In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory. Recent works have pointed out instabilities of deep neural networks for several image reconstruction tasks. In analogy to adversarial attacks in classification, it was shown that slight distortions in the input domain may cause severe artifacts. The present article sheds new light on this concern, by conducting an extensive study of the robustness of deep-learning-based algorithms for solving underdetermined inverse problems. This covers compressed sensing with Gaussian measurements as well as image recovery from Fourier and Radon measurements, including a real-world scenario for magnetic resonance imaging (using the NYU-fastMRI dataset). Our main focus is on computing adversarial perturbations of the measurements that maximize the reconstruction error. A distinctive feature of our approach is the quantitative and qualitative comparison with total-variation minimization, which serves as a provably robust reference method. In contrast to previous findings, our results reveal that standard end-to-end network architectures are not only resilient against statistical noise, but also against adversarial perturbations. All considered networks are trained by common deep learning techniques, without sophisticated defense strategies.

The ability to record activities from hundreds of neurons simultaneously in the brain has placed an increasing demand for developing appropriate statistical techniques to analyze such data. Recently, deep generative models have been proposed to fit neural population responses. While these methods are flexible and expressive, the downside is that they can be difficult to interpret and identify. To address this problem, we propose a method that integrates key ingredients from latent models and traditional neural encoding models. Our method, pi-VAE, is inspired by recent progress on identifiable variational auto-encoder, which we adapt to make appropriate for neuroscience applications. Specifically, we propose to construct latent variable models of neural activity while simultaneously modeling the relation between the latent and task variables (non-neural variables, e.g. sensory, motor, and other externally observable states). The incorporation of task variables results in models that are not only more constrained, but also show qualitative improvements in interpretability and identifiability. We validate pi-VAE using synthetic data, and apply it to analyze neurophysiological datasets from rat hippocampus and macaque motor cortex. We demonstrate that pi-VAE not only fits the data better, but also provides unexpected novel insights into the structure of the neural codes.

Despite recent progress in Graph Neural Networks (GNNs), explaining predictions made by GNNs remains a challenging open problem. The leading method independently addresses the local explanations (i.e., important subgraph structure and node features) to interpret why a GNN model makes the prediction for a single instance, e.g. a node or a graph. As a result, the explanation generated is painstakingly customized for each instance. The unique explanation interpreting each instance independently is not sufficient to provide a global understanding of the learned GNN model, leading to the lack of generalizability and hindering it from being used in the inductive setting. Besides, as it is designed for explaining a single instance, it is challenging to explain a set of instances naturally (e.g., graphs of a given class). In this study, we address these key challenges and propose PGExplainer, a parameterized explainer for GNNs. PGExplainer adopts a deep neural network to parameterize the generation process of explanations, which enables PGExplainer a natural approach to explaining multiple instances collectively. Compared to the existing work, PGExplainer has better generalization ability and can be utilized in an inductive setting easily. Experiments on both synthetic and real-life datasets show highly competitive performance with up to 24.7% relative improvement in AUC on explaining graph classification over the leading baseline.

Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly active area of research. Recent work has shown that deep neural networks can be optimized in randomly-projected subspaces of much smaller dimensionality than their native parameter space. While such training is promising for more efficient and scalable optimization schemes, its practical application is limited by inferior optimization performance. Here, we improve on recent random subspace approaches as follows: Firstly, we show that keeping the random projection fixed throughout training is detrimental to optimization. We propose re-drawing the random subspace at each step, which yields significantly better performance. We realize further improvements by applying independent projections to different parts of the network, making the approximation more efficient as network dimensionality grows. To implement these experiments, we leverage hardware-accelerated pseudo-random number generation to construct the random projections on-demand at every optimization step, allowing us to distribute the computation of independent random directions across multiple workers with shared random seeds. This yields significant reductions in memory and is up to 10 times faster for the workloads in question.

The 2020 Multi-channel Magnetic Resonance Reconstruction (MC-MRRec) Challenge had two primary goals: 1) compare different MR image reconstruction models on a large dataset and 2) assess the generalizability of these models to datasets acquired with a different number of receiver coils (i.e., multiple channels). The challenge had two tracks: Track 01 focused on assessing models trained and tested with 12-channel data. Track 02 focused on assessing models trained with 12-channel data and tested on both 12-channel and 32-channel data. While the challenge is ongoing, here we describe the first edition of the challenge and summarise submissions received prior to 5 September 2020. Track 01 had five baseline models and received four independent submissions. Track 02 had two baseline models and received two independent submissions. This manuscript provides relevant comparative information on the current state-of-the-art of MR reconstruction and highlights the challenges of obtaining generalizable models that are required prior to clinical adoption. Both challenge tracks remain open and will provide an objective performance assessment for future submissions. Subsequent editions of the challenge are proposed to investigate new concepts and strategies, such as the integration of potentially available longitudinal information during the MR reconstruction process. An outline of the proposed second edition of the challenge is presented in this manuscript.

