einsum while calculating free energy

[lqiang2003cn]

hi, guys, i have a question about calculating the free energy. While calculating einsum, why only sum to the first dim:

arg_list = [X, list(range(X.ndim))] + list(chain(*([x[xdim_i],[dims[xdim_i]]] for xdim_i in range(len(x))))) + [[0]]

and then use:

spm_dot(likelihood, qs)[0]

to fetch only the first level of s0 (suppose hidden state s is factorized as s0, s1, ... ) ?

in my opinion, we should sum over all the tensor by removing the last + [[0]] and the Y should just be a scalar.
am I totally wrong, if i am, please correct me, thanks a lot!

[conorheins]

Hi @lqiang2003cn ,

Thanks for noticing this, and many apologies for the late reply! I think you're absolutely right about this -- I will look into this and fix, but feel free to submit a PR / your own fix if you'd like.

I'm imagining the solution would be to do exactly what you're saying, namely:

arg_list = [X, list(range(X.ndim))] + list(chain(*([x[xdim_i],[dims[xdim_i]]] for xdim_i in range(len(x))))) # leave out the [[0]] at the end
accuracy = np.einsum(*arg_list)

But I'm debating whether to make that an additional gating condition within spm_dot (with another if statement), or whether to just do it in-line in the calc_free_energy function...

An aside: + [[0]]in the arguments to einsum is a vestige of the typical use of spm_dot, where you're trying to sum out everything except the first dimension (typically, the support of the variable over which you're computing a marginal distribution).

[lqiang2003cn]

But I'm debating whether to make that an additional gating condition within spm_dot (with another if statement), or whether to just do it in-line in the calc_free_energy function...

spm_dot is already complex enough (for me), i'd do it in-line in the calc_free_energy function :).

[conorheins]

I fixed the bug, and have merged the resulting PR into master. Nice job again @lqiang2003cn for spotting this, and thank you. This is by far the most technically-nuanced error someone has noticed so far; I'm impressed that you managed to parse that line of preparation for the einsum arguments in spm_dot :)

Will close this issue upon release of pymdp 0.0.7

[conorheins]

Closing now that v0.0.7 is released