Related papers: Geometric Deep Learning: Grids, Groups, Graphs, Ge…
The task of generating natural images from 3D scenes has been a long standing goal in computer graphics. On the other hand, recent developments in deep neural networks allow for trainable models that can produce natural-looking images with…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
We examine a Geometric Deep Learning model as a thermodynamic system treating the weights as non-quantum and non-relativistic particles. We employ the notion of temperature previously defined in [7] and study it in the various layers for…
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…
Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…
This theoretical paper is devoted to developing a rigorous theory for demystifying the global convergence phenomenon in a challenging scenario: learning over-parameterized Rectified Linear Unit (ReLU) nets for very high dimensional dataset…
Integrating invariance into data representations is a principled design in intelligent systems and web applications. Representations play a fundamental role, where systems and applications are both built on meaningful representations of…
Graphs provide a powerful means for representing complex interactions between entities. Recently, deep learning approaches are emerging for representing and modeling graph-structured data, although the conventional deep learning methods…
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…
Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we…
Some extremely low-dimensional yet crucial geometric eigen-lengths often determine the success of some geometric tasks. For example, the height of an object is important to measure to check if it can fit between the shelves of a cabinet,…
The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured…
Recent studies revealed the mathematical connection of deep neural network (DNN) and dynamic system. However, the fundamental principle of DNN has not been fully characterized with dynamic system in terms of optimization and generalization.…
Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems…
Neural networks are playing a crucial role in everyday life, with the most modern generative models able to achieve impressive results. Nonetheless, their functioning is still not very clear, and several strategies have been adopted to…
Continual learning, the ability of a model to adapt to an ongoing sequence of tasks without forgetting earlier ones, is a central goal of artificial intelligence. To better understand its underlying mechanisms, we study the limitations of…
Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine…
Neural network models can now recognise images, understand text, translate languages, and play many human games at human or superhuman levels. These systems are highly abstracted, but are inspired by biological brains and use only…
While both shape and texture are fundamental to visual recognition, research on deep neural networks (DNNs) has predominantly focused on the latter, leaving their geometric understanding poorly probed. Here, we show: first, that optimized…
The paper uses statistical and differential geometric motivation to acquire prior information about the learning capability of an artificial neural network on a given dataset. The paper considers a broad class of neural networks with…