Convex and Bilevel Optimization for Neuro-Symbolic Inference and Learning

Understand

We leverage convex and bilevel optimization techniques to develop a general gradient-based parameter learning framework for neural-symbolic (NeSy) systems.

• We demonstrate our framework with NeuPSL, a state-of-the-art NeSy architecture.
• To achieve this, we propose a smooth primal and dual formulation of NeuPSL inference and show learning gradients are functions of the optimal dual variables.
• Additionally, we develop a dual block coordinate descent algorithm for the new formulation that naturally exploits warm-starts.