Updating specific values in tensor (and ignoring rest in cost function)

I’m trying to build a Hidden Markov Model in PyTorch where I specify a transition matrix as a set of weights I’d like to update. The tensor looks something like:


I’m trying to solve for the w’s in this tensor while holding the c’s fixed (that is, they cannot be updated during optimization). The constraint I am solving under is that the row sums of the tensor is 1 (X.sum(axis=1) = [1, 1, 1, 1]).

I guess two things that aren’t obvious to me are (1) how to fix specific values of a Tensor (prevent them from updating during optimization or factoring into the error function?) (2) how to symbolically represent certain weights (notice that w_{b} is repeated at multiple entries!). At first I confused myself into thinking this is a system of linear equations that I can solve, but now I am thinking maybe I need to use a deep learning framework to approximate these values. Does PyTorch have this flexibility?

To freeze certain parameters, you could either zero out their gradients (e.g. using hooks) or avoid passing them to the optimizer. Note that parameters could still be updated, if your optimizer uses internal running estimates or a momentum even if the gradients are zero.

It should have the flexibility, as there are some HMM implementations in PyTorch, e.g. here.