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Why does Deep Learning work? What representations does it capture? How do higher-order representations emerge? We study these questions from the perspective of group theory, thereby opening a new approach towards a theory of Deep learning.…

In this paper, we study deep diagonal circulant neural networks, that is deep neural networks in which weight matrices are the product of diagonal and circulant ones. Besides making a theoretical analysis of their expressivity, we…

Understanding how information is represented in neural networks is a fundamental challenge in both neuroscience and artificial intelligence. Despite their nonlinear architectures, recent evidence suggests that neural networks encode…

Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…

Understanding complex machine learning models such as deep neural networks with explanations is crucial in various applications. Many explanations stem from the model perspective, and may not necessarily effectively communicate why the…

Interpretability of deep neural networks (DNNs) is essential since it enables users to understand the overall strengths and weaknesses of the models, conveys an understanding of how the models will behave in the future, and how to diagnose…

Selective classification techniques (also known as reject option) have not yet been considered in the context of deep neural networks (DNNs). These techniques can potentially significantly improve DNNs prediction performance by trading-off…

While deep neural networks take loose inspiration from neuroscience, it is an open question how seriously to take the analogies between artificial deep networks and biological neuronal systems. Interestingly, recent work has shown that deep…

We explore a new class of end-to-end learnable models wherein data processing nodes (or network layers) are defined in terms of desired behavior rather than an explicit forward function. Specifically, the forward function is implicitly…

Deep neural networks provide flexible frameworks for learning data representations and functions relating data to other properties and are often claimed to achieve 'super-human' performance in inferring relationships between input data and…

Neural networks leverage robust internal representations in order to generalise. Learning them is difficult, and often requires a large training set that covers the data distribution densely. We study a common setting where our task is not…

This paper aims to quantitatively explain rationales of each prediction that is made by a pre-trained convolutional neural network (CNN). We propose to learn a decision tree, which clarifies the specific reason for each prediction made by…

This paper addresses the task of set prediction using deep feed-forward neural networks. A set is a collection of elements which is invariant under permutation and the size of a set is not fixed in advance. Many real-world problems, such as…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

Complex nonlinear models such as deep neural network (DNNs) have become an important tool for image classification, speech recognition, natural language processing, and many other fields of application. These models however lack…

We propose a new interpretability method for neural networks, which is based on a novel mathematico-philosophical theory of reasons. Our method computes a vector for each neuron, called its reasons vector. We then can compute how strongly…

Learning neural program embeddings is key to utilizing deep neural networks in program languages research --- precise and efficient program representations enable the application of deep models to a wide range of program analysis tasks.…

We consider deep feedforward neural networks with rectified linear units from a signal processing perspective. In this view, such representations mark the transition from using a single (data-driven) linear representation to utilizing a…

The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and…

Performing the inference step of deep learning in resource constrained environments, such as embedded devices, is challenging. Success requires optimization at both software and hardware levels. Low precision arithmetic and specifically low…