This paper introduces a novel optimization method for differential neural architecture search, based on the theory of prediction with expert advice. Its optimization criterion is well fitted for an architecture-selection, i.e., it minimizes the regret incurred by a sub-optimal selection of operations. Unlike previous search relaxations, that require hard pruning of architectures, our method is designed to dynamically wipe out inferior architectures and enhance superior ones. It achieves an optimal worst-case regret bound and suggests the use of multiple learning-rates, based on the amount of information carried by the backward gradients. Experiments show that our algorithm achieves a strong performance over several image classification datasets. Specifically, it obtains an error rate of 1.6% for CIFAR-10, 24% for ImageNet under mobile settings, and achieves state-of-the-art results on three additional datasets.

Neural networks are vulnerable to adversarial examples, i.e. inputs that are imperceptibly perturbed from natural data and yet incorrectly classified by the network. Adversarial training, a heuristic form of robust optimization that alternates between minimization and maximization steps, has proven to be among the most successful methods to train networks that are robust against a pre-defined family of perturbations. This paper provides a partial answer to the success of adversarial training. When the inner maximization problem can be solved to optimality, we prove that adversarial training finds a network of small robust train loss. When the maximization problem is solved by a heuristic algorithm, we prove that adversarial training finds a network of small robust surrogate train loss. The analysis technique leverages recent work on the analysis of neural networks via Neural Tangent Kernel (NTK), combined with online-learning when the maximization is solved by a heuristic, and the expressiveness of the NTK kernel in the $\ell_\infty$-norm.

Generative modeling is a rapidly advancing area of machine learning research finding applications in multiple fields such as, generated art, on-demand video, image denoising [1], exploration in reinforcement learning [2], collaborative filtering [3], inpainting [4] and many more. In general, three approaches have been used in generative modeling tasks. First, graphical models based on a probabilistic framework with latent variables such as variational auto-encoders [5] and Restricted Boltzmann Machines (RBMs) [6, 7]. Then, more recently proposed models based on adversarial training such as Generative Adversarial Networks (GANs) [8] and its many variants. Furthermore, autoregressive models such as Pixel Recurrent Neural Networks (PixelRNNs) [9] that models the conditional distribution of every individual pixel given previous pixels and generation involves sequentially predicting the pixels in an image along the two spatial dimensions.

Accelerating magnetic resonance imaging (MRI) has been an ongoing research topic since its invention in the 1970s. Among a variety of acceleration techniques, compressed sensing (CS) has become an important strategy during the past decades. Although CS-based methods can achieve high performance with many theoretical guarantees, it is challenging to determine the numerical uncertainties in the reconstruction model such as the optimal sparse transformations, sparse regularizer in the transform do-main, regularization parameters and the parameters of the optimization algorithm. Recently, deep learning has been introduced in MR reconstruction to address these issues and shown potential to significantly improve image quality.In this paper, we propose a general framework combining the CS-MR model with deep learning to maximize the potential of deep learning and model-based reconstruction for fast MR imaging and attempt to provide a guideline on how to improve the image quality with deep learning based on the traditional reconstruction algorithms.

We study the problem of inverting a deep generative model with ReLU activations. Inversion corresponds to finding a latent code vector that explains observed measurements as much as possible. In most prior works this is performed by attempting to solve a non-convex optimization problem involving the generator. In this paper we obtain several novel theoretical results for the inversion problem. We show that for the realizable case, single layer inversion can be performed exactly in polynomial time, by solving a linear program. Further, we show that for multiple layers, inversion is NP-hard and the pre-image set can be non-convex. For generative models of arbitrary depth, we show that exact recovery is possible in polynomial time with high probability, if the layers are expanding and the weights are randomly selected. Very recent work analyzed the same problem for gradient descent inversion. Their analysis requires significantly higher expansion (logarithmic in the latent dimension) while our proposed algorithm can provably reconstruct even with constant factor expansion. We also provide provable error bounds for different norms for reconstructing noisy observations. Our empirical validation demonstrates that we obtain better reconstructions when the latent dimension is large.

It has been shown that deep neural networks (DNNs) may be vulnerable to adversarial attacks, raising the concern on their robustness particularly for safety-critical applications. Recognizing the local nature and limitations of existing adversarial attacks, we present a new type of global adversarial attacks for assessing global DNN robustness. More specifically, we propose a novel concept of global adversarial example pairs in which each pair of two examples are close to each other but have different class labels predicted by the DNN. We further propose two families of global attack methods and show that our methods are able to generate diverse and intriguing adversarial example pairs at locations far from the training or testing data. Moreover, we demonstrate that DNNs hardened using the strong projected gradient descent (PGD) based (local) adversarial training are vulnerable to the proposed global adversarial example pairs, suggesting that global robustness must be considered while training robust deep learning networks.

