Deductive Association Networks

TL;DR

This paper introduces Deductive Association Networks (DANs), a novel network architecture capable of deductive reasoning, demonstrated through applying group theory to MNIST data for deductive learning.

Contribution

The paper presents DANs, a new approach that integrates deductive reasoning into neural networks, enabling high-dimensional logical inference within machine learning models.

Findings

Successfully applied deductive reasoning to MNIST data

Demonstrated the ability to infer new relationships from axioms

Showed potential for logical inference in neural networks

Abstract

we introduce deductive association networks(DANs), a network that performs deductive reasoning. To have high-dimensional thinking, combining various axioms and putting the results back into another axiom is necessary to produce new relationships and results. For example, it would be given two propositions: "Socrates is a man." and "All men are mortals." and two propositions could be used to infer the new proposition, "Therefore Socrates is mortal.". To evaluate, we used MNIST Dataset, a handwritten numerical image dataset, to apply it to the group theory and show the results of performing deductive learning.