We propose a novel memory cell for recurrent neural networks that dynamically maintains information across long windows of time using relatively few resources. The Legendre Memory Unit (LMU) is mathematically derived to orthogonalize its continuous-time history -- doing so by solving $d$ coupled ordinary differential equations (ODEs), whose phase space linearly maps onto sliding windows of time via the Legendre polynomials up to degree $d - 1$. Backpropagation across LMUs outperforms equivalently-sized LSTMs on a chaotic time-series prediction task, improves memory capacity by two orders of magnitude, and significantly reduces training and inference times. LMUs can efficiently handle temporal dependencies spanning $100\text{,}000$ time-steps, converge rapidly, and use few internal state-variables to learn complex functions spanning long windows of time -- exceeding state-of-the-art performance among RNNs on permuted sequential MNIST. These results are due to the network's disposition to learn scale-invariant features independently of step size.

We propose a recurrent neural-network for real-time reconstruction of acoustic camera spherical maps. The network, dubbed DeepWave, is both physically and algorithmically motivated: its recurrent architecture mimics iterative solvers from convex optimisation, and its parsimonious parametrisation is based on the natural structure of acoustic imaging problems. Each network layer applies successive filtering, biasing and activation steps to its input, which can be interpreted as generalised deblurring and sparsification steps. To comply with the irregular geometry of spherical maps, filtering operations are implemented efficiently by means of graph signal processing techniques. Unlike commonly-used imaging network architectures, DeepWave is moreover capable of directly processing the complex-valued raw microphone correlations, learning how to optimally back-project these into a spherical map.

When training complex neural networks, memory usage can be an important bottleneck. The question of when to rematerialize, i.e., to recompute intermediate values rather than retaining them in memory, becomes critical to achieving the best time and space efficiency. In this work we consider the rematerialization problem and devise efficient algorithms that use structural characterizations of computation graphs---treewidth and pathwidth---to obtain provably efficient rematerialization schedules. Our experiments demonstrate the performance of these algorithms on many common deep learning models. Papers published at the Neural Information Processing Systems Conference.

The skip-connections used in residual networks have become a standard architecture choice in deep learning due to the increased generalization and stability of networks with this architecture, although there have been limited theoretical guarantees for this improved performance. In this work, we analyze overparameterized deep residual networks trained by gradient descent following random initialization, and demonstrate that (i) the class of networks learned by gradient descent constitutes a small subset of the entire neural network function class, and (ii) this subclass of networks is sufficiently large to guarantee small training error. By showing (i) we are able to demonstrate that deep residual networks trained with gradient descent have a small generalization gap between training and test error, and together with (ii) this guarantees that the test error will be small. Our optimization and generalization guarantees require overparameterization that is only logarithmic in the depth of the network, which helps explain why residual networks are preferable to fully connected ones. Papers published at the Neural Information Processing Systems Conference.

Discriminative neural networks offer little or no performance guarantees when deployed on data not generated by the same process as the training distribution. On such out-of-distribution (OOD) inputs, the prediction may not only be erroneous, but confidently so, limiting the safe deployment of classifiers in real-world applications. One such challenging application is bacteria identification based on genomic sequences, which holds the promise of early detection of diseases, but requires a model that can output low confidence predictions on OOD genomic sequences from new bacteria that were not present in the training data. We introduce a genomics dataset for OOD detection that allows other researchers to benchmark progress on this important problem. We investigate deep generative model based approaches for OOD detection and observe that the likelihood score is heavily affected by population level background statistics.

We present a new deep multi-state Dynamic Recurrent Neural Network (DRNN) architecture for Brain Machine Interface (BMI) applications. Our DRNN is used to predict Cartesian representation of a computer cursor movement kinematics from open-loop neural data recorded from the posterior parietal cortex (PPC) of a human subject in a BMI system. We design the algorithm to achieve a reasonable trade-off between performance and robustness, and we constrain memory usage in favor of future hardware implementation. We feed the predictions of the network back to the input to improve prediction performance and robustness. We apply a scheduled sampling approach to the model in order to solve a statistical distribution mismatch between the ground truth and predictions.

Encouraged by the success of deep convolutional neural networks on a variety of visual tasks, much theoretical and experimental work has been aimed at understanding and interpreting how vision networks operate. At the same time, deep neural networks have also achieved impressive performance in audio processing applications, both as sub-components of larger systems and as complete end-to-end systems by themselves. Despite their empirical successes, comparatively little is understood about how these audio models accomplish these tasks.In this work, we employ a recently developed statistical mechanical theory that connects geometric properties of network representations and the separability of classes to probe how information is untangled within neural networks trained to recognize speech. We observe that speaker-specific nuisance variations are discarded by the network's hierarchy, whereas task-relevant properties such as words and phonemes are untangled in later layers. Higher level concepts such as parts-of-speech and context dependence also emerge in the later layers of the network.

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.

Mixup \cite{zhang2017mixup} is a recently proposed method for training deep neural networks where additional samples are generated during training by convexly combining random pairs of images and their associated labels. While simple to implement, it has shown to be a surprisingly effective method of data augmentation for image classification; DNNs trained with mixup show noticeable gains in classification performance on a number of image classification benchmarks. In this work, we discuss a hitherto untouched aspect of mixup training -- the calibration and predictive uncertainty of models trained with mixup. We find that DNNs trained with mixup are significantly better calibrated -- i.e the predicted softmax scores are much better indicators of the actual likelihood of a correct prediction -- than DNNs trained in the regular fashion. We conduct experiments on a number of image classification architectures and datasets -- including large-scale datasets like ImageNet -- and find this to be the case.

Reducing the model redundancy is an important task to deploy complex deep learning models to resource-limited or time-sensitive devices. Directly regularizing or modifying weight values makes pruning procedure less robust and sensitive to the choice of hyperparameters, and it also requires prior knowledge to tune different hyperparameters for different models. To build a better generalized and easy-to-use pruning method, we propose AutoPrune, which prunes the network through optimizing a set of trainable auxiliary parameters instead of original weights. The instability and noise during training on auxiliary parameters will not directly affect weight values, which makes pruning process more robust to noise and less sensitive to hyperparameters. Moreover, we design gradient update rules for auxiliary parameters to keep them consistent with pruning tasks. Our method can automatically eliminate network redundancy with recoverability, relieving the complicated prior knowledge required to design thresholding functions, and reducing the time for trial and error.