When Witnesses Defend: A Witness Graph Topological Layer for Adversarial Graph Learning

Naheed Anjum Arafat, Debabrota Basu, Yulia Gel, Yuzhou Chen

Primary Area: learning on graphs and other geometries & topologies

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Keywords: Graph Neural Networks, Topological Data Analysis, Witness Complex, Adversarial Attacks

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Abstract:

Capitalizing on the intuitive premise that shape characteristics are more robust to perturbations, we bridge adversarial graph learning with the emerging tools from computational topology, namely, persistent homology representations of graphs. We introduce the concept of witness complex to adversarial analysis on graphs, which allows us to focus only on the salient shape characteristics of graphs, yielded by the subset of the most essential nodes (i.e., landmarks), with minimal loss of topological information on the whole graph. The remaining nodes are then used as witnesses, governing which higher-order graph substructures are incorporated into the learning process. Armed with the witness mechanism, we design Witness Graph Topological Layer (WGTL), which systematically integrates both
local and global topological graph feature representations whose impact are in turn automatically controlled by the robust regularized topological loss. We derive the important stability guarantees of both local and global topology encodings and the associated robust topological loss, given the attacker's budget. We illustrate versatility of WGTL by its integration with GNNs and existing non-topological defense mechanisms. Our extensive experiments demonstrate that WGTL boosts the robustness of GNNs against of a wide spectrum of adversarial attacks, leading to relative gains up to 18%.

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Submission Number: 5896