We present a deep learning algorithm for the numerical solution of parametric families of high-dimensional linear Kolmogorov partial differential equations (PDEs). Our method is based on reformulating the numerical approximation of a whole family of Kolmogorov PDEs as a single statistical learning problem using the Feynman-Kac formula. Successful numerical experiments are presented, which empirically confirm the functionality and efficiency of our proposed algorithm in the case of heat equations and Black-Scholes option pricing models parametrized by affine-linear coefficient functions. We show that a single deep neural network trained on simulated data is capable of learning the solution functions of an entire family of PDEs on a full space-time region. Most notably, our numerical observations and theoretical results also demonstrate that the proposed method does not suffer from the curse of dimensionality, distinguishing it from almost all standard numerical methods for PDEs.

In recent years, convolutional neural network (CNN) and other deep learning models have been gradually introduced into the area of gravitational-wave (GW) data processing. Compared with the traditional matched-filtering techniques, CNN has significant advantages in efficiency in GW signal detection tasks. In addition, matched-filtering techniques are based on the template bank of the existing theoretical waveform, which makes it difficult to find GW signals beyond theoretical expectation. In this paper, based on the task of GW detection of binary black holes, we introduce the optimization techniques of deep learning, such as batch normalization and dropout, to CNN models. Detailed studies of model performance are carried out. Through this study, we recommend to use batch normalization and dropout techniques in CNN models in GW signal detection tasks. Furthermore, we investigate the generalization ability of CNN models on different parameter ranges of GW signals. We point out that CNN models are robust to the variation of the parameter range of the GW waveform. This is a major advantage of deep learning models over matched-filtering techniques.

Inspired by the developments in deep generative models, we propose a model-based RL approach, coined Reinforced Deep Markov Model (RDMM), designed to integrate desirable properties of a reinforcement learning algorithm acting as an automatic trading system. The network architecture allows for the possibility that market dynamics are partially visible and are potentially modified by the agent's actions. The RDMM filters incomplete and noisy data, to create better-behaved input data for RL planning. The policy search optimisation also properly accounts for state uncertainty. Due to the complexity of the RKDF model architecture, we performed ablation studies to understand the contributions of individual components of the approach better. To test the financial performance of the RDMM we implement policies using variants of Q-Learning, DynaQ-ARIMA and DynaQ-LSTM algorithms. The experiments show that the RDMM is data-efficient and provides financial gains compared to the benchmarks in the optimal execution problem. The performance improvement becomes more pronounced when price dynamics are more complex, and this has been demonstrated using real data sets from the limit order book of Facebook, Intel, Vodafone and Microsoft.

Modern mobile devices, although resourceful, cannot train state-of-the-art machine learning models without the assistance of servers, which require access to privacy-sensitive user data. Split learning has recently emerged as a promising technique for training complex deep learning (DL) models on low-powered mobile devices. The core idea behind this technique is to train the sensitive layers of a DL model on the mobile devices while offloading the computationally intensive layers to a server. Although a lot of works have already explored the effectiveness of split learning in simulated settings, a usable toolkit for this purpose does not exist. In this work, we propose SplitEasy, a framework for training ML models on mobile devices using split learning. Using the abstraction provided by SplitEasy, developers can run various DL models under split learning setting by making minimal modifications. We provide a detailed explanation of SplitEasy and perform experiments under varying networks to demonstrate its versatility. We demonstrate how SplitEasy can be used to train state-of-the-art models while incurring nearly constant computational cost on mobile devices.

Training a neural network (NN) depends on multiple factors, including but not limited to the initial weights. In this paper, we focus on initializing deep NN parameters such that it performs better, comparing to random or zero initialization. We do this by reducing the process of initialization into an SMT solver. Previous works consider certain activation functions on small NNs, however the studied NN is a deep network with different activation functions. Our experiments show that the proposed approach for parameter initialization achieves better performance comparing to randomly initialized networks.