Neural Constraint Solvers Need Symbolic Integration for Correctness

While neural networks have shown impressive accuracy in solving constraint satisfaction problems, they fundamentally struggle with ensuring absolute correctness, particularly when encountering data outside their training distribution. A new position paper highlights that these neural solvers can still produce invalid solutions, even with high confidence. The authors contend that for applications where hard constraints exist and verifying a solution is computationally inexpensive, neural constraint reasoning must prioritize integration with symbolic methods over purely learning-based approaches. The paper uses Sudoku as a prime example, illustrating the asymmetry between the difficulty of solving (NP-complete) and the ease of verifying a solution (polynomial time). It surveys various solving methods, concluding that neural-only approaches lack the provable correctness that symbolic or neuro-symbolic methods can provide. The proposed solution involves a bidirectional integration: neural networks can enhance symbolic solvers by learning heuristics and converting perceptual data into symbolic representations, while symbolic methods can rigorously verify the outputs of neural networks. This multi-agent certified reasoning framework aims to combine computational efficiency with guaranteed correctness.