A Generalized Tikhonov Layer for Interpretable-by-design Graph Neural Networks
We propose the Tikhonov 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. For any input feature $x$, the layer output $Rx$ is the exact minimizer of a generalized graph Tikhonov problem that trades off node-level data fidelity against a topology-driven regularization penal...
| Authors | Nicolas Tremblay, Benjamin Ricaud, Filippo Maria Bianchi |
|---|---|
| Primary category | cs.LG |
| Published | 27 May 2026 |
| Last updated at source | 27 May 2026 |
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