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The cause of this problem is speculated to be due to the activation function that selects the Relu.(I observed a difference in the negative values of your data). At the same time, I also found this asymmetry in the prediction case given, which can be alleviated by changing the activation function to Tanh.
I hope I can give you some help!
https://colab.research.google.com/drive/1iRu82bcKd1aF8DgZB_x-deIJbt-GNf-R?usp=sharing
as u can see the above image uncertainty from the positive side of the graph seems to be reducing even though it should be increasing similar to left side of the graph
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