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.