Deep generative models play an increasingly important role in machine learning and computer vision. However there are two fundamental issues hindering real-world applications of these techniques: the learning difficulty of variational inference in Variational AutoEncoder (VAE) and the functional absence of encoding samples in Generative Adversarial Network (GAN). In this paper, we manage to address these issues in one framework by proposing a novel algorithm named Latently Invertible Autoencoder (LIA). A deep invertible network and its inverse mapping are symmetrically embedded in the latent space of VAE. Thus the partial encoder first transforms inputs to be feature vectors and then the distribution of these feature vectors is reshaped to approach a prior by the invertible network. The decoder proceeds in reverse order of composite mappings of the complete encoder. The two-stage stochasticity-free training is devised to train LIA via adversarial learning, in the sense that we first train a standard GAN whose generator is the decoder of LIA and then an autoencoder in the adversarial manner by detaching the invertible network from LIA. Experiments conducted on the FFHQ dataset validate the effectiveness of LIA for inference and generation tasks.

Two distinct limits for deep learning as the net width $h\to\infty$ have been proposed, depending on how the weights of the last layer scale with $h$. In the "lazy-learning" regime, the dynamics becomes linear in the weights and is described by a Neural Tangent Kernel $\Theta$. By contrast, in the "feature-learning" regime, the dynamics can be expressed in terms of the density distribution of the weights. Understanding which regime describes accurately practical architectures and which one leads to better performance remains a challenge. We answer these questions and produce new characterizations of these regimes for the MNIST data set, by considering deep nets $f$ whose last layer of weights scales as $\frac{\alpha}{\sqrt{h}}$ at initialization, where $\alpha$ is a parameter we vary. We performed systematic experiments on two setups (A) fully-connected Softplus momentum full batch and (B) convolutional ReLU momentum stochastic. We find that (1) $\alpha^*=\frac{1}{\sqrt{h}}$ separates the two regimes. (2) for (A) and (B) feature learning outperforms lazy learning, a difference in performance that decreases with $h$ and becomes hardly detectable asymptotically for (A) but is very significant for (B). (3) In both regimes, the fluctuations $\delta f$ induced by initial conditions on the learned function follow $\delta f\sim1/\sqrt{h}$, leading to a performance that increases with $h$. This improvement can be instead obtained at intermediate $h$ values by ensemble averaging different networks. (4) In the feature regime there exists a time scale $t_1\sim\alpha\sqrt{h}$, such that for $t\ll t_1$ the dynamics is linear. At $t\sim t_1$, the output has grown by a magnitude $\sqrt{h}$ and the changes of the tangent kernel $\|\Delta\Theta\|$ become significant. Ultimately, it follows $\|\Delta\Theta\|\sim(\sqrt{h}\alpha)^{-a}$ for ReLU and Softplus activation, with $a<2$ & $a\to2$ when depth grows.

Explainability in Artificial Intelligence has been revived as a topic of active research by the need of conveying safety and trust to users in the `how' and `why' of automated decision-making. Whilst a plethora of approaches have been developed for post-hoc explainability, only a few focus on how to use domain knowledge, and how this influences the understandability of an explanation from the users' perspective. In this paper we show how ontologies help the understandability of interpretable machine learning models, such as decision trees. In particular, we build on Trepan, an algorithm that explains artificial neural networks by means of decision trees, and we extend it to include ontologies modeling domain knowledge in the process of generating explanations. We present the results of a user study that measures the understandability of decision trees in domains where explanations are critical, namely, in finance and medicine. Our study shows that decision trees taking into account domain knowledge during generation are more understandable than those generated without the use of ontologies.

State representation learning, or the ability to capture latent generative factors of an environment, is crucial for building intelligent agents that can perform a wide variety of tasks. Learning such representations without supervision from rewards is a challenging open problem. We introduce a method that learns state representations by maximizing mutual information across spatially and temporally distinct features of a neural encoder of the observations. We also introduce a new benchmark based on Atari 2600 games where we evaluate representations based on how well they capture the ground truth state variables. We believe this new framework for evaluating representation learning models will be crucial for future representation learning research. Finally, we compare our technique with other state-of-the-art generative and contrastive representation learning methods.