Related papers: Towards Explaining Hypercomplex Neural Networks

Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…

In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…

Deep Convolutional Neural Networks (CNNs) have been one of the most influential recent developments in computer vision, particularly for categorization. There is an increasing demand for explainable AI as these systems are deployed in the…

Recently, graph-based models designed for downstream tasks have significantly advanced research on graph neural networks (GNNs). GNN baselines based on neural message-passing mechanisms such as GCN and GAT perform worse as the network…

Heterogeneous graph neural networks (HGNNs) have powerful capability to embed rich structural and semantic information of a heterogeneous graph into node representations. Existing HGNNs inherit many mechanisms from graph neural networks…

The analyses relying on 3D point clouds are an utterly complex task, often involving million of points, but also requiring computationally efficient algorithms because of many real-time applications; e.g. autonomous vehicle. However, point…

Many problems in computer vision and machine learning can be cast as learning on hypergraphs that represent higher-order relations. Recent approaches for hypergraph learning extend graph neural networks based on message passing, which is…

Graph Convolutional Network (GCN) has achieved extraordinary success in learning effective task-specific representations of nodes in graphs. However, regarding Heterogeneous Information Network (HIN), existing HIN-oriented GCN methods still…

Identifying the structural priors that enable Deep Neural Networks (DNNs) to overcome the curse of dimensionality is a fundamental challenge in machine learning theory. Existing literature suggests that effective high-dimensional learning…

In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features. However, many neurons exhibit $\textit{mixed selectivity}$, i.e., they represent multiple unrelated features. A…

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…

Deep neural networks (DNNs) transform stimuli across multiple processing stages to produce representations that can be used to solve complex tasks, such as object recognition in images. However, a full understanding of how they achieve this…

Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in…

Deep-predictive-coding networks (DPCNs) are hierarchical, generative models. They rely on feed-forward and feed-back connections to modulate latent feature representations of stimuli in a dynamic and context-sensitive manner. A crucial…

We introduce a parameter sharing scheme, in which different layers of a convolutional neural network (CNN) are defined by a learned linear combination of parameter tensors from a global bank of templates. Restricting the number of templates…

This work studies the design of neural networks that can process the weights or gradients of other neural networks, which we refer to as neural functional networks (NFNs). Despite a wide range of potential applications, including learned…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

Detection of cell nuclei in microscopic images is a challenging research topic, because of limitations in cellular image quality and diversity of nuclear morphology, i.e. varying nuclei shapes, sizes, and overlaps between multiple cell…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…