Title: Extract Local Inference Chains of Deep Neural Nets. Abstract: We study how to explain the main steps/chains of inference that a deep neural net (DNN) relies on to produce predictions in a local region of data space. This problem is related to network pruning and interpretable machine learning but the highlighted differences are: (1) fine-tuning of neurons/filters is forbidden: only exact copies are allowed; (2) we target an extremely high pruning rate, e.g., $\geq 95\%$; (3) the interpretation is for the whole inference process in a local region rather than for individual neurons/filters or on a single sample. In this paper, we introduce an efficient method, \name, to extract the local inference chains by optimizing a differentiable sparse scoring for the filters and layers to preserve the outputs on given data from a local region. Thereby, \name~can extract an extremely small sub-network composed of filters exactly copied from the original DNN by removing the filters/layers with small scores. We then visualize the sub-network by applying existing interpretation technique to the retained layer/filter/neurons and on any sample from the local region. Its architecture reveals how the inference process stitches and integrates the information layer by layer and filter by filter. We provide detailed and insightful case studies together with three quantitative analyses over thousands of trials to demonstrate the quality, sparsity, fidelity and accuracy of the interpretation within the assigned local regions and over unseen data. In our empirical study, \name~significantly enriches the interpretation and makes the inner mechanism of DNNs more transparent than before. 