this measure into a simple algorithm that allows us to search for powerful networks without any training in a matter of seconds on a single GPU, and verify its effectiveness on NAS-Bench-101, NAS-Bench-201, NATS-Bench, and Network Design Spaces. Our approach can be readily combined with more expensive search methods; we examine a simple adaptation of regularised evolutionary search. Code for reproducing our experiments is available at //github.com/BayesWatch/nas-without-training.

Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit relationship networks of the time series; (C2) how to model the implicit relationship of the temporal dynamics. We propose a novel model called Network of Tensor Time Series, which is comprised of two modules, including Tensor Graph Convolutional Network (TGCN) and Tensor Recurrent Neural Network (TRNN). TGCN tackles the first challenge by generalizing Graph Convolutional Network (GCN) for flat graphs to tensor graphs, which captures the synergy between multiple graphs associated with the tensors. TRNN leverages tensor decomposition to model the implicit relationships among co-evolving time series. The experimental results on five real-world datasets demonstrate the efficacy of the proposed method.

Since hardware resources are limited, the objective of training deep learning models is typically to maximize accuracy subject to the time and memory constraints of training and inference. We study the impact of model size in this setting, focusing on Transformer models for NLP tasks that are limited by compute: self-supervised pretraining and high-resource machine translation. We first show that even though smaller Transformer models execute faster per iteration, wider and deeper models converge in significantly fewer steps. Moreover, this acceleration in convergence typically outpaces the additional computational overhead of using larger models. Therefore, the most compute-efficient training strategy is to counterintuitively train extremely large models but stop after a small number of iterations. This leads to an apparent trade-off between the training efficiency of large Transformer models and the inference efficiency of small Transformer models. However, we show that large models are more robust to compression techniques such as quantization and pruning than small models. Consequently, one can get the best of both worlds: heavily compressed, large models achieve higher accuracy than lightly compressed, small models.