Title: Scaling Laws and Complexity of Generative Models: A Multifractal Perspective
Primary area: generative models
Keywords: Multifractal, Characterization, Generative Models

Abstract: Assessing the functional aspects of a generative model (GM) is crucial to technological advancement. However, existing evaluation metrics are often insensitive to distributional changes and rarely correlate with perceptual fidelity. In addition, their oversimplified assumptions limit their ability to assess morphological fidelity and contextuality in application areas such as medical imaging and industrial machine vision. Hence, domain-agnostic, robust, and reliable GM evaluation remains an unresolved problem in generative AI and is an ongoing research paradigm. So, this work introduces the concept of multifractality, a scaling technique adapted from statistical physics for GM evaluation. Several multifractal markers are proposed as new metrics to analyze the scaling behavior of GMs. They characterize the structural complexity of long-range correlation patterns in GM-generated images. Non-parametric statistics-based hypothesis testing is formulated to assess the disparity in morphological organization between synthesized and actual data. These metrics are extensively validated using benchmark GMs on real-world datasets. Furthermore, multifractal spectrum analysis provides deeper insights into a GM's complexity origin and plausible spectral bias explainability.

TL;DR: Multifractal Characterization of Generative Models