Analytical Derivation of Universal ReLU Networks via Segmented Linear Regression Model (SLRM)

Traditional Artificial Neural Networks (ANNs) rely on stochastic optimization to approximate non-linear functions, often resulting in high computational entropy and "black-box" opacity. This paper presents the Segmented Linear Regression Model (SLRM), a deterministic framework that treats function approximation as a geometric compression task. By employing a two-stage elimination process —Lossless Geometric Invariance and Lossy epsilon-Tolerance— we demonstrate that SLRM can analytically deduce the exact weights of a ReLU-based architecture without iterative training.