Neuron Empirical Gradient: Connecting Neurons' Linear Controllability and Representational Capacity

Although neurons in the feed-forward layers of pre-trained language models (PLMs) can store factual knowledge, most prior analyses remain qualitative, leaving the quantitative relationship among knowledge representation, neuron activations, and model output poorly understood. In this study, by performing neuron-wise interventions using factual probing datasets, we first reveal the linear relationship between neuron activations and output token probabilities. We refer to the gradient of this linear relationship as ``neuron empirical gradients.'' and propose NeurGrad, an efficient method for their calculation to facilitate quantitative neuron analysis. We next investigate whether neuron empirical gradients in PLMs encode general task knowledge by probing skill neurons. To this end, we introduce MCEval8k, a multi-choice knowledge evaluation benchmark spanning six genres and 22 tasks. Our experiments confirm that neuron empirical gradients effectively capture knowledge, while skill neurons exhibit efficiency, generality, inclusivity, and interdependency. These findings link knowledge to PLM outputs via neuron empirical gradients, shedding light on how PLMs store knowledge. The code and dataset are released.