Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. Recent advances in sparse identification show encouraging success in distilling closed-form governing equations from data for a wide range of nonlinear dynamical systems. However, the fundamental bottleneck of this approach lies in the robustness and scalability with respect to data scarcity and noise. This work introduces a novel physics-informed deep learning framework to discover governing partial differential equations (PDEs) from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this approach seamlessly integrates the strengths of deep neural networks for rich representation learning, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the PDEs. The efficacy and robustness of this method are demonstrated on discovering a variety of PDE systems with different levels of data scarcity and noise. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.

Neural networks are effective function approximators, but hard to train in the reinforcement learning (RL) context mainly because samples are correlated. For years, scholars have got around this by employing experience replay or an asynchronous parallel-agent system. This paper proposes Discrete-to-Deep Supervised Policy Learning (D2D-SPL) for training neural networks in RL. D2D-SPL discretises the continuous state space into discrete states and uses actor-critic to learn a policy. It then selects from each discrete state an input value and the action with the highest numerical preference as an input/target pair. Finally it uses input/target pairs from all discrete states to train a classifier. D2D-SPL uses a single agent, needs no experience replay and learns much faster than state-of-the-art methods. We test our method with two RL environments, the Cartpole and an aircraft manoeuvring simulator.

Whereas adversarial training is employed as the main defence strategy against specific adversarial samples, it has limited generalization capability and incurs excessive time complexity. In this paper, we propose an attack-agnostic defence framework to enhance the intrinsic robustness of neural networks, without jeopardizing the ability of generalizing clean samples. Our Feature Pyramid Decoder (FPD) framework applies to all block-based convolutional neural networks (CNNs). It implants denoising and image restoration modules into a targeted CNN, and it also constraints the Lipschitz constant of the classification layer. Moreover, we propose a two-phase strategy to train the FPD-enhanced CNN, utilizing $\epsilon$-neighbourhood noisy images with multi-task and self-supervised learning. Evaluated against a variety of white-box and black-box attacks, we demonstrate that FPD-enhanced CNNs gain sufficient robustness against general adversarial samples on MNIST, SVHN and CALTECH. In addition, if we further conduct adversarial training, the FPD-enhanced CNNs perform better than their non-enhanced versions.

We consider the problem of maximizing the $\ell_1$ norm of a linear map over the sphere, which arises in various machine learning applications such as orthogonal dictionary learning (ODL) and robust subspace recovery (RSR). The problem is numerically challenging due to its nonsmooth objective and nonconvex constraint, and its algorithmic aspects have not been well explored. In this paper, we show how the manifold structure of the sphere can be exploited to design fast algorithms for tackling this problem. Specifically, our contribution is threefold. First, we present a manifold proximal point algorithm (ManPPA) for the problem and show that it converges at a sublinear rate. Furthermore, we show that ManPPA can achieve a quadratic convergence rate when applied to the ODL and RSR problems. Second, we propose a stochastic variant of ManPPA called StManPPA, which is well suited for large-scale computation, and establish its sublinear convergence rate. Both ManPPA and StManPPA have provably faster convergence rates than existing subgradient-type methods. Third, using ManPPA as a building block, we propose a new approach to solving a matrix analog of the problem, in which the sphere is replaced by the Stiefel manifold. The results from our extensive numerical experiments on the ODL and RSR problems demonstrate the efficiency and efficacy of our proposed methods.

A new robust algorithm based of the explanation method SurvLIME called SurvLIME-KS is proposed for explaining machine learning survival models. The algorithm is developed to ensure robustness to cases of a small amount of training data or outliers of survival data. The first idea behind SurvLIME-KS is to apply the Cox proportional hazards model to approximate the black-box survival model at the local area around a test example due to the linear relationship of covariates in the model. The second idea is to incorporate the well-known Kolmogorov-Smirnov bounds for constructing sets of predicted cumulative hazard functions. As a result, the robust maximin strategy is used, which aims to minimize the average distance between cumulative hazard functions of the explained black-box model and of the approximating Cox model, and to maximize the distance over all cumulative hazard functions in the interval produced by the Kolmogorov-Smirnov bounds. The maximin optimization problem is reduced to the quadratic program. Various numerical experiments with synthetic and real datasets demonstrate the SurvLIME-KS efficiency.

