Distinguishing Energy-Based Models from MLPs: Analyzing OOD Handling and Discontinuous Distributions

Expert Analysis: The EBM-MLP Dichotomy in Out-of-Distribution and Discontinuous Regimes Fundamental Mechanisms and Behavioral Divergence The divergence between Energy-Based Models (EBMs) and Multi-Layer Perceptrons (MLPs) hinges on their core mechanisms for handling variable configurations and extrapolation. EBMs associate a scalar energy to variable configurations, minimizing this energy for both inference and learning. This process inherently avoids assumptions of continuity and linearity, enabling EBMs to handle discontinuous distributions and unsampled kinks without imposing artificial structures. In contrast, MLPs rely on piecewise linear extrapolation near training data boundaries due to ReLU activation, intrinsically assuming continuity and linearity. This architectural difference manifests in distinct observable effects: EBMs exhibit an absence of spandrels in out-of-distribution (OOD) regions and robustly handle discontinuities, whereas MLPs produce spandrels and artificial ki