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In deep learning, dense layer connectivity has become a key design principle in deep neural networks (DNNs), enabling efficient information flow and strong performance across a range of applications. In this work, we model densely connected…

A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…

We study randomly initialized residual networks using mean field theory and the theory of difference equations. Classical feedforward neural networks, such as those with tanh activations, exhibit exponential behavior on the average when…

With the increasing deployment of machine learning models in many socially sensitive tasks, there is a growing demand for reliable and trustworthy predictions. One way to accomplish these requirements is to allow a model to abstain from…

We study the problem of explaining a rich class of behavioral properties of deep neural networks. Distinctively, our influence-directed explanations approach this problem by peering inside the network to identify neurons with high influence…

We study the role of depth in training randomly initialized overparameterized neural networks. We give a general result showing that depth improves trainability of neural networks by improving the conditioning of certain kernel matrices of…

Deep neural networks (DNN) have shown remarkable success in the classification of physiological signals. In this study we propose a method for examining to what extent does a DNN's performance rely on rediscovering existing features of the…

We address the fundamental question of why deep neural networks generalize by establishing a pointwise generalization theory for fully connected networks. This framework resolves long-standing barriers to characterizing the rich nonlinear…

Deep Neural Networks (DNNs) have been successfully applied to a wide range of problems. However, two main limitations are commonly pointed out. The first one is that they require long time to design. The other is that they heavily rely on…

We explore the hyperparameters and introduce a methodological framework to convert disease patterns from time series data of blood test results into correlation graphs for causal hypothesis exploration. The networks represent hypotheses…

Understanding the evolution of brain functional networks over time is of great significance for the analysis of cognitive mechanisms and the diagnosis of neurological diseases. Existing methods often have difficulty in capturing the…

We provide novel guaranteed approaches for training feedforward neural networks with sparse connectivity. We leverage on the techniques developed previously for learning linear networks and show that they can also be effectively adopted to…

Deep learning methods have shown great success in several domains as they process a large amount of data efficiently, capable of solving complex classification, forecast, segmentation, and other tasks. However, they come with the inherent…

Deep neural networks (DNNs) achieve state-of-the-art results in a variety of domains. Unfortunately, DNNs are notorious for their non-interpretability, and thus limit their applicability in hypothesis-driven domains such as biology and…

We propose a new, more actionable view of neural network interpretability and data analysis by leveraging the remarkable matching effectiveness of representations derived from deep networks, guided by an approach for class-conditional…

In this short note, we propose a new method for quantizing the weights of a fully trained neural network. A simple deterministic pre-processing step allows us to quantize network layers via memoryless scalar quantization while preserving…

Neural networks are more expressive when they have multiple layers. In turn, conventional training methods are only successful if the depth does not lead to numerical issues such as exploding or vanishing gradients, which occur less…

We introduce an algorithm to do backpropagation on a spiking network. Our network is "spiking" in the sense that our neurons accumulate their activation into a potential over time, and only send out a signal (a "spike") when this potential…

Wide neural networks have proven to be a rich class of architectures for both theory and practice. Motivated by the observation that finite width convolutional networks appear to outperform infinite width networks, we study scaling laws for…

Deep neural networks are often considered opaque systems, prompting the need for explainability methods to improve trust and accountability. Existing approaches typically attribute test-time predictions either to input features (e.g.,…