Related papers: Towards Explaining Hypercomplex Neural Networks
Capsule networks were proposed as an alternative approach to Convolutional Neural Networks (CNNs) for learning object-centric representations, which can be leveraged for improved generalization and sample complexity. Unlike CNNs, capsule…
This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…
Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many…
Deep neural networks (DNNs) have achieved unprecedented performance on a wide range of complex tasks, rapidly outpacing our understanding of the nature of their solutions. This has caused a recent surge of interest in methods for rendering…
Convolutional neural networks (CNN) are increasingly used in many areas of computer vision. They are particularly attractive because of their ability to "absorb" great quantities of labeled data through millions of parameters. However, as…
The fast development of self-supervised learning lowers the bar learning feature representation from massive unlabeled data and has triggered a series of research on change detection of remote sensing images. Challenges in adapting…
Piecewise affine neural networks (PANNs) provide a principled geometric perspective on neural network expressivity by characterizing the input--output map as a continuous piecewise affine (CPA) function whose complexity is governed by the…
Hypergraph neural networks are a class of powerful models that leverage the message passing paradigm to learn over hypergraphs, a generalization of graphs well-suited to describing relational data with higher-order interactions. However,…
Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications. Investigation of deep learning for HOIs, thus, has become a valuable agenda for the data mining and machine learning communities. As networks of…
Deep convolutional neural networks (DCNNs) have attracted much attention recently, and have shown to be able to recognize thousands of object categories in natural image databases. Their architecture is somewhat similar to that of the human…
Hyperbolic geometry has emerged as a powerful tool for modeling complex, structured data, particularly where hierarchical or tree-like relationships are present. By enabling embeddings with lower distortion, hyperbolic neural networks offer…
Real-world visual data exhibit intrinsic hierarchical structures that can be represented effectively in hyperbolic spaces. Hyperbolic neural networks (HNNs) are a promising approach for learning feature representations in such spaces.…
Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent…
Deep learning utilizing deep neural networks (DNNs) has achieved a lot of success recently in many important areas such as computer vision, natural language processing, and recommendation systems. The lack of convexity for DNNs has been…
Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…
In current noisy intermediate-scale quantum devices, hybrid quantum-classical neural networks (HQNNs) represent a promising solution that combines the strengths of classical machine learning with quantum computing capabilities. Compared to…
Neural networks have achieved remarkable success across various fields. However, the lack of interpretability limits their practical use, particularly in critical decision-making scenarios. Post-hoc interpretability, which provides…
In the present work, neural networks are applied to formulate parametrised hyperelastic constitutive models. The models fulfill all common mechanical conditions of hyperelasticity by construction. In particular, partially input-convex…
We investigate the complexity of deep neural networks through the lens of functional equivalence, which posits that different parameterizations can yield the same network function. Leveraging the equivalence property, we present a novel…
Convolutional neural networks (CNN) have made significant advances in hyperspectral image (HSI) classification. However, standard convolutional kernel neglects the intrinsic connections between data points, resulting in poor region…