Emergent Convexity

Emergent convexity explores the surprising appearance of convex structures in non-convex systems, particularly within machine learning and neural networks. Research focuses on understanding how convexity arises in various contexts, including the analysis of push-forward constraints in optimization problems, the impact of learning rules on neural network attractor landscapes, and the characterization of convexity in deep learning representations. These investigations are crucial for improving the efficiency and generalizability of machine learning algorithms, as well as for gaining insights into the underlying principles governing complex systems. The findings are impacting algorithm design, optimization strategies, and the interpretation of learned representations.