Finite Size

Finite-size effects in various machine learning models, such as Restricted Boltzmann Machines, neural networks (including feedforward, convolutional, and residual networks), and percolation models, are a significant area of current research. Studies focus on understanding how finite network size impacts training dynamics, phase transitions, signal propagation, and generalization performance, often employing techniques like finite-size scaling and mean-field theory to bridge the gap between theoretical analyses of infinite-size models and practical applications. This research is crucial for improving the accuracy and efficiency of machine learning algorithms, as it helps to explain and mitigate the discrepancies between theoretical predictions and real-world performance in finite-sized systems. The insights gained are also relevant to understanding fundamental aspects of learning and critical phenomena in complex systems.