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

2026-01-01

arXiv.org

AI Summary

Existing neural reasoning approaches—such as large language models and supervised learning—exhibit insufficient reliability on simple deductive tasks, struggle to uniformly handle both classical and disjunctive syllogisms, and are prone to catastrophic forgetting. This work proposes a novel neural reasoning architecture grounded in explicit model construction, which uniquely embeds logical concepts as points on an n-dimensional hypersphere and represents logical negation via complementary spherical caps. Rigorous inference is achieved by filtering out inconsistent geometric configurations of these caps. The proposed method attains 100% accuracy across all 16 syllogistic reasoning tasks, demonstrating unified competence in both classical and disjunctive reasoning while exhibiting no catastrophic forgetting, thereby significantly outperforming current state-of-the-art approaches.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• neural reasoning
• disjunctive syllogism
• catastrophic forgetting
• reliable decision-making
• logical reasoning

Innovation

• Sphere Neural Networks
• disjunctive syllogistic reasoning
• catastrophic forgetting
• explicit model-based reasoning
• logical negation