Title: An AI Monkey Gets Grapes for Sure -- Sphere Neural Networks for Reliable Decision-Making
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: Neural Reasoning, Deterministic Reasoning, Syllogism

Abstract: By increasing the amount and the quality of training data, we may improve the logical reasoning performances of LLMs, but they are still unreliable and struggle with simple decision-making, an ability that animals may develop without language. 
This paper proposes a new version of Sphere Neural Networks that embeds concepts as circles on the surface of an n-dimensional sphere. This new version enables the representation of the negation operator through complement circles and can achieve reliable decision-making by eliminating unsatisfiable circle configurations. Comparative experiments with supervised neural reasoning are performed by retraining Euler Net for disjunctive syllogistic reasoning, the foundation for decision-making. We demonstrate that the proposed Sphere Neural Network achieves rigorous disjunctive syllogistic reasoning as well as 15 other syllogistic-style reasoning tasks, while preserving the rigour of classical syllogistic reasoning. In contrast, an Euler Net achieving 100.00% in classic syllogistic reasoning can be trained to reach 100% accuracy in disjunctive syllogistic reasoning. However, after that, its performances dropped to 6.25% in classic syllogistic reasoning, then subsequently dropped to 75.00%, 53.57%, and 46.43% when input images had random colour, random colour and boundary thickness, or filled circles, respectively. This comparison favours the method of neural reasoning with explicit model construction and suggests seeking alternative neural methods to enhance the reliability of neural decision-making.