A homotopy-type-theoretic generalization of neurosymbolic inference

This article introduces a novel framework for neurosymbolic (NeSy) inference using homotopy type theory, which replaces traditional set-based structures with types to preserve critical information about symmetries and proofs. The proposed belief-weighted homotopy cardinality allows for more accurate reasoning in NeSy systems, demonstrating improved calibration on MNIST reasoning-shortcut benchmarks compared to diversity-trained ensembles, while maintaining label accuracy. The framework's implementation is available on GitHub, providing a valuable resource for practitioners aiming to enhance NeSy methodologies.