A Primitive Theory of General Intelligence: A Global Mathematical Verification Closed-Loop Framework for Next-Generation Models (Research Proposal)

Abstract

Existing Transformer and large language model frameworks adopt a "prediction-first" paradigm, defining intelligence as fitting real-world data distributions and next-token prediction. This work presents a novel primitive account of intelligence: intelligence arises from continuous, multi-layered global closed-loop mathematical verification and constraint checking. All AI behaviors including fitting, reasoning, association, generation, generalization, error correction and cognition can be reinterpreted as mathematical comparison, constraint validation, differential stability checking and vector structure matching across dimensions. Low-level Transformer operations such as embedding, QKV dot-product attention, backpropagation and distribution fitting are not inherently predictive behaviors, but statistical-level checking operations. Hallucinations, logical failures and generalization limitations of current large models stem from relying solely on statistical distribution checking, lacking rigorous axiomatic, differential and topological structural verification. This theory establishes a dual-layer unified checking intelligence system, outlining a paradigm shift from probability-fitting intelligence toward global mathematical-verification intelligence. The framework provides design principles for next-generation native intelligent systems with reduced hallucination, stronger logical consistency, self-correction and ontological cognition.

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