Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

All right, it's July 18th, 2023, and we're in our second discussion on Chapter 8. So, where would anyone like to begin or any general remark on Chapter 8? Well, I can say something. I added a couple of questions into the list at the very end on Box 8.1, but we can go through some other stuff first, if you want. Sounds good. All right, let's look at the first question. Thank you. Perhaps if I put some background in of my understanding. So, my understanding is we have – well, I think if we go to – there's Raphael Boyatch or Bogatch's paper, a tutorial on free energy, which starts off with looking at a single neuron with an input distribution of a particular mean and variance. Yeah. And he then builds that up to the point where you've got a multi-layer system with multiple nodes. And the synapses represent means and variances. So, I think there's – we're not seriously suggesting that synapses actually represent particular means and variances or whatever. But I think there's the idea that collectively a population of neurons is going to encode mean values and variances. And precision is inverse variance, of course. So, I suppose my other frame of reference is Gaussian mixture models where you've got Gaussians characterized by weights or amplitude, mean and variance. So, then going on to box 8.1, I'm confused that there seems to be a way of treating precision as a magnitude, as an amplitude. Or changing that, changing the Gaussian perhaps by reducing the variance, increasing the precision is going to increase the peak to make it more prominent, which seems a strange way of doing things. Yeah, exactly. So, for me, well, precision and attention are not synonyms. So, attention seems to be something at the neuromodulation timescale as opposed to synaptic weights at a much slower timescale or general influence with usual synaptic – well, some neurotransmitters. So, yeah, it doesn't make sense how a lot of that box. You're on mute, Daniel. Yeah. Ali or anyone, do you want to give a thought? Or… Okay. So, here, the precision being described is the precision to the sensory input. And so, equivalent to attention to sensory input in the sense that if the… and reflected by the A matrix. So, if the incoming sensory data are inferred to be accurate, then they will update the hidden state more. So, if the sensory data incoming, if the sensory data incoming were not believed to be accurate, low precision, low attention, then observations wouldn't update hidden states. So, I don't think that that necessarily refers to the psychological concept of attention. But is your question about… … … … … … … … … … … … … … … ! … ! ! weighting rescales the attention to different variables is what dictates the influence that they have on the overall free energy gradient descent. If you have two variables and they both are equally attended to, then the free energy is a 50-50 compromise such that there's going to be a flat manifold where one of them is getting better by one point and one's getting worse by one point. Whereas if you're attending to one of them 10 times more than the other, so it's 10 times more precision on that belief, then each increment of free energy minimization, you'd be willing to accept 10 decrements on the other one. So the attention blends the role of each parameter being optimized on the overall scalar gradient descent. Yeah, I've still got a bit of a block on that. I'll go away and have a think about that. But I think what you've said just leads naturally on to my other point. So as I see it, as you say, that rebalancing of the attention. So if we have attention given to extraceptive input, then you're sensing the outside world, you're treating that as important. If you then shift to proprioceptive attention, then that's more likely to lead or that would lead to action. Or there's the whole thing about sensory attenuation. Why does sensory attenuation happen? Is it a random thing? Well, there's the splitting across and there's a…