An AI Monkey Gets Grapes for Sure -- Sphere Neural Networks for Reliable Decision-Making

TL;DR

This paper introduces Sphere Neural Networks that embed concepts on a sphere to enable reliable logical reasoning, outperforming traditional neural methods in syllogistic tasks and avoiding catastrophic forgetting.

Contribution

It proposes Sphere Neural Networks with concept embeddings on a sphere, improving logical reasoning reliability and handling negation effectively, surpassing existing neural reasoning approaches.

Findings

Sphere Neural Networks master 16 syllogistic reasoning tasks.

They effectively represent negation via complement circles.

They outperform LLMs and supervised learning in reliability.

Abstract

This paper compares three methodological categories of neural reasoning: LLM reasoning, supervised learning-based reasoning, and explicit model-based reasoning. LLMs remain unreliable and struggle with simple decision-making that animals can master without extensive corpora training. Through disjunctive syllogistic reasoning testing, we show that reasoning via supervised learning is less appealing than reasoning via explicit model construction. Concretely, we show that an Euler Net trained to achieve 100.00% in classic syllogistic reasoning can be trained to reach 100.00% accuracy in disjunctive syllogistic reasoning. However, the retrained Euler Net suffers severely from catastrophic forgetting (its performance drops to 6.25% on already-learned classic syllogistic reasoning), and its reasoning competence is limited to the pattern level. We propose a new version of Sphere Neural Networks that embeds concepts as circles on the surface of an n-dimensional sphere. These Sphere Neural Networks enable the representation of the negation operator via complement circles and achieve reliable decision-making by filtering out illogical statements that form unsatisfiable circular configurations. We demonstrate that the Sphere Neural Network can master 16 syllogistic reasoning tasks, including rigorous disjunctive syllogistic reasoning, while preserving the rigour of classical syllogistic reasoning. We conclude that neural reasoning with explicit model construction is the most reliable among the three methodological categories of neural reasoning.