Request for help on MNIST RGM classifier

[Arun-Niranjan]

Hello everyone,

I am attempting to implement a renormalised generative model MNIST image classifier as per the scale free active inference paper. I have a question on the paper I could use some help with if anyone has further context:

Question 1. Parameter Learning (Active)
Parameter learning updates occur according to P(u) defined in equation (6)

where σ is a softmax (which reduces to a sigmoid in the case of a single number) and α is a precision hyperparameter controlling the sensitivity of parameter updates (a larger α means we are doing Bayesian Model Selection, a lower α corresponds to Bayesian Model Averaging)

My issue is with the free energy calculation in the case of a classifier. If I understand correctly, the cost(or utility) term is 0 (a classifier has no preferences on what it sees, we are in pure perception mode). therefore the free energy is equivalent to the mutual information. the mutual information is a KL divergence and therefore always greater than 0. this means that once you resolve all the minus signs, the input to the sigmoid is always greater than or equal to 0, which corresponds to a range of P = [0.5, 1], whereas the paper says that for bayesian model selection we should have a range of [0, 1].

Have I missed something here? How does the implementation in the paper "accept ~20% of samples" if P can never be 0? should the sigmoid be some other activation function?

[tverbele]

The softmax does not reduce to the sigmoid in this case, as variable u has a dimension of 2: u0 = the old parameters and u1 = the old parameters + the delta in Dirichlet counts should you 'learn' from this sample (see Eq 5). There is indeed no utility in play, but Eq 6 is calculating the mutual information for those both cases and comparing with the softmax (with a very high temperature in the MNIST example). So basically it's saying: only add the Dirichlet counts if the resulting parameters yield higher mutual information between s and o than what it was.

[Arun-Niranjan]

Thanks @tverbele that's a bit clearer - I was using calc_pA_info_gain which was returning me a single number, I'll give this another look and see if I need a new method or can adapt the existing one with different inputs

[tverbele]

you'll need to call that function twice, once with the 'old' pA (or cache that value of a previous call), and once with the new pA which has the Dirichlet counts added; and then check which one is higher / calculate the softmax

[Arun-Niranjan]

ok I think I am nearly there with a working classifier (although the best accuracy I am currently getting is ~70%, I'm sure we can do better).

will start loading up my code into a notebook, first PR is here #357