The success of Large Language Models (LLMs), e.g., ChatGPT, is witnessed by
their planetary popularity, their capability of human-like question-answering,
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 minimalist 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. Instead of training data, SphNN
uses a neuro-symbolic transition map of neighbourhood spatial relations to
guide transformations from 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 by constructing sphere configurations as
Euler diagrams, with the worst computational complexity of O(N^2). SphNN can
evolve into various types of reasoning, such as spatio-temporal reasoning,
logical reasoning with negation and disjunction, event reasoning,
neuro-symbolic reasoning, 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.

通过在计算构件中将向量泛化为球体，我们提出了球形神经网络（SphNNs）进行人类级推理，包括主义推理、逻辑推理、事件推理、神经符号推理和幽默理解。这项工作认为，球体的非零半径是阻止传统深度学习系统进入理性推理领域，并使得大型语言模型在幻觉的泥沼中陷入困境的缺失组件。