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This lecture by the instructor focuses on the concept of explainable neural networks, specifically addressing the challenge of understanding the influence of input variables on the output of neural networks. The lecture delves into the statistical significance test developed for neural networks, emphasizing the importance of interpretability in various fields, particularly in finance. Through a detailed explanation of the test methodology and its application in a case study on house price valuation, the instructor highlights the potential of this approach in improving the transparency and usability of neural network models. The lecture concludes by discussing future research directions and the flexibility of the derivative-based approach in exploring higher-order properties of neural networks.