Low Dimension

Low-dimensionality research focuses on understanding and leveraging the often surprisingly low-dimensional structure underlying high-dimensional data, particularly in machine learning contexts. Current efforts investigate how neural networks, including deep networks with various activation functions and architectures (e.g., ReLU, piecewise linear), learn and represent this low-dimensional structure, often employing techniques like Lasso regression and analyzing bottleneck structures within the networks. This work is significant because it improves our understanding of model generalization, efficiency, and robustness, with implications for applications ranging from robot navigation and knowledge graph embedding to regression analysis and efficient training algorithms.