Large language models (LLMs) store extensive factual knowledge, but the underlying mechanisms remain unclear. Previous research suggests that factual knowledge is stored within multi-layer perceptron weights, and some storage units exhibit degeneracy, referred to as Degenerate Knowledge Neurons (DKNs). Despite the novelty and unique properties of this concept, it has not been rigorously defined or systematically studied. We first consider the connection weight patterns of MLP neurons and define DKNs from both structural and functional aspects. Based on this, we introduce the Neurological Topology Clustering method, which allows the formation of DKNs in any numbers and structures, leading to a more accurate DKN acquisition. Furthermore, inspired by cognitive science, we explore the relationship between DKNs and the robustness, evolvability, and complexity of LLMs. Our execution of 34 experiments under 6 settings demonstrates the connection between DKNs and these three properties. The code will be available soon.
