Sphere Neural-Networks for Rational Reasoning (2403.15297v4)

Abstract: The success of LLMs, e.g., ChatGPT, is witnessed by their planetary popularity, their capability of human-like communication, and also by their steadily improved reasoning performance. However, it remains unclear whether LLMs reason. It is an open problem how traditional neural networks can be qualitatively extended to go beyond the statistic paradigm and achieve high-level cognition. Here, we present a novel qualitative extension by generalising computational building blocks from vectors to spheres. We propose Sphere Neural Networks (SphNNs) for human-like reasoning through model construction and inspection, and develop SphNN for syllogistic reasoning, a microcosm of human rationality. SphNN is a hierarchical neuro-symbolic Kolmogorov-Arnold geometric GNN, and uses a neuro-symbolic transition map of neighbourhood spatial relations to transform the current sphere configuration towards the target. SphNN is the first neural model that can determine the validity of long-chained syllogistic reasoning in one epoch without training data, with the worst computational complexity of O(N). SphNN can evolve into various types of reasoning, such as spatio-temporal reasoning, logical reasoning with negation and disjunction, event reasoning, neuro-symbolic unification, and humour understanding (the highest level of cognition). All these suggest a new kind of Herbert A. Simon's scissors with two neural blades. SphNNs will tremendously enhance interdisciplinary collaborations to develop the two neural blades and realise deterministic neural reasoning and human-bounded rationality and elevate LLMs to reliable psychological AI. This work suggests that the non-zero radii of spheres are the missing components that prevent traditional deep-learning systems from reaching the realm of rational reasoning and cause LLMs to be trapped in the swamp of hallucination.

• The paper introduces SphNNs as a neuro-symbolic method that uses sphere computations to achieve deterministic syllogistic reasoning.
• It employs a neuro-symbolic transition map that ensures precise model construction and valid counterexample generation for reasoning tasks.
• The approach paves the way for integrating SphNNs with LLMs to reduce hallucinations and advance robust neuro-symbolic AI.

Sphere Neural-Networks for Rational Reasoning

Introduction to Sphere Neural-Networks (SphNNs)

In recent years, the success of LLMs such as ChatGPT has significantly highlighted the potential of neural networks in approximating human-like cognition, particularly in tasks involving natural language processing and reasoning. The introduction of Sphere Neural-Networks (SphNNs) marks a pivotal advancement in the quest for imbuing neural networks with capabilities for more complex and deterministic forms of reasoning, including syllogistic reasoning—a foundational element of human rationality.

Qualitative Extension of Computational Paradigms

SphNNs represent a minimalist yet profound qualitative extension of traditional neural computing paradigms by transitioning from vector-based to sphere-based computations. This shift introduces the concepts of proximity and boundary relations (contact and non-contact relations), fundamental to spatial reasoning, into neural computing. Spheres, with their inherent set-theoretic representations, enable the encoding of both spatial and non-spatial reasoning tasks, facilitating model construction and inspection—a methodology akin to human rational reasoning processes.

The Neuro-Symbolic Transition Map

Central to the functioning of SphNNs is the neuro-symbolic transition map, a construct that guides the transformation of sphere configurations to achieve desired spatial relationships. This map delineates the operations necessary for transitioning between different spatial configurations, ensuring a deterministic approach to reasoning. The transition map's effectiveness is exemplified in its application to syllogistic reasoning tasks, where SphNNs demonstrate the ability to construct counter-examples for invalid inferences, thereby determining their validity.

Contributions to Rational Reasoning

SphNNs' introduction signifies a significant leap toward deterministic neural reasoning, particularly in the field of syllogistic reasoning. By leveraging the principles of model construction and inspection, SphNNs not only solve syllogistic reasoning tasks with remarkable accuracy but also showcase the potential for a wide array of rational reasoning tasks, including but not limited to probabilistic reasoning, logic reasoning with negation, and even humor understanding. Furthermore, SphNNs bridge the gap between neural learning systems and symbolic representations, providing a foundation for neuro-symbolic unification—a harmonization of machine learning's predictive power with the interpretability and determinism of symbolic logic.

Implications and Future Directions

The development of SphNNs paves the way for advanced interdisciplinary collaborations aimed at enhancing our understanding of deterministic neural reasoning and its applications. As we venture further into the exploration of SphNNs, several implications and potential directions emerge:

• Synergistic Collaboration with LLMs: SphNNs can function as System 2 reasoning models, inspecting and guiding the outputs of LLMs towards more deterministic reasoning processes. This synergy offers a new avenue for mitigating hallucinations in LLMs and enhancing their reliability.
• Advancement in Neuro-Symbolic AI: The unification of vector embeddings with explicit boundary relations in SphNNs hints at a promising direction for neuro-symbolic AI, where the integration of neural networks with symbolic reasoning can be achieved seamlessly, fostering advancements in AI interpretability and robustness.
• Exploration of High-Level Cognition: The ability of SphNNs to simulate complex reasoning tasks, including humor understanding, highlights the potential for neural networks to mimic higher levels of human cognition, pushing the boundaries of AI's capabilities in replicating sophisticated human thought processes.

In summary, Sphere Neural-Networks represent a groundbreaking advancement in the quest for deterministic neural reasoning. By extending traditional neural paradigms and introducing the concept of sphere-based computations, SphNNs unlock new potentials in the field of rational reasoning, presenting exciting opportunities for future research and applications in AI.