12:17:41 So!
12:17:44 Black Flip, thank.
12:17:51 This is. This is the brain of this, this is your brain.
12:18:01 So also in the break people came and said, This is all really fantastic, for me. Why should we care if we think about statistical learning?
12:18:12 So I thought, I'll give 2 other angles of of these models, and hopefully I try. And I'm not selling this to anyone. But it's just kind of a word.
12:18:26 This could be, might be a useful way to think about things.
12:18:28 So one element is the issue of if we have good ways to describe the nature of activity of the neurons who do whatever it is you care about in terms of the then this means that you can start exploring the details of this code book, not just in terms of talking about what the rules of the penins are but maybe something about what they
12:18:53 need, and the other side is which I'll also mention is maybe this notion of thinking about simple set of features with which you try to learn things can be used to look at other other kind of tasks that you might want to know.
12:19:08 So I want to try and kind of go back to this notion of, you know these models that compute the likelihood of their own inputs have a clear notion of how this could be related to any Bayesian inference learning or pacification that you want to play with but I want to
12:19:27 take it a little bit further, and say, I mean, if we really say, Well, this is the circuit that does some kind of learning of any task that you care about statistical or not, how should we deal with understanding what's going on here, and in particular, because at large population nothing ever repeats your brain needs to do some kind of
12:19:48 inference I've never seen this, but this means, or similar to that thing which I know means whatever it is.
12:19:57 So so here's kind of a shortfall into how you can use these things to try and learn something about the structure of the semantic structure of the newer code, and how you can use it.
12:20:09 And so and this goes back to the really fantastic paper from Jonathan and Keith Popora, and trying to come up with metric measures for neural activity.
12:20:22 By that you can say Well, I mean, here's one that I see, and this is another one so how far A and B from one another?
12:20:32 And so they they use a very nice eddy distance metric I'm thinking about, maybe what you should think about is how you should move the spikes, or what's the cost of deleting them to try.
12:20:44 And this is how you might be able to do some of these things.
12:20:47 However, there's something weird about this that we felt that maybe we should look at it a different way which is this has a very intuitive notion about the kind of basic operations that the code might rely on.
12:21:01 And so maybe we should not use any of these notions, because you know, this is 80% overlap.
12:21:09 I don't know how we should interpret the meaning of it.
12:21:15 So so the thing we came up with is that if we have good models of the code of how the neurons respond to stimuli, maybe I can now judge the similarity of 2 activity patterns or learn the nature of the semantic organization of the code by asking if each of these patterns, comes or
12:21:33 might appear for different kind of stimuli. Can I try and learn something about the similarity of these 2 patterns, in terms of which them would actually use to encode and can I use that to be able to then figure things about patterns that I've never seen before?
12:21:50 So I want to learn something in terms of the distance between 2 patterns in terms of the distribution of the patterns in terms of the distribution over stimuli.
12:22:00 This is the Bayesian inverse of so I want to learn something in terms of the distance between 2 patterns in terms of the distribution over stimuli.
12:22:08 This is the B stimuli might be causing this particular response.
12:22:10 And so the similarity between 2 words is going to be measured by an overlap of these 2 distributions, and because I have these models, I can actually do that.
12:22:20 So if I now and this is an example, and again for the retina, if I look at their responses to a repeated movie, I can look at what happens in a particular point in time.
12:22:32 And this is over 600 repeats of the movie. These 20 neurons were doing at this particular point in the movie.
12:22:37 So these are the different variants that we know. The rest of the brain would know about the world from looking at this particular thing.
12:22:46 So they are clearly obvious. Common themes here. But there's variation here which means something or might mean something.
12:22:52 And this is for a natural movie then again, you see the similar kind of structure.
12:22:57 So if we build these kind of models that Gashboard discussed earlier, that we say we want to talk about the probability of getting a particular response for a particular stimuli, so I'm learning these kind of models where the these parameters might depend on the stimulus I end up
12:23:13 with this stimulus-dependent maximum entropy models.
12:23:17 And then, when I build these, and let me skip this for the sake of time, I can use that, and then to go back to learn this distribution over a stimuli space, even a particular response.
12:23:27 So we did this for a population of neurons looking at their and say, Well, let's not stake all the thousands of different patterns that we got in an experiment over these 20 neurons.
12:23:39 And this is this big matrix is the distance between all the words.
12:23:44 Now that I go back to the stimulus space and say which were used to encode.
12:23:51 So now for every different pair of words. There's the how they point back to the space of stimuli and so I ordered this matrix based on the number of spikes per each of these binary patterns.
