KLay: Accelerating Arithmetic Circuits for Neurosymbolic AI

Jaron Maene, Vincent Derkinderen, Pedro Zuidberg Dos Martires

Keywords: Neurosymbolic AI, Arithmetic Circuits, Sparse Inference

TL;DR: We speed-up neurosymbolic AI by evaluating arithmetic circuits efficiently on the GPU.

Abstract:

A popular approach to neurosymbolic AI involves mapping logic formulas to arithmetic circuits (computation graphs consisting of sums and products) and passing the outputs of a neural network through these circuits. This approach enforces symbolic constraints onto a neural network in a principled and end-to-end differentiable way. Unfortunately, arithmetic circuits are challenging to run on modern tensor accelerators as they exhibit a high degree of irregular sparsity. To address this limitation, we introduce knowledge layers (KLay), a new data structure to represent arithmetic circuits that can be efficiently parallelized on GPUs. Moreover, we contribute two algorithms used in the translation of traditional circuit representations to KLay and a further algorithm that exploits parallelization opportunities during circuit evaluations. We empirically show that KLay achieves speedups of multiple orders of magnitude over the state of the art, thereby paving the way towards scaling neurosymbolic AI to larger real-world applications.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

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Submission Number: 4580