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The growth of Graph Convolution Network (GCN) model sizes has revolutionizednumerous applications, surpassing human performance in areas such as personalhealthcare and financial systems. The deployment of GCNs in the cloud raisesprivacy concerns due to potential adversarial attacks on client data. Toaddress security concerns, Privacy-Preserving Machine Learning (PPML) usingHomomorphic Encryption (HE) secures sensitive client data. However, itintroduces substantial computational overhead in practical applications. Totackle those challenges, we present LinGCN, a framework designed to reducemultiplication depth and optimize the performance of HE based GCN inference.LinGCN is structured around three key elements: (1) A differentiable structurallinearization algorithm, complemented by a parameterized discrete indicatorfunction, co-trained with model weights to meet the optimization goal. Thisstrategy promotes fine-grained node-level non-linear location selection,resulting in a model with minimized multiplication depth. (2) A compactnode-wise polynomial replacement policy with a second-order trainableactivation function, steered towards superior convergence by a two-leveldistillation approach from an all-ReLU based teacher model. (3) an enhanced HEsolution that enables finer-grained operator fusion for node-wise activationfunctions, further reducing multiplication level consumption in HE-basedinference. Our experiments on the NTU-XVIEW skeleton joint dataset reveal thatLinGCN excels in latency, accuracy, and scalability for homomorphicallyencrypted inference, outperforming solutions such as CryptoGCN. Remarkably,LinGCN achieves a 14.2x latency speedup relative to CryptoGCN, while preservingan inference accuracy of 75% and notably reducing multiplication depth.

LinGCN: Structural Linearized Graph Convolutional Network for Homomorphically Encrypted Inference