Predicate Neuron: Differentiable Quantization of Predicate Relations in Gradient-based Learning

Abstract

In machine learning, symbolic reasoning approaches often rely on static architectures that hinder integration into deep neural networks and gradient-based optimization. To address this, we introduce the Native Predicate Neuron, a differentiable logic-reasoning neural module that enriches standard architectures with symbolic reasoning capabilities via first-order logic quantization. The proposed neuron models relational logic by learning to alternate between operations using a single trainable parameter. It features a tailored gradient mechanism with a dual-nature formulation: executing hard logical operations during training while maintaining differentiability for backpropagation. By quantizing both its input and choice state, the Predicate Neuron approximates continuous and non-continuous functions, effectively resolving discontinuities that standard deep learning architectures struggle with. We evaluate the Predicate Neuron across Fully-Connected, Convolutional, Recurrent, and Transformer architectures on benchmarks like MNIST and Wikitext. Results show that incorporating Predicate Neurons accelerates convergence, boosts accuracy, and lowers loss in general, with particularly strong improvements in tasks requiring monotonic reasoning or handling discontinuities. Overall, the Predicate Neuron natively integrates into standard neural networks to enable fuzzy logic operations and is available in Keras and PyTorch.