PRISM: Privacy-preserving Inference System with Homomorphic Encryption and Modular Activation

With the rapid advancements in machine learning, models have become increasingly capable of learning and making predictions in various industries. However, deploying these models in critical infrastructures presents a major challenge, as concerns about data privacy prevent unrestricted data sharing. Homomorphic encryption (HE) offers a solution by enabling computations on encrypted data, but it remains incompatible with machine learning models like convolutional neural networks (CNNs), due to their reliance on non-linear activation functions. To bridge this gap, this work proposes an optimized framework that replaces standard non-linear functions with homomorphically compatible approximations, ensuring secure computations while minimizing computational overhead. The proposed approach restructures the CNN architecture and introduces an efficient activation function approximation method to mitigate the performance trade-offs introduced by encryption. Experiments on CIFAR-10 achieve 94.4% accuracy with 2.42 s per single encrypted sample and 24,000 s per 10,000 encrypted samples, using a degree-4 polynomial and Softplus activation under CKKS, balancing accuracy and privacy.

CUR Decompositions, Similarity Matrices, and Subspace Clustering

A general framework for solving the subspace clustering problem using the CUR decomposition is presented. The CUR decomposition provides a natural way to construct similarity matrices for data that come from a union of unknown subspaces $\mathscr{U}=\underset{i=1}{\overset{M}\bigcup}S_i$. The similarity matrices thus constructed give the exact clustering in the noise-free case. Additionally, this decomposition gives rise to many distinct similarity matrices from a given set of data, which allow enough flexibility to perform accurate clustering of noisy data. We also show that two known methods for subspace clustering can be derived from the CUR decomposition. An algorithm based on the theoretical construction of similarity matrices is presented, and experiments on synthetic and real data are presented to test the method. Additionally, a heuristic algorithm for motion segmentation is presented which yields the best overall performance to date for clustering the Hopkins155 motion dataset.