NeSyCat Torch Advances Neurosymbolic AI Learning Framework

The field of neurosymbolic AI often faces fragmentation due to differing definitions of truth across classical, fuzzy, probabilistic, and neural systems. NeSyCat Torch is presented as a significant step towards unifying these semantics under a single inductive definition, building upon the existing NeSyCat framework. This new implementation specifically addresses the previous lack of integration for predicates and functions learned by neural networks. NeSyCat Torch interprets computational symbols through neural networks, leveraging probabilistic programming and tensor-based backends. It employs a distribution monad for reference semantics and metric evaluation, complemented by a lazy log-tensor monad for numerically stable and differentiable training. A batch monad further enhances efficiency for batch processing. The framework's effectiveness was demonstrated on the MNIST addition task, where its HaskTorch, JAX, and PyTorch implementations outperformed established neurosymbolic methods like LTN and DeepProbLog in both speed and accuracy. While achieving nearly the accuracy of DeepStochLog, NeSyCat Torch maintains a more uniform and extensible framework, capable of applying to a broader range of first-order neurosymbolic approaches by being parametric in the monad.