Abstract How neural networks actually reason remains a mystery. This paper identifies the core mechanism: language understanding and reasoning are definite computations over internal semantic structure, realized as conditional semantic transformations performed by cognitive neural operators. These operators recognize concepts, relations, and roles, compare them, suppress invalid cases, and transform valid semantic structures into new ones. We make this mechanism explicit through a parameter-level circuit that maps “C belongs to A; all A have B” to “C has B.” The complete word-to-conclusion pipeline is specified at the level of individual weight parameters and passes all 16,680 exact simulation tests. This mechanism is further verified experimentally: trained models form the theory-predicted cognitive-reasoning process stages and functionally equivalent operator topologies, or variants thereof. This provides the first explicit, neuron-level, parameter-interpretable realization of natural-language reasoning—distinct from Boolean truth-value circuits, which cannot express genuine semantics, and from the qualitative circuit descriptions typical of large-model interpretability work. The same neural-operator mechanism also offers a cogent account of emergence, scaling laws, generalization, and hallucination, and points toward neuron-level operator interpretability, hallucination control, AI-safety tooling, neural editing, and theory-guided model design. In our experiments, this mechanism shifts model architecture design from empirical search toward mechanistic calculation: the required cognitive operators and reasoning chains can be used to theoretically derive model width, neuron count, and network depth, and to locate immature operators, layers, and local structures during training for targeted optimization. Small-model experiments show that this mechanism-guided approach achieves more efficient training, lower compute cost, and faster inference. More broadly, it reduces cognition from the level of symbolic rules to neuron-level computation, opening the black box at the level of mechanism.
Duan et al. (Fri,) studied this question.