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Yes, a deep learning model can be initially trained with low precision and then refined with high precision. This is called mixed-precision training, where the model uses low precision (e.g. 16-bit) for the forward and backward computations during the initial training but switches to higher precision (e.g. 32-bit) for certain operations during the refinement phase. The rationale behind this approach is that lower precision calculations require less memory and computation, which can speed up the initial training process. However, higher precision can improve the model's accuracy and stability, allowing for better generalization and improved performance on unseen data. Mixed-precision training has been shown to be successful in various deep learning tasks, including image classification, object detection, and natural language processing.