A Generalized Tikhonov Layer for Interpretable-by-design Graph Neural Networks

ArXi:2605.28578v1 Announce Type: new We propose the Tikhono layer, a graph neural network layer that is interpretable by design: once trained, its learned parameters directly reveal which node features and which aspects of the graph topology were leveraged for prediction. In practice, the layer's propagation matrix takes the closed-form $R = (p(L)+Q)^{-1} Q$, where $L$ is the normalized graph Laplacian, $Q = diag(q_1,.,q_n)$ a learnable diagonal matrix of positive node-importance scores, and $p(\cdot)$ a learnable polynomial.