To bring more explanation in the supplement the definition is the logits total_counts convention for a negative binomial (r, p and lambda instead of rho, theta and l_n). See our code on how this changes computation:
scvi-tools/src/scvi/distributions/_negative_binomial.py at main · scverse/scvi-tools · GitHub.
To make it very short, theta is the mean variance relationship and the mean is independent of theta.
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