CryptoKANs+: KAN-Inspired Self-Learning Polynomial Networks for Efficient Privacy-Preserving Machine Learning

Processing sensitive data in cloud-based neural networks raises privacy concerns, which Homomorphic Encryption addresses by enabling privacy-preserving machine learning. In our previous work, we introduced CryptoKANs, enabling efficient Kolmogorov–Arnold Network (KAN) inference over encrypted data via polynomial approximation of spline-based activation functions using KAN symbolization. To avoid performance degradation, CryptoKAN required min–max scaling of pre-activation inputs to a small interval—a requirement that could negatively affect training. In addition, a direct theoretical structural comparison with Multi-Layer Perceptron (MLP)-based solutions, such as CryptoNets, was missing. In this work, we address these limitations by presenting CryptoKAN+, a KAN-inspired network integrating self-learned polynomial activations through a Fully Connected Quadratic Transformation (FCQT) layer. By enforcing polynomial activations during training, this design replaces spline functions without post-training symbolization, eliminates the need for interval scaling, absorbs subsequent linear transformations, and reduces multiplicative depth for efficient encrypted inference. Experiments show that CryptoKAN+ achieves competitive accuracy while slightly improving encrypted inference efficiency—a natural consequence of compacting weights with self-learned activations. Overall, this work provides a formal analysis of the structural relationship between KANs and MLPs and demonstrates how enforcing polynomial activations during training enables efficient encrypted inference while preserving accuracy.