Related papers: Artificial Neural Networks on Graded Vector Spaces
Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…
Artificial neural networks have gone through a recent rise in popularity, achieving state-of-the-art results in various fields, including image classification, speech recognition, and automated control. Both the performance and…
Deep Learning, driven by neural networks, has led to groundbreaking advancements in Artificial Intelligence by enabling systems to learn and adapt like the human brain. These models have achieved remarkable results, particularly in…
With great progress in the development of Generative Adversarial Networks (GANs), in recent years, the quest for insights in understanding and manipulating the latent space of GAN has gained more and more attention due to its wide range of…
There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High…
Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…
Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by…
We study possible applications of artificial neural networks to examine the string landscape. Since the field of application is rather versatile, we propose to dynamically evolve these networks via genetic algorithms. This means that we…
This paper presents a novel approach to neural network pruning by integrating a graph-based observation space into an AutoML framework to address the limitations of existing methods. Traditional pruning approaches often depend on…
In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…
Artificial Neural Networks are computational network models inspired by signal processing in the brain. These models have dramatically improved the performance of many learning tasks, including speech and object recognition. However,…
Graph Drawing techniques have been developed in the last few years with the purpose of producing aesthetically pleasing node-link layouts. Recently, the employment of differentiable loss functions has paved the road to the massive usage of…
Neural networks have achieved remarkable empirical performance, while the current theoretical analysis is not adequate for understanding their success, e.g., the Neural Tangent Kernel approach fails to capture their key feature learning…
This work analyzes Graph Neural Networks, a generalization of Fully-Connected Deep Neural Nets on Graph structured data, when their width, that is the number of nodes in each fullyconnected layer is increasing to infinity. Infinite Width…
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines…
Recently, the deep learning community has given growing attention to neural architectures engineered to learn problems in relational domains. Convolutional Neural Networks employ parameter sharing over the image domain, tying the weights of…
Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is…
Neural Networks sequentially build high-level features through their successive layers. We propose here a new neural network model where each layer is associated with a set of candidate mappings. When an input is processed, at each layer,…
Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design…
In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures…