Homomorphic WiSARDs: Efficient Weightless Neural Network training over encrypted data

The widespread application of machine learning algorithms is a matter of increasing concern for the data privacy research community, and many have sought to develop privacy-preserving techniques for it. Among existing approaches, the homomorphic evaluation of ML algorithms stands out by performing operations directly over encrypted data, enabling strong guarantees of confidentiality. The homomorphic evaluation of inference algorithms is practical even for relatively deep Convolution Neural Networks (CNNs). However, training is still a major challenge, with current solutions often resorting to lightweight algorithms that can be unfit for solving more complex problems, such as image recognition. This work introduces the homomorphic evaluation of Wilkie, Stonham, and Aleksander's Recognition Device (WiSARD) and subsequent Weightless Neural Networks (WNNs) for training and inference on encrypted data. Compared to CNNs, WNNs offer better performance with a relatively small accuracy drop. We develop a complete framework for it, including several building blocks that can be of independent interest. Our framework achieves 91.7% accuracy on the MNIST dataset after only 3.5 minutes of encrypted training (multi-threaded), going up to 93.8% in 3.5 hours. For the HAM10000 dataset, we achieve 67.9% accuracy in just 1.5 minutes, going up to 69.9% after 1 hour. Compared to the state of the art on the HE evaluation of CNN training, Glyph (Lou et al., NeurIPS 2020), these results represent a speedup of up to 1200 times with an accuracy loss of at most 5.4%. For HAM10000, we even achieved a 0.65% accuracy improvement while being 60 times faster than Glyph. We also provide solutions for small-scale encrypted training. In a single thread on a desktop machine using less than 200MB of memory, we train over 1000 MNIST images in 12 minutes or over the entire Wisconsin Breast Cancer dataset in just 11 seconds.