While feed-forward neurons in pre-trained language models (PLMs) can encode knowledge, past research targeted a small subset of neurons that heavily influence outputs.This leaves the broader role of neuron activations unclear, limiting progress in areas like knowledge editing.We uncover a global linear relationship between neuron activations and outputs using neuron interventions on a knowledge probing dataset.The gradient of this linear relationship, which we call the **neuron empirical gradient (NEG)**, captures how changes in activations affect predictions.To compute NEG efficiently, we propose **NeurGrad**, enabling large-scale analysis of neuron behavior in PLMs.We also show that NEG effectively captures language skills across diverse prompts through skill neuron probing. Experiments on **MCEval8k**, a multi-genre multiple-choice knowledge benchmark, support NEG’s ability to represent model knowledge. Further analysis highlights the key properties of NEG-based skill representation: efficiency, robustness, flexibility, and interdependency.Code and data are released.