FactorHD: A Hyperdimensional Computing Model for Multi-Object Multi-Class Representation and Factorization

Abstract: Neuro-symbolic artificial intelligence (neuro-symbolic AI) excels in logical analysis and reasoning. Hyperdimensional Computing (HDC), a promising brain-inspired computational model, is integral to neuro-symbolic AI. Various HDC models have been proposed to represent class-instance and class-class relations, but when representing the more complex class-subclass relation, where multiple objects associate different levels of classes and subclasses, they face challenges for factorization, a crucial task for neuro-symbolic AI systems. In this article, we propose FactorHD, a novel HDC model capable of representing and factorizing the complex class-subclass relation efficiently. FactorHD features a symbolic encoding method that embeds an extra memorization clause, preserving more information for multiple objects. In addition, it employs an efficient factorization algorithm that selectively eliminates redundant classes by identifying the memorization clause of the target class. Such model significantly enhances computing efficiency and accuracy in representing and factorizing multiple objects with class-subclass relation, overcoming limitations of existing HDC models such as "superposition catastrophe" and "the problem of 2". Evaluations show that FactorHD achieves approximately 5667x speedup at a representation size of 10^9 compared to existing HDC models. When integrated with the ResNet-18 neural network, FactorHD achieves 92.48% factorization accuracy on the Cifar-10 dataset.