Hello,
Well factorization problems can suffer from non-identifiability sometimes:
I don’t really know your specific problem but one could run into such a problem for U and V perhaps (scaling one up and the other down would still give the same result for instance)? Although signs of non-identifiability might be different than what you are observing its worth a check as is done above.
Are the posterior HDIs for alpha_U and alpha_V very large and containing the true values? That could also be a sign of non-identifiability. Looking at posterior plots and trace plots using arviz to see if you get multimodal behaviour is another way to check. It might also help others here if you either put some posterior plots or a full code with simulated data.