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For reliability, it is important that the predictions made by machine learning methods are interpretable by human. In general, deep neural networks (DNNs) can provide accurate predictions, although it is difficult to interpret why such predictions are obtained by DNNs. On the other hand, interpretation of linear models is easy, although their predictive performance would be low since real-world data is often intrinsically non-linear. To combine both the benefits of the high predictive performance of DNNs and high interpretability of linear models into a single model, we propose neural generators of sparse local linear models (NGSLLs). The sparse local linear models have high flexibility as they can approximate non-linear functions. The NGSLL generates sparse linear weights for each sample using DNNs that take original representations of each sample (e.g., word sequence) and their simplified representations (e.g., bag-of-words) as input. By extracting features from the original representations, the weights can contain rich information to achieve high predictive performance. Additionally, the prediction is interpretable because it is obtained by the inner product between the simplified representations and the sparse weights, where only a small number of weights are selected by our gate module in the NGSLL. In experiments with real-world datasets, we demonstrate the effectiveness of the NGSLL quantitatively and qualitatively by evaluating prediction performance and visualizing generated weights on image and text classification tasks.