Linear Region

Linear regions, the piecewise linear segments partitioning the input space of neural networks, are a key focus in understanding network expressiveness and generalization. Current research investigates the number and distribution of these regions in various architectures, including ReLU, Maxout, and graph convolutional networks (GCNs), employing techniques like polyhedral complex analysis and multi-resolution segmentation to analyze their structure and impact on performance. Understanding the relationship between linear region geometry, network sparsity, and model accuracy is crucial for improving network design, optimization, and ultimately, the performance of machine learning models in diverse applications. This research also helps clarify the role of network depth and width in determining model complexity.