Expressive Power

Expressive power in machine learning focuses on quantifying the ability of models, particularly neural networks, to represent and distinguish complex data structures and functions. Current research emphasizes developing theoretical frameworks to analyze the expressive capabilities of various architectures, including graph neural networks (GNNs), transformers, and state-space models, often using techniques like the Weisfeiler-Lehman test and analysis of approximation rates. This research is crucial for designing more powerful and efficient models, improving their generalization performance, and ultimately advancing applications across diverse fields like graph analysis, natural language processing, and scientific computing. Understanding expressive power also helps in developing more robust and reliable models by identifying and addressing limitations in their representational capacity.