Cognitive Symbiotic Field: An Information-Geometric Theory of Multi-Agent Self-Evolution (认知共生场:多Agent自进化的信息几何理论)

Multi-agent self-evolution is a key pathway toward artificial general intelligence, yet existing approaches lack a unified theoretical framework to explain the spontaneous differentiation, sharing, and improvement of strategies, knowledge, and capabilities among agents. This paper proposes the Cognitive Symbiotic Field (CSF) — an information-geometric theory of multi-agent self-evolution over parameterized strategy spaces. CSF treats the strategy space of all agents as a Riemannian manifold, characterizing the emergence, propagation, and differentiation of collective intelligence through a scalar field (the symbiotic field) defined on this manifold. We prove that under appropriate cognitive curvature coupling coefficients, the self-evolution trajectories of agents satisfy geodesic equations and converge to global or local cognitive equilibria. Based on CSF, we derive three fundamental propositions on strategy divergence and knowledge emergence. Experimental results: Cooperative push-box +16.5% (5-seed avg), MPE adversary +34.1%, tag -15.9%, spread -3.1%.