Lipschitz-based robustness estimation for hyperdimensional learning

With the adoption of machine learning models in various practical domains, there is a growing need for evaluating and increasing model robustness. Hyperdimensional computing (HDC) is a neurosymbolic computational paradigm that represents symbols as high dimensional vectors and symbolic operations as vector operations, seamlessly interfacing between neuro- and symbolic components of a model. However, there is a notable gap in HDC research regarding the robustness of HDC models to input perturbations. This study presents a novel theoretical framework tailored to evaluate the robustness of hyperdimensional classifiers against perturbations in the input space. In particular, our proposed measure of robustness gives a theoretical upper bound for the magnitude of noise a model can tolerate without changing its prediction for any given data point. We also propose a method to enhance the robustness of the model based on our proposed measure of robustness. Our approach introduces several methods to calculate model robustness as a function of the specific dataset and type of hyperdimensional encoding used. The results show that the average robustness of HDC models increases under the proposed optimization scheme while maintaining accuracy by varying the variance of the Gaussian distribution used to encode hypervectors. The practical effectiveness of our proposed measure of robustness is also demonstrated.