ULLER

NeSyCat Torch: Differentiable tensor framework unifying neurosymbolic semantics via monadic abstraction

NeSyCat Torch extends the NeSyCat/ULLER neurosymbolic framework with neural network support for predicates and functions, implemented via probabilistic programming and tensor backends (HaskTorch, JAX, PyTorch). The key technical contribution is a lazy log-tensor monad over the log-semiring enabling numerically stable, differentiable training, alongside a batch monad for efficient batched inference. On MNIST addition benchmarks, the implementations outperform LTN and DeepProbLog in speed and accuracy while remaining within a uniform categorical framework that generalizes across first-order neurosymbolic approaches. The work positions itself as a unifying foundation for classical, fuzzy, probabilistic, and neural truth semantics.