Higher-order Graph Neural Networks (HOGNNs) based on the 2-FWL test achieve superior expressivity by modeling 2-node and 3-node interactions, but incur cubic computational cost. Existing efficiency methods typically reduce this burden at the expense of expressivity. We propose Co-Sparsify, a connectivity-aware sparsification framework that eliminates provably redundant computations while preserving full 2-FWL expressive power. Our key insight is that 3-node interactions are expressively necessary only within biconnected components, namely, maximal subgraphs where every node pair lies on a cycle. Outside these components, structural relationships are fully captured via 2-node message passing and graph readouts, rendering higher-order modeling unnecessary. Co-Sparsify restricts 2-node message passing to connected components and 3-node interactions to biconnected components, eliminating redundant computation without approximation or sampling. We prove that Co-Sparsified GNNs match the expressivity of the 2-FWL test. Empirically, when applied to PPGN, Co-Sparsify matches or exceeds accuracy on synthetic substructure counting tasks and achieves state-of-the-art performance on real-world benchmarks (ZINC, QM9 and TUD). This study demonstrates that high expressivity and scalability are not mutually exclusive: principled, topology-guided sparsification enables powerful, efficient GNNs with theoretical guarantees.

Despite the theoretical expressiveness of 2-dimensional Folklore Weisfeiler-Lehman (2-FWL) Graph Neural Networks (GNNs), a significant gap persists between their theoretical capacity and their practical performance. To bridge this gap, we identify a critical limitation in current Graph Structural Encodings (GSEs): insufficient sensitivity to subtle structural variations, particularly in local connectivity, spectral features, and distance-based patterns. We show that widely used GSEs-such as Relative Random Walk Probability (RRWP) and monomial-based methods-lack full sensitivity across spectral frequency bands and long-range distances. Moreover, they fail to capture fine-grained local connectivity, which is essential for identifying cut nodes, biconnected components, and other higher-order structures that 2-FWL GNNs theoretically encode. To address these limitations, we propose CSDGSE (Connectivity, Spectral, and Distance Graph Structural Encoding), a novel GSE framework that jointly enhances sensitivity to: (1) exact local connectivity via hierarchical graph decomposition(2) full-frequency spectral features using expressive graph polynomials (e.g., Chebyshev), and (3) full-range distance interactions. A key innovation is our scalable divide-and-conquer algorithm for computing exact local connectivity across all node pairs, enabling efficient integration into modern GSEs. Extensive experiments show that CSDGSE outperforms existing GSEs in capturing complex structural patterns, achieving state-of-the-art results on molecular property prediction benchmarks like ZINC. Our work sets a new standard for GSEs by aligning theoretical expressiveness with practical effectiveness through enhanced structural sensitivity.

Online advertising is widely used by commercial companies to attract customers. Tuning advertisement delivery to achieve a high conversion rate (CVR) is crucial for improving advertising effectiveness. Because advertisers require demandside platforms (DSPs) to deliver a certain number of ads within a fixed period, it is challenging to maximize CVR while satisfying ads delivery constraints. Such a combinatorial optimization problem is NP-hard when we have a considerable number of both ads and users. In this paper, we adopt Digital Annealer (DA), a quantum-inspired Ising computer, to solve the combinatorial optimization problem. The experimental evaluation result shows that the proposed method increases accuracy from 0.176 to 0.326 and achieves 20.8 times speed-up compared to baseline.