Compositional neurosymbolic representations enable efficient active exploration.

Autonomous systems that learn and explore over long horizons face a problem. Standard methods scale poorly in the number of observations, n, precluding sustained operation on bounded hardware. We show that compositional, high-dimensional vector representations inspired by neural computation address these constraints. We use these representations to construct a Bayesian optimization (BO) algorithm that operates in complex spaces and reduces the time and memory requirements compared to state-of-the-art BO algorithms on diverse tasks. Whereas standard methods incur O(n3) time and O(n2) memory complexity, our approach holds both at O(d2) in the embedding dimension, which remains constant over the algorithm's lifetime. Our algorithm reduces compute time by 60-200 × without loss in accuracy. Implementation on neuromorphic hardware reduces energy consumption per sample by 30-188 × . These efficiencies stem from converting sample selection into continuous optimization on a compact domain, implementable by gradient methods or neural dynamics, enabling long-term, resource-bound, autonomous exploration.