12:24:06 And you get something that's very hard to make sense of what are the blue stripes?
12:24:09 So the blue stripes are the separation between the cases of parents that had 0 1 0 2, and so on.
12:24:17 So, but if you cluster this thing just to try and get something out, it's clear that there is this kind of reorder.
12:24:27 The entries of the matrix. Now there are clear that there are words that are very similar in terms of what they mean.
12:24:33 Again by this measure of how they point back to stimulus space.
12:24:36 And this is true both for the artificial stimuli that we use here and for natural ones that we use here.
12:24:42 And if you look back at what are these patterns? It's kind of said that it captures something which is the essence.
12:24:48 Variations on a theme that seem to be coding to particular stimuli.
12:24:53 If you try the notion of some hamming distance between the patterns which is our natural way of doing this, and you clust.
12:25:00 This is what you do after you get the clustering, the right metric for neural spike Plains is not going to be the usual things.
12:25:08 We are used to thinking about. It's something else. And these models actually uncover that.
12:25:12 And what this structured mean is that if you think about the space of patterns, there is this set of think of ellipsoids, of the space, of all the patterns that these groups actually seem to be encoding similar stimuli, and so we tried to I mean this thing that this is actually trying to embed
12:25:30 these patterns based on the distances in space. And this reminded us of the old notion of how should you build a code book going back to Shannon, of saying, If you want to talk about things and you have code words to do them?
12:25:42 And you have some noise in how you convey things. You should put the code words far enough in space that even if there are fluctuations or noise, you're going to be able to decode them.
12:25:55 Basic notion of building the redundancy. So you can do real decoding.
12:25:58 And so this is what we actually see in this response of the population.
12:26:03 And so what we asked is, if I think about the stimuli, and I take all of these patterns, and I'm going to say, well, based on this clustered view, I can try and think of which is there a small number functional classes.
12:26:16 Of the codebook that really matter here. So, in a sense, each of these patterns is going to be assigned to one family of responses and I'm going to ask, how much do I know about the movie?
12:26:30 If I, instead of giving you the actual pattern, I tell you which class it belongs to.
12:26:35 So when we did that, what we find is that basically, if you just instead of coding, giving the detailed binary code I just tell you which cluster it belongs to by the time I have about 100 clusters, so I get most of the information, I can get about the actual movie so
12:26:53 that's kind of a way in which this thing allows me to learn the semantic organization of the code and then try.
12:27:00 And we can actually test this to decode new things from you.
12:27:05 And the last thing I want to say about this is before we can talk about other more general notions.
12:27:11 What these kinds of feature-based models can give us in terms of learning.
12:27:16 So this is a completely different game. But just the idea is going to be similar.
12:27:22 We play with a task of people, and then monkeys needing to classify visual objects.
12:27:28 So this particular case, there are black and white squares on the screen.
12:27:31 So you get 4 patterns of 4 squares, and there's some thing you need to learn to how to classify them into into a one of 2 classes that we don't know about.
12:27:40 So you get a pattern you need to classify. These are individual learning curves of people trying to learn this game were what they need to figure out.
12:27:48 That one of the squares really matters, and the other one is not so.
12:27:53 This is performance of 10 different people over this task over time.
12:27:58 The pink ones are the really good students of the white men.
12:28:02 Are the not so good students, and this is all the faculty failing what's really cool is that if you ask people, even the ones that got to 85% or 95% correct answers, what did they do?
12:28:13 You get 3 kinds of answers are ones who are really close to their actual rules.
12:28:17 They figured it out. That's about a third of the people.
12:28:19 A third. Say, I'm terribly sorry. I just went with my gut, feeling.
12:28:23 What can you say about your gut finger? I have no idea.
12:28:28 And then they still got 95% correct. And the most amusing ones who want to give you a very detailed answer that has nothing to do with what they did, because, had they done the thing that described you, they would be at 50% so whoever's working whoever's talking about this are not the
12:28:42 same. Anyhow. So we find a figure. Can we describe this kind of lagging in similar terms and so what we did is to say just like this, random features or pairwise or triple thing?
12:28:55 Can we think about the way you learn to classify them as mixture of features of some in that space?
12:29:00 And so when we've done this, we just to give you the server.
12:29:06 This gave us an ability to imitate individual performance to an extremely high degree of accuracy.
12:29:11 The blue lines are the performance of individual subjects on individual walls, and this red thing with the variance around them, is in the models that we try to learn from the beginning of their trial to try and predict how their learning would behave again based on these set of random features that we try to see how they
12:29:32 might learn to combine them. So the models are not.
