The ability to compare objects, scenes, or situations is crucial for effective decision-making and problem-solving in everyday life. For instance, comparing the freshness of apples enables better choices during grocery shopping, while comparing sofa designs helps optimize the aesthetics of our living space. Despite its significance, the comparative capability is largely unexplored in artificial general intelligence (AGI).

Modern deep neural networks, while strong in many domains [29], have notmastered comparable language-basedgeneralization challenges, afactconjectured tounderlie their sample inefficiencyand inflexibility [26,25,8].

In this paper, we present a theory of stochastic optimal control (SOC) tailored to infinite-dimensional spaces, aiming to extend diffusion-based algorithms to function spaces. Specifically, we demonstrate how Doob's

We introduce a general framework for active learning in regression problems.