Ill-defined loss function depending on eigenvector phase

[souryadey]

Running StatePred.train_net() produces RuntimeError: linalg_eig_backward: The eigenvectors in the complex case are specified up to multiplication by e^{i phi}. The specified loss function depends on this quantity, so it is ill-defined.

[souryadey]

This happens due to numerical instabilities.

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Possible cause:

The dominant eigenvalue has magnitude significantly greater than 1.

Capturing this:

The magnitude of the dominant eigenvalue is recorded in the log file after each epoch.

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Possible cause:

Training data is not normalized.

Solution:

Set normalize_Xdata = True in config.py. This is the default.

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Possible cause:

StatePred.rank is too high.

Solution:

Reduce rank to $<$ encoded_size. This is because rank is supposed to reduce the effective number of encoded states to a lower value than encoded_size. (Note that numerical issues can also occur if rank is higher than any of the numbers in encoder_hidden_layers).