In this paper, we present a novel framework of graded neural networks (GNNs) built on the grade vector space $\V_\w^n$, which extends traditional neural network architectures by incorporating algebraic grading. We introduce grade neurons, layers, activation functions, and loss functions that adapt to feature importance by exploiting the coordinate-wise grade structure with scalar actions $\lambda \star \x = (\lambda^{q_i} x_i)$, defined by tuples $\w = (q_0, \ldots, q_{n-1})$. After establishing the theoretical properties of the grade space, we present a comprehensive GNN design that addresses computational challenges such as numerical stability and gradient scaling. Potential applications span machine learning and photonic systems, exemplified by a high-speed laser-based implementation. This work provides a foundational step toward grade computation that combines mathematical rigor with practical potential, and paves the way for future empirical and hardware explorations.
