Neural Acceleration for Graph Partitioning

Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We consider the problem of learning over this Laplacian in a distributed streaming setting, where new edges of the graph are observed in real time by a network of workers. In this setting, it is hard to learn quickly or approximately while keeping a distributed representation of L. To address this challenge, we present a novel algorithm, GSQUEAK, which efficiently sparsifies the Laplacian by maintaining a small subset of effective resistances. We show that our algorithm produces sparsifiers with strong spectral approximation guarantees, all while processing edges in a single pass and in a distributed fashion.

It is well established that spectral graph neural networks (GNNs) can universally approximate node signals; however, their expressive power remains bounded by the 1-dimensional Weisfeiler-Lehman test, which is mirrored in their lack of universality for higher-order signals. To go beyond this bound, we propose the Full-Spectrum GNNs (FSpecGNNs), a second-order generalization of classical spectral GNNs. FSpecGNN advances spectral filtering from two perspectives: (1) it lifts signals from the node domain to the node-pair domain; and (2) it extends the univariate spectral filter over eigenvalues to a bivariate filter over eigenvalue pairs. We show that classical spectral GNNs arise as a diagonal special case of FSpecGNNs, and prove that FSpecGNNs can be at most as expressive as Local 2-GNN while universally approximating node-pair signals, the latter being particularly beneficial for heterophilic graph learning. Moreover, FSpecGNN admits scalable implementations that avoid explicit node-pair-level computations; combined with a low-rank approximation that reduces full-spectrum convolution to a combination of polynomial spectral filters, it enables learning on large graphs. Empirically, FSpecGNN validates the predicted expressivity and delivers strong performance on heterophilic benchmarks.

Efficient computation of shortest paths in weighted graphs is a fundamental problem with many applications. Neuromorphic hardware platforms promise massively parallel, efficient computation, changing parallelism tradeoffs. In this work, we introduce NEURO-MAPP (Neuromorphic-based Min-Add Parallel Propagation), a distributed shortest path algorithm designed to use the local computation and network communication available in neuromorphic systems. We provide an optimized implementation of the algorithm on the SpiNNaker 2 platform and evaluate its performance on a selection of synthetic and real-world graphs. These results are compared to Dijkstra's algorithm on a modern CPU. We find that the NEURO-MAPP implementation scales favorably in terms of runtime for many graph types while consuming less energy per shortest-path query than the CPU implementation in almost all cases. These findings highlight the potential of neuromorphic hardware featuring sparse, spike-based communication as a scalable and energy-efficient platform for computation in graph search and related tasks.