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Due to domain shift, deep neural networks (DNNs) usually fail to generalize well on unknown test data in practice. Domain generalization (DG) aims to overcome this issue by capturing domain-invariant representations from source domains.…

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible…

With the widespread applications of deep convolutional neural networks (DCNNs), it becomes increasingly important for DCNNs not only to make accurate predictions but also to explain how they make their decisions. In this work, we propose a…

Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean response of a sample of the microstructure to external loading for…

Neural network training is typically viewed as gradient descent on a loss surface. We propose a fundamentally different perspective: learning is a structure-preserving transformation (a functor L) between the space of network parameters…

Recent work has attempted to interpret residual networks (ResNets) as one step of a forward Euler discretization of an ordinary differential equation, focusing mainly on syntactic algebraic similarities between the two systems. Discrete…

As deep neural networks are increasingly used in solving high-stake problems, there is a pressing need to understand their internal decision mechanisms. Visualization has helped address this problem by assisting with interpreting complex…

Domain Generalization (DG) is a fundamental challenge for machine learning models, which aims to improve model generalization on various domains. Previous methods focus on generating domain invariant features from various source domains.…

In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as…

Residual neural networks are state-of-the-art deep learning models. Their continuous-depth analog, neural ordinary differential equations (ODEs), are also widely used. Despite their success, the link between the discrete and continuous…

Deep learning based methods hold state-of-the-art results in image denoising, but remain difficult to interpret due to their construction from poorly understood building blocks such as batch-normalization, residual learning, and feature…

Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…

Invariants and conservation laws convey critical information about the underlying dynamics of a system, yet it is generally infeasible to find them from large-scale data without any prior knowledge or human insight. We propose ConservNet to…

Deep learning models are prone to learning shortcut solutions to problems using spuriously correlated yet irrelevant features of their training data. In high-risk applications such as medical image analysis, this phenomenon may prevent…

Deep neural networks have become ubiquitous for applications related to visual recognition and language understanding tasks. However, it is often prohibitive to use typical neural networks on devices like mobile phones or smart watches…

Deep neural networks (DNNs) have significantly advanced machine learning, with model depth playing a central role in their successes. The dynamical system modeling approach has recently emerged as a powerful framework, offering new…

Discriminative features play an important role in image and object classification and also in other fields of research such as semi-supervised learning, fine-grained classification, out of distribution detection. Inspired by Linear…

Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to…

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…

Applying network science approaches to investigate the functions and anatomy of the human brain is prevalent in modern medical imaging analysis. Due to the complex network topology, for an individual brain, mining a discriminative network…