A learnability analysis on neuro-symbolic learning

This paper presents a comprehensive theoretical analysis of the learnability of neuro-symbolic (NeSy) tasks within hybrid systems. We characterize the learnability of NeSy tasks by their derived constraint satisfaction problems (DCSPs), demonstrating that a task is learnable if and only if its corresponding DCSP admits a unique solution. Under mild assumptions, we establish the sample complexity for learnable tasks and show that, for general tasks, the asymptotic expected concept error is controlled by the degree of disagreement among DCSP solutions. Our findings unify the characterization of learnability and the phenomenon of reasoning shortcuts, providing theoretical guarantees and actionable guidance for the principled design of NeSy systems.