First Principle Neural Networks: Explicit Causal Disentanglement via Dual-Stream Encoders and HSIC Constraints

Deep learning models notoriously rely on spurious correlations (e.g., "green background" implies "frog"), leading to poor generalization. In this work, we propose the First Principle Neural Network (FPNN), a framework grounded in the fundamental causal axiom: Observation = Truth + Assumption. Unlike prior methods that optimize implicit objectives, FPNN realizes this axiom structurally. By explicitly modeling the "Assumption" (Bias) via a frozen encoder and mathematically "subtracting" it from the "Observation" via HSIC orthogonality constraints, we recover the "Truth". We demonstrate this approach on Colored MNIST, Waterbirds (83.6% WGA), and NICO++ (89.7% Accuracy), providing white-box visual proofs that the model physically decouples object features from context.