12:29:35 They don't see the they just see the same stimuli that the human C, so they see the behaviour of the subjects up to here, and then they need to predict whether they don't exist.
12:29:46 So so this models give us a way to learn a metric on the space of neural responses.
12:29:56 You can actually even use that to try and learn a metric from the neurons about the space of steam will, I?
12:30:02 So this is kind of looking at the actual substance that does learning of any kinds.
12:30:07 Or can we actually look at the details of the code that implements these things?
12:30:10 There's other issues about getting biological implications for these models that I didn't get to talk about.
12:30:17 And then this notion of what happens when you think about really large populations doing things, this ideas of are their goals, of the code that we have implications for what you might learn and how you can learn these things that Elia has shown with the fact that things emerge even if you didn't
12:30:37 mean to in large structures when you have certain limits on the kinds of interactions, maybe tell us something that you know use that our networks or our brains are tuned to be able to solve particular things.
12:30:50 And I think I'll start hearing if there are questions.
12:31:03 Yeah, I have a question regarding to the foot show. Right?
12:31:07 Actually the clustering of activity. So to what extent, if you look at the stimuli which are writing these clusters, is there some similarity or is to what extent is this structure?
12:31:21 Yeah, coming from from the architecture of the circuits of the statistics of their movie.
12:31:28 So this, of course, it's related to some extent to this particular stimuli.
12:31:35 You use, it's going to be different, although we try different stimuli with the same circuit and it wasn't that sensitive.
12:31:45 But whatever so the point here, I guess, I think, is that the semantic metric on the neurons is very far from our usual notion of how you should measure the similarity.
12:31:59 Again. If you can extend this to us, what does it say about the space of stimuli?
12:32:05 And you can learn a metric on the space of stimuli, which is extremely orthogonal to what you might think are similar.
12:32:16 Obviously similar things in the stimulus space. So these metrics are very far from the ones we used to play with, and still you convert them from the normal code itself.
12:32:26 This is a really cool paper. By gosh, perfume! I don't know. 10 years ago.
12:32:31 Yes, yeah, this is. I had a question about. So I was curious whether the attaching semantics to the meanings or specific kinds of responses.
12:32:42 I was curious about whether, like, for example, in signing high level cognition, rather things like word learning in humans like the fact that you decide to assign the same word like literally in English, like the same word to a group of stimuli based on some structure, and there are these like flaws that emerge even at
12:33:00 that level of clustering at the level of like, you know, learning, language.
12:33:04 So it's curious about like you think that. And there are a bunch of different kinds of explanations in that phs, which are partially about constraints right?
12:33:13 That you know, as if sort of power or distributed distribution over different clusters, and sort of easier to represent.
12:33:19 It requires few fewer bits to represent so there's a sort of constraints based explanation.
12:33:25 But also sort of this is the optimal way to generalize this best.
12:33:27 That's like, you know, you don't need to memorize this man, you know.
12:33:29 Yeah, there are a few different kinds of there's curious about how you think this.
12:33:32 Like useful algorithms between those, or whether it's sort of like, not ready that I.
12:33:39 So so there's this wonderful book which is supposedly for kids.
12:33:45 But the guy who wrote the Xkcb. Ping, and he had try to write an encyclopedia where every ante they use only the most, the thought, the most common.
12:34:00 1,000 words in English and it's a fantastic thing, because he explains rather complicated structures with just the top 1,000 words a at Bagfield, mostly with water, that life is made of is a cell right?
12:34:17 So it's a fantastic book that if you haven't seen you should go check it out.
12:34:21 There's something really fundamental, not aside from the size of the vocabulary that people have because of Tiktok is decaying.
12:34:32 There is something here about the fact that if I think about if I have a thousand neurons, and I think about the 2 to the 1,000 possible patterns that I have, I can name every particle in the universe with a 2 to the 1,000 possible boards, right so we don't have that many neurons, because
12:34:52 we need to give a name for every single thing. We're going to meet.
12:34:56 It's all about being able to somehow represent things in a way that's presumably something that we can work with and make sense of without being too smart.
12:35:09 And this is something that I think is kind of, and Sarah Sarah is going to be here next week and talk about learning these kind of structures as well.
12:35:18 But I think there's something fundamental about these code books which also affect our capacity to do things.
12:35:26 There has to be a relatively small things compared to the size that could be here, and Zip is a nice way to see this, and there must be substructures.
12:35:37 Some latent things. That's I don't know the spirit of the day.