Answer Set Programming Energised! End-to-End Neurosymbolic Reasoning and Learning with ASP and Energy Based Models

ASPEn (Answer Set Programming Energised) addresses the challenge of integrating high-level symbolic reasoning with low-level neural perception. While many neurosymbolic systems treat reasoning as a post-processing step or a filter for neural outputs, ASPEn embeds symbolic semantics directly into the learning loop. It achieves this by mapping ASP stable models to configurations in a continuous energy landscape, where logical rules define the feasible hypothesis space and neural networks provide the energy scores.

At the core of ASPEn is the concept of 'energised' atoms. Users define an ASP program that includes standard logical rules alongside special energy predicates. These predicates link symbolic atoms to neural energy functions. During inference, the system uses the Clingo solver to find the stable model that minimizes the total energy—the sum of the neural outputs for the active atoms. During training, the framework employs a contrastive free-energy objective. It pushes down the energy of stable models that satisfy supervision constraints (positive phase) while pushing up the energy of unconstrained models (negative phase), effectively shaping the neural network's parameters to align with the symbolic domain knowledge.

This approach is particularly powerful for dynamic, real-world domains where partial observability and noise are prevalent. By allowing symbolic constraints (like commonsense knowledge about space and motion) to influence the neural optimization process, ASPEn ensures that the learned representations remain consistent with the underlying logic of the problem. The authors demonstrate that this methodology scales from simple tasks like MNIST digit addition to complex benchmarks like CLEVR for visual reasoning and MOT for multi-object tracking.