Optimal hyperdimensional representation for learning and cognitive computation

Hyperdimensional Computing (HDC) is a neurally inspired computing paradigm that leverages lightweight, high-dimensional operations to emulate key brain functions. Recent advances in HDC have primarily targeted two domains: learning, where the goal is to extract and generalize patterns for tasks such as classification, and cognitive computation, which requires accurate information retrieval for human-like reasoning. Although state-of-the-art HDC methods achieve strong performance in both areas, they lack a principled understanding of the fundamentally different requirements imposed by learning vs. cognition. In particular, existing works provide limited guidance on designing encoding methods that generate optimal hyperdimensional representations for these distinct tasks. In this study, we proposed the first universal hyperdimensional encoding method that dynamically adapts to the needs of both learning and cognitive computation. Our approach is based on neural-symbolic techniques that assign random complex hypervectors to atomic bases (e.g., alphabet definitions) and then apply algebraic operations in the high-dimensional hyperspace to control the correlation structure among encoded data points. Through theoretical analysis, we show that learning tasks benefit from correlated representations to maximize memorization and generalization capacity, whereas cognitive tasks require orthogonal, highly separable representations to enable accurate decoding and reasoning. We further derived a separation metric that quantifies this trade-off and validated it empirically across image classification and decoding tasks. Our results demonstrate that tuning the encoder to increase correlation improves classification accuracy from 65% to 95%, while maximizing separation enhances decoding accuracy from 85% to 100%. These findings provide the first systematic framework for designing hyperdimensional encoders that unify learning and cognition under a single, theoretically grounded representation model.