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Sharing genomic databases is critical to the collaborative research in computational biology. A shared database is more informative than specific genome-wide association studies (GWAS) statistics as it enables do-it-yourself calculations. Genomic databases involve intellectual efforts from the curator and sensitive information of participants, thus in the course of data sharing, the curator (database owner) should be able to prevent unauthorized redistributions and protect genomic data privacy. As it becomes increasingly common for a single database be shared with multiple recipients, the shared genomic database should also be robust against collusion attack, where multiple malicious recipients combine their individual copies to forge a pirated one with the hope that none of them can be traced back. The strong correlation among genomic entries also make the shared database vulnerable to attacks that leverage the public correlation models. In this paper, we assess the robustness of shared genomic database under both collusion and correlation threats. To this end, we first develop a novel genomic database fingerprinting scheme, called Gen-Scope. It achieves both copyright protection (by enabling traceability) and privacy preservation (via local differential privacy) for the shared genomic databases. To defend against collusion attacks, we augment Gen-Scope with a powerful traitor tracing technique, i.e., the Tardos codes. Via experiments using a real-world genomic database, we show that Gen-Scope achieves strong fingerprint robustness, e.g., the fingerprint cannot be compromised even if the attacker changes 45% of the entries in its received fingerprinted copy and colluders will be detected with high probability. Additionally, Gen-Scope outperforms the considered baseline methods. Under the same privacy and copyright guarantees, the accuracy of the fingerprinted genomic database obtained by Gen-Scope is around 10% higher than that achieved by the baseline, and in terms of preservations of GWAS statistics, the consistency of variant-phenotype associations can be about 20% higher. Notably, we also empirically show that Gen-Scope can identify at least one of the colluders even if malicious receipts collude after independent correlation attacks. 

Graph neural networks (GNNs) have shown great potential in learning on graphs, but they are known to perform sub-optimally on link prediction tasks. Existing GNNs are primarily designed to learn node-wise representations and usually fail to capture pairwise relations between target nodes, which proves to be crucial for link prediction. Recent works resort to learning more expressive edge-wise representations by enhancing vanilla GNNs with structural features such as labeling tricks and link prediction heuristics, but they suffer from high computational overhead and limited scalability. To tackle this issue, we propose to learn structural link representations by augmenting the message-passing framework of GNNs with Bloom signatures. Bloom signatures are hashing-based compact encodings of node neighborhoods, which can be efficiently merged to recover various types of edge-wise structural features. We further show that any type of neighborhood overlap-based heuristic can be estimated by a neural network that takes Bloom signatures as input. GNNs with Bloom signatures are provably more expressive than vanilla GNNs and also more scalable than existing edge-wise models. Experimental results on five standard link prediction benchmarks show that our proposed model achieves comparable or better performance than existing edge-wise GNN models while being 3-200 × faster and more memory-efficient for online inference. 

Set representation has become ubiquitous in deep learning for modeling the inductive bias of neural networks that are insensitive to the input order. DeepSets is the most widely used neural network architecture for set representation. It involves embedding each set element into a latent space with dimension L, followed by a sum pooling to obtain a whole-set embedding, and finally mapping the whole-set embedding to the output. In this work, we investigate the impact of the dimension L on the expressive power of DeepSets. Previous analyses either oversimplified high-dimensional features to be one-dimensional features or were limited to analytic activations, thereby diverging from practical use or resulting in L that grows exponentially with the set size N and feature dimension D. To investigate the minimal value of L that achieves sufficient expressive power, we present two set-element embedding layers: (a) linear + power activation (LP) and (b) linear + exponential activations (LE). We demonstrate that L being poly(N,D) is sufficient for set representation using both embedding layers. We also provide a lower bound of L for the LP embedding layer. Furthermore, we extend our results to permutation-equivariant set functions and the complex field. 

Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) \emph{Non-uniqueness}: there are many different eigendecompositions of the same Laplacian, and (2) \emph{Instability}: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to poor generalization on unseen graph structures. We identify the cause of instability to be a ``hard partition'' of eigenspaces. Hence, we introduce Stable and Expressive Positional Encodings (SPE), an architecture for processing eigenvectors that uses eigenvalues to ``softly partition'' eigenspaces. SPE is the first architecture that is (1) provably stable, and (2) universally expressive for basis invariant functions whilst respecting all symmetries of eigenvectors. Besides guaranteed stability, we prove that SPE is at least as expressive as existing methods, and highly capable of counting graph structures. Finally, we evaluate the effectiveness of our method on molecular property prediction, and out-of-distribution generalization tasks, finding improved generalization compared to existing positional encoding methods.