Related papers: Neural Feature Geometry Evolves as Discrete Ricci …

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

Discrete curvatures are quantities associated to the nodes and edges of a graph that reflect the local geometry around them. These curvatures have a rich mathematical theory and they have recently found success as a tool to analyze networks…

Graph data often exhibits complex geometric heterogeneity, where structures with varying local curvature, such as tree-like hierarchies and dense communities, coexist within a single network. Existing geometric GNNs, which embed graphs into…

Representational similarity analysis (RSA) is widely used to analyze the alignment between humans and neural networks; however, conclusions based on this approach can be misleading without considering the underlying representational…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of…

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…

Deep Implicit Functions (DIFs) represent 3D geometry with continuous signed distance functions learned through deep neural nets. Recently DIFs-based methods have been proposed to handle shape reconstruction and dense point correspondences…

Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

Graph neural networks have shown significant success in the field of graph representation learning. Graph convolutions perform neighborhood aggregation and represent one of the most important graph operations. Nevertheless, one layer of…

A novel method to identify salient computational paths within randomly wired neural networks before training is proposed. The computational graph is pruned based on a node mass probability function defined by local graph measures and…

Neural networks transform data through learned representations whose geometry affects separation, contraction, and generalization. Recent work studies this geometry using discrete curvature on neighborhood graphs, suggesting Ricci-flow-like…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data. However, it remains an open question how deep networks perform hierarchical feature learning across layers. In this…

This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…

This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…