Neural Network Language Models (NNLMs) generate probability distributions by applying a softmax function to a distance metric formed by taking the dot product of a prediction vector with all word vectors in a high-dimensional embedding space. The dot-product distance metric forms part of the inductive bias of NNLMs. Although NNLMs optimize well with this inductive bias, we show that this results in a sub-optimal ordering of the embedding space that structurally impoverishes some words at the expense of others when assigning probability. We present numerical, theoretical and empirical analyses showing that words on the interior of the convex hull in the embedding space have their probability bounded by the probabilities of the words on the hull.

The right to be forgotten states that a data owner has the right to erase her data from an entity storing it. In the context of machine learning (ML), the right to be forgotten requires an ML model owner to remove the data owner's data from the training set used to build the ML model, a process known as machine unlearning. While originally designed to protect the privacy of the data owner, we argue that machine unlearning may leave some imprint of the data in the ML model and thus create unintended privacy risks. In this paper, we perform the first study on investigating the unintended information leakage caused by machine unlearning. We propose a novel membership inference attack which leverages the different outputs of an ML model's two versions to infer whether the deleted sample is part of the training set. Our experiments over five different datasets demonstrate that the proposed membership inference attack achieves strong performance. More importantly, we show that our attack in multiple cases outperforms the classical membership inference attack on the original ML model, which indicates that machine unlearning can have counterproductive effects on privacy. We notice that the privacy degradation is especially significant for well-generalized ML models where classical membership inference does not perform well. We further investigate two mechanisms to mitigate the newly discovered privacy risks and show that the only effective mechanism is to release the predicted label only. We believe that our results can help improve privacy in practical implementation of machine unlearning.

Federated learning has emerged as an umbrella term for centralized coordination strategies in multi-agent environments. While many federated learning architectures process data in an online manner, and are hence adaptive by nature, most performance analyses assume static optimization problems and offer no guarantees in the presence of drifts in the problem solution or data characteristics. We consider a federated learning model where at every iteration, a random subset of available agents perform local updates based on their data. Under a non-stationary random walk model on the true minimizer for the aggregate optimization problem, we establish that the performance of the architecture is determined by three factors, namely, the data variability at each agent, the model variability across all agents, and a tracking term that is inversely proportional to the learning rate of the algorithm. The results clarify the trade-off between convergence and tracking performance.

Machine learning algorithms operating on mobile networks can be characterized into three different categories. First is the classical situation in which the end-user devices send their data to a central server where this data is used to train a model. Second is the distributed setting in which each device trains its own model and send its model parameters to a central server where these model parameters are aggregated to create one final model. Third is the federated learning setting in which, at any given time $t$, a certain number of active end users train with their own local data along with feedback provided by the central server and then send their newly estimated model parameters to the central server. The server, then, aggregates these new parameters, updates its own model, and feeds the updated parameters back to all the end users, continuing this process until it converges. The main objective of this work is to provide an information-theoretic framework for all of the aforementioned learning paradigms. Moreover, using the provided framework, we develop upper and lower bounds on the generalization error together with bounds on the privacy leakage in the classical, distributed and federated learning settings. Keywords: Federated Learning, Distributed Learning, Machine Learning, Model Aggregation.

The overfitting is one of the cursing subjects in the deep learning field. To solve this challenge, many approaches were proposed to regularize the learning models. They add some hyper-parameters to the model to extend the generalization; however, it is a hard task to determine these hyper-parameters and a bad setting diverges the training process. In addition, most of the regularization schemes decrease the learning speed. Recently, Tai et al. [1] proposed low-rank tensor decomposition as a constrained filter for removing the redundancy in the convolution kernels of CNN. With a different viewpoint, we use Low-Rank matrix Factorization (LRF) to drop out some parameters of the learning model along the training process. However, this scheme similar to [1] probably decreases the training accuracy when it tries to decrease the number of operations. Instead, we use this regularization scheme adaptively when the complexity of a layer is high. The complexity of any layer can be evaluated by the nonlinear condition numbers of its learning system. The resulted method entitled "AdaptiveLRF" neither decreases the training speed nor vanishes the accuracy of the layer. The behavior of AdaptiveLRF is visualized on a noisy dataset. Then, the improvements are presented on some small-size and large-scale datasets. The preference of AdaptiveLRF on famous dropout regularizers on shallow networks is demonstrated. Also, AdaptiveLRF competes with dropout and adaptive dropout on the various deep networks including MobileNet V2, ResNet V2, DenseNet, and Xception. The best results of AdaptiveLRF on SVHN and CIFAR-10 datasets are 98%, 94.1% F-measure, and 97.9%, 94% accuracy. Finally, we state the usage of the LRF-based loss function to improve the quality of the learning model.