Graph Neural Networks (GNNs) excel at jointly modeling node features and topology, yet their black-box nature limits their adoption in real-world applications where interpretability is desired. Inspired by the success of interpretable Neural Additive Models (NAM) for tabular data, Graph Neural Additive Network (GNAN) extends the additive modeling approach to graph data to overcome limitations of GNNs. While being interpretable, GNAN representation learning overlooks the importance of local aggregation and more importantly suffers from parameter complexity. To mitigate the above challenges, we introduce Graph Neural Additive Model with Random Fourier Features (G-NAMRFF), a lightweight, self‐interpretable graph additive architecture. G-NAMRFF represents each node embedding as the sum of feature‐wise contributions where contributions are modeled via a Gaussian process (GP) with a graph- and feature-aware kernel. Specifically, we construct a kernel using Radial Basis Function (RBF) with graph structure induced by Laplacian and learnable Finite Impulse Response (FIR) filter. We approximate the kernel using Random Fourier Features (RFFs) which transforms the GP prior to a Bayesian formulation, which are subsequently learnt using a single layer neural network with size equal to number of RFF features. G-NAMRFF is light weight with $168\times$ fewer parameters compared to GNAN. Despite its compact size, G-NAMRFF matches or outperforms state-of-the-art GNNs and GNAN on node and graph classification tasks, delivering real-time interpretability without sacrificing accuracy.

In this work, we focus on recovering signals over simplicial complexes from subsampled observations. In particular, we subsample a simplicial signal of a certain order and focus on recovering multi-order bandlimited simplicial signals of one order higher and one order lower, wherein the observations are collected using a neighborhood aggregation sampling mechanism. To do so, we assume that the simplicial signal admits the Hodge decomposition that relates simplicial signals of different orders. Next, we propose a simple least squares estimator for recovery. We also provide theoretical conditions on the number of aggregations and size of the sampling set required for faithful reconstruction as a function of the bandwidth of simplicial signals to be recovered. Numerical experiments are provided to show the effectiveness of the proposed method.

We consider recovery of signals over product cell structures from subsampled observations. In particular, we consider product cell complexes, which can be factorized as the Cartesian product of two simplicial complexes. We focus on recovering edge and node signals from subsampled signals on the factor simplicial complexes. To do so, we first express bandlimited edge signals on the product cell complex as a direct sum of the Kronecker product of bandlimited edge and node signals on the factor simplicial complexes. Then, we propose a simple least squares solution for estimating the edge signal on the product complex. Next, we leverage the Helmholtz-Hodge decomposition on product spaces and propose a simple least squares estimator to recover node signals on the product cell complex. We evaluate the proposed method on both synthetic and real data.