I would like to analyse learning rates as it was done by Lawson et al. (2017, Nature Neuroscience). In the paper, the learning rate alpha2 is defined as
Based on that definition, I would assume that the learning rate alpha3 would be computed as
alpha3 = (muhat(t,2) - muhat(t-1,2) ) / da(t,2),
where muhat is computed as follows, based on the general definition of muhat from Mathys et al. (2014, Frontiers in Human Neuroscience):
muhat(t,2) = mu(t-1,2)
However, I see that in Lawson et al. (2017, Nature Neuroscience), alpha3 is computed as
alpha3 = ((mu(t,3) - mu(t-1,3))/da(t,2)
What is the difference between the two versions of alpha3? Why in the paper alpha2 is computed using muhat at the first level, but alpha3 is computed using mu on the third level?
I would like to analyse learning rates as it was done by Lawson et al. (2017, Nature Neuroscience). In the paper, the learning rate
alpha2is defined asalpha2(t) = (muhat(t,1) - muhat(t-1,1) ) / da(t,1),where
muhat(t,1) = s(mu(t-1,2)).Based on that definition, I would assume that the learning rate
alpha3would be computed asalpha3 = (muhat(t,2) - muhat(t-1,2) ) / da(t,2),where
muhatis computed as follows, based on the general definition ofmuhatfrom Mathys et al. (2014, Frontiers in Human Neuroscience):muhat(t,2) = mu(t-1,2)However, I see that in Lawson et al. (2017, Nature Neuroscience),
alpha3is computed asalpha3 = ((mu(t,3) - mu(t-1,3))/da(t,2)What is the difference between the two versions of
alpha3? Why in the paperalpha2is computed usingmuhatat the first level, butalpha3is computed usingmuon the third level?