Rpn model

To model the underlying data distribution mapping \(f: R^m \to R^n\), the RPN model disentangle the input data from model parameters into three component functions:

• Data Expansion Function: \(\kappa: R^m \to R^D\).
• Parameter Reconciliatoin Function: \(\psi: R^l \to R^{n \times D}\).
• Remainder Function \(\pi: R^m \to R^n\).

So, the underlying mapping \(f\) can be approximated by RPN as the inner product of the expansion function with the reconciliation function, subsequentlly summed with the remainder function: $$ g(\mathbf{x} | \mathbf{w}) = \left \langle \kappa(\mathbf{x}), \psi(\mathbf{w}) \right \rangle + \pi(\mathbf{x}). $$