Related papers: Exploring Neural Ordinary Differential Equations a…

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

We propose a novel perspective to understand deep neural networks in an interpretable disentanglement form. For each semantic class, we extract a class-specific functional subnetwork from the original full model, with compressed structure…

The lack of interpretability and transparency are preventing economists from using advanced tools like neural networks in their empirical research. In this paper, we propose a class of interpretable neural network models that can achieve…

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

Exponential growth in Electronic Healthcare Records (EHR) has resulted in new opportunities and urgent needs for discovery of meaningful data-driven representations and patterns of diseases in Computational Phenotyping research. Deep…

Neural Ordinary Differential Equations (NODEs) are a new class of models that transform data continuously through infinite-depth architectures. The continuous nature of NODEs has made them particularly suitable for learning the dynamics of…

Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient,…

The field of machine learning has seen tremendous progress in recent years, with deep learning models delivering exceptional performance across a range of tasks. However, these models often come at the cost of interpretability, as they…

Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…

Deployment of machine learning models in real high-risk settings (e.g. healthcare) often depends not only on the model's accuracy but also on its fairness, robustness, and interpretability. Generalized Additive Models (GAMs) are a class of…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

We propose a novel approach for image segmentation that combines Neural Ordinary Differential Equations (NODEs) and the Level Set method. Our approach parametrizes the evolution of an initial contour with a NODE that implicitly learns from…

Human brains lie at the core of complex neurobiological systems, where the neurons, circuits, and subsystems interact in enigmatic ways. Understanding the structural and functional mechanisms of the brain has long been an intriguing pursuit…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Recent research in deep learning has shown that neural networks can learn differential equations governing dynamical systems. In this paper, we adapt this concept to Virtual Analog (VA) modeling to learn the ordinary differential equations…

This paper claims that machine learning models deployed in high stakes domains such as medicine must be interpretable, shareable, reproducible and accountable. We argue that these principles should form the foundational design criteria for…

Graphs are ubiquitous due to their flexibility in representing social and technological systems as networks of interacting elements. Graph representation learning methods, such as node embeddings, are powerful approaches to map nodes into a…

A novel approach for supervised classification is presented which sits at the intersection of machine learning and dynamical systems theory. At variance with other methodologies that employ ordinary differential equations for classification…

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…