The variational autoencoder is a well defined deep generative model that utilizes an encoder-decoder framework where an encoding neural network outputs a non-deterministic code for reconstructing an input. The encoder achieves this by sampling from a distribution for every input, instead of outputting a deterministic code per input. The great advantage of this process is that it allows the use of the network as a generative model for sampling from the data distribution beyond provided samples for training. We show in this work that utilizing batch normalization as a source for non-determinism suffices to turn deterministic autoencoders into generative models on par with variational ones, so long as we add a suitable entropic regularization to the training objective.

We propose a statistical adaptive procedure called SALSA for automatically scheduling the learning rate (step size) in stochastic gradient methods. SALSA first uses a smoothed stochastic line-search procedure to gradually increase the learning rate, then automatically switches to a statistical method to decrease the learning rate. The line search procedure ``warms up'' the optimization process, reducing the need for expensive trial and error in setting an initial learning rate. The method for decreasing the learning rate is based on a new statistical test for detecting stationarity when using a constant step size. Unlike in prior work, our test applies to a broad class of stochastic gradient algorithms without modification. The combined method is highly robust and autonomous, and it matches the performance of the best hand-tuned learning rate schedules in our experiments on several deep learning tasks.

Given the knowledge of the separable structure of the function, one can design a sparse network to represent the function very accurately, or even exactly. When such structural information is not available, and we may only use a dense neural network, the optimization procedure to find the sparse network embedded in the dense network is similar to finding the needle in a haystack, using a given number of samples of the function. We demonstrate that the cost (measured by sample complexity) of finding the needle is directly related to the Barron norm of the function. While only a small number of samples is needed to train a sparse network, the dense network trained with the same number of samples exhibits large test loss and a large generalization gap. In order to control the size of the generalization gap, we find that the use of explicit regularization becomes increasingly more important as d increases. The numerically observed sample complexity with explicit regularization scales as O(d 2.5), which is in fact better than the theoretically predicted sample complexity that scales as O(d 4). Without explicit regularization (also called implicit regularization), the numerically observed sample complexity is significantly higher and is close to O(d 4.5).

We develop exact representations of two layer neural networks with rectified linear units in terms of a single convex program with number of variables polynomial in the number of training samples and number of hidden neurons. Our theory utilizes semi-infinite duality and minimum norm regularization. Moreover, we show that certain standard multi-layer convolutional neural networks are equivalent to L1 regularized linear models in a polynomial sized discrete Fourier feature space. We also introduce exact semi-definite programming representations of convolutional and fully connected linear multi-layer networks which are polynomial size in both the sample size and dimension.

Learning rich representation from data is an important task for deep generative models such as variational auto-encoder (VAE). However, by extracting high-level abstractions in the bottom-up inference process, the goal of preserving all factors of variations for top-down generation is compromised. Motivated by the concept of "starting small", we present a strategy to progressively learn independent hierarchical representations from high- to low-levels of abstractions. The model starts with learning the most abstract representation, and then progressively grow the network architecture to introduce new representations at different levels of abstraction. We quantitatively demonstrate the ability of the presented model to improve disentanglement in comparison to existing works on two benchmark data sets using three disentanglement metrics, including a new metric we proposed to complement the previously-presented metric of mutual information gap. We further present both qualitative and quantitative evidence on how the progression of learning improves disentangling of hierarchical representations. By drawing on the respective advantage of hierarchical representation learning and progressive learning, this is to our knowledge the first attempt to improve disentanglement by progressively growing the capacity of VAE to learn hierarchical representations.

In safety-critical but computationally resource-constrained applications, deep learning faces two key challenges: lack of robustness against adversarial attacks and large neural network size (often millions of parameters). While the research community has extensively explored the use of robust training and network pruning \emph{independently} to address one of these challenges, we show that integrating existing pruning techniques with multiple types of robust training techniques, including verifiably robust training, leads to poor robust accuracy even though such techniques can preserve high regular accuracy. We further demonstrate that making pruning techniques aware of the robust learning objective can lead to a large improvement in performance. We realize this insight by formulating the pruning objective as an empirical risk minimization problem which is then solved using SGD. We demonstrate the success of the proposed pruning technique across CIFAR-10, SVHN, and ImageNet dataset with four different robust training techniques: iterative adversarial training, randomized smoothing, MixTrain, and CROWN-IBP. Specifically, at 99\% connection pruning ratio, we achieve gains up to 3.2, 10.0, and 17.8 percentage points in robust accuracy under state-of-the-art adversarial attacks for ImageNet, CIFAR-10, and SVHN dataset, respectively. Our code and compressed networks are publicly available at https://github.com/inspire-group/compactness-robustness

In this work, we propose a novel probabilistic sequence model that excels at capturing high variability in time series data, both across sequences and within an individual sequence. Our method uses temporal latent variables to capture information about the underlying data pattern and dynamically decodes the latent information into modifications of weights of the base decoder and recurrent model. The efficacy of the proposed method is demonstrated on a range of synthetic and real-world sequential data that exhibit large scale variations, regime shifts, and complex dynamics.

Nearest neighbors is a successful and long-standing technique for anomaly detection. Significant progress has been recently achieved by self-supervised deep methods (e.g. RotNet). Self-supervised features however typically under-perform Imagenet pre-trained features. In this work, we investigate whether the recent progress can indeed outperform nearest-neighbor methods operating on an Imagenet pretrained feature space. The simple nearest-neighbor based-approach is experimentally shown to outperform self-supervised methods in: accuracy, few shot generalization, training time and noise robustness while making fewer assumptions on image distributions.

Batch normalization has multiple benefits. It improves the conditioning of the loss landscape, and is a surprisingly effective regularizer. However, the most important benefit of batch normalization arises in residual networks, where it dramatically increases the largest trainable depth. We identify the origin of this benefit: At initialization, batch normalization downscales the residual branch relative to the skip connection, by a normalizing factor proportional to the square root of the network depth. This ensures that, early in training, the function computed by deep normalized residual networks is dominated by shallow paths with well-behaved gradients. We use this insight to develop a simple initialization scheme which can train very deep residual networks without normalization. We also clarify that, although batch normalization does enable stable training with larger learning rates, this benefit is only useful when one wishes to parallelize training over large batch sizes. Our results help isolate the distinct benefits of batch normalization in different architectures.

Generative Adversarial Networks (GANs) are a revolutionary class of Deep Neural Networks (DNNs) that have been successfully used to generate realistic images, music, text, and other data. However, it is well known that GAN training can be notoriously resource-intensive and presents many challenges. Further, a potential weakness in GANs is that discriminator DNNs typically provide only one value (loss) of corrective feedback to generator DNNs (namely, the discriminator's assessment of the generated example). By contrast, we propose a new class of GAN we refer to as LogicGAN, that leverages recent advances in (logic-based) explainable AI (xAI) systems to provide a "richer" form of corrective feedback from discriminators to generators. Specifically, we modify the gradient descent process using xAI systems that specify the reason as to why the discriminator made the classification it did, thus providing the richer corrective feedback that helps the generator to better fool the discriminator. Using our approach, we show that LogicGANs learn much faster on MNIST data, achieving an improvement in data efficiency of 45% in single and 12.73% in multi-class setting over standard GANs while maintaining the same quality as measured by Fr\'echet Inception Distance. Further, we argue that LogicGAN enables users greater control over how models learn than standard GAN systems.