Geometries of Learning

About this Research Topic

Background

Deep neural networks have demonstrated great success in many computer vision applications where intelligent recognition and analysis are performed based on high-dimensional visual data. However, in contrast to the rapid development of advanced architectures and training schemes, developments have been limited in the theory of analyzing deep neural networks and deep learning training through the lens of geometries. The lack of such analysis prevents further understanding and affects the acceptance of deep neural networks for practical applications. For example, deep neural networks are often challenged by their vulnerability to adversarial attacks, their lack of systematic guarantees on effectiveness and stability, and their degraded generalization capability outside the distribution of training data.

Geometric analysis holds promise in providing revolutionary insights into these challenges. In practice, observed visual data often lie on some low-dimensional manifolds embedded in a high-dimensional data space describing various latent properties such as the shape, color, or pose of imaged entities, the illumination of scenes and the characterization of sensors. Proper modeling and better understanding of such manifolds would create enormous opportunities for improving current deep learning technologies. For example, characterization of noises or sparsity patterns based on data manifolds can be leveraged to capture robust network mappings, while localization of data samples with respect to underlying manifolds can provide more informative descriptions other than recognition labels.

This Research Topic aims to collect state-of-the-art research tackling fundamental problems of deep learning from the perspective of geometries. We encourage submissions on novel theories, methods, and tools for investigating geometries of data manifolds which facilitate further understanding of the behavior of deep neural networks. We also encourage contributions on improving the design and training of deep neural networks based on manifold studies.

Topics of interests include, but are not limited to:
- Manifold learning for data and models in computer vision
- Topological analysis of deep neural networks
- Robustness, uniqueness, and stability of deep neural networks
- Geometric analysis applied to adversarial AI
- Geometric analysis applied to trainable AI with limited data/labels
- Geometric analysis applied to explainable AI

Keywords: deep learning, geometric analysis, manifold learning, adversarial AI, explainable AI, trainable AI, trustworthy AI

Important note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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