Numenta General Neuroscience, 11 Feb 2010

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From YouTube: (3/5) Michael Berry. Plenary Lecture 3, LACONEU 2010

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Lectura Plenaria dictada por Michael Berry (Princeton U, USA) en el Instituto de Sistemas Complejos de Valparaíso (ISCV, www.iscv.cl), el día 22 de enero de 2010, en el marco de la VIII Escuela de Verano en Sistemas Complejos LACONEU 2010 (Latin American Summer School in Computational Neuroscience and Biomedical Applications). Más información: http://www.cnv.cl/laconeu2010/laconeu2010.htm

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You know anywhere in the visual field, so they're kind of constantly reading out retinal populations and trying you know and potentially giving the answer that they think that there's a spider there. So you know uh there could be a false alarm and because there's so many of these detect detector circuits that are kind of all operating in parallel for spiders. For you know all of the visual stimuli, the false alarm error, if it's very large for any one of those kind of detector circuits.

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If you add it up over all the detectors, it's going to be it's going to be really horrible, so I think it's particularly important to have kind of low false alarm error rates. Okay, yeah, wouldn't false positives. The worst time you like, when you see, there's lots of people that are startled by small small things that have nothing to do with the spider.

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But you would imagine that you know a car, for instance, that even if you jump back, you know 100 times, you know in a month when there actually is a car there, it's important to jump back so it it seems like.

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Like um uh false positives, they're sort of like a balance yeah I mean- I don't think false positives are important too. It's just that. What I'm saying is that there there's so many potential false alarm.

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You know events every moment that uh that just just be because of those sheer numbers, it means that, for any one kind of you know detector, that's reading out, you know population retina, giving a decision um it's going to have to have an even lower false alarm error, because if there are tens of thousands of you know millions of those kind of potential detections per per moment, you know one in a million error rate is still going to be.

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You know multiple events per per second, which should be sort of you, know overwhelming level of hallucination. um So just the sheer numbers, uh okay and then the last thing I want to point out is that is that in general, there's there's an ambiguity problem. So it's not just uh the issue that single neurons have noisy responses. They also have ambiguous responses and I'll I'll kind of talk about that more uh in the next slide.

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So, for all these reasons, I think uh it's actually beneficial to have large populations that are uh they're quite redundant to kind of allow fast, unambiguous and low error coding. Okay- and let me just mention a little bit more about ambiguity, um you know so so single uh ganglion cells uh tend to have broad tuning. What that means is you can get the same firing rate from many different stimuli? Okay, so if you have a you flash a dot on the receptive field, it gets bigger, bigger, bigger the firing rate goes up.

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If you have the same dot size, you make the contrast go up and your firing rate goes up. Saturates, um you know you change the position of the dot and your firing rate has some tuning curve, uh and so, if you observe a single firing rate from the ganglion cell, you don't know whether it's a big dot at low contrast or a medium dot of high contrast, a little bit to the side of the receptive field, etc, etc.

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So there are a lot of uh you know these, these different properties that all contribute to the response, uh and you can't disentangle that when you, when you look at one ganglion cell, but the idea is with the whole population, uh you can tell those things uh apart.

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Okay, so um so so the idea here is I'm going to describe. uh You know this, this kind of first experiment, uh where we've begun to kind of explore these. uh These issues of you know, reading out uh population code, uh and so what we've done is uh is a shape discrimination task. So uh what that means? Is you flash? You know one of these uh 36 different shapes onto the retina. For you know, half a second.

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I have to sign off um record from a whole bunch of cells, in this case 162 um and uh and just a kind of important technical detail here. So uh when we did these experiments, our our array, technology, uh wouldn't let us record from all these cells in one preparation.

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So this is uh multiple retinas, uh and so uh we don't have any noise correlation, so cells here are in this case, have correlations they're only induced by the stimulus, but uh you know I'm happy to talk about uh what the noise correlations that specifically are doing.

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um It's uh you know for single patches, it's kind of 20 to 30 cells.

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And yeah, and then you repeat, the same stimulus for all the different preparations: um okay, so uh these these stimuli are are likely to be ambiguous because um basically, uh each one of these letters is about as big as the the receptive field size of the ganglion cell, um just to kind of mention uh these letters each one of these shapes have kind of 400 black pixels, and you know the rest of the screen is gray.

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Each uh pixel is about the size of a photoreceptor okay, so uh you expect that there's pretty high signal to noise ratio for discriminating these shapes, at least in the photoreceptor layer, um uh and so now we're kind of looking at the ganglion cell there and and so because, they're all about the same size of the ganglion cell receptive field. uh You know, if you just do kind of a linear averaging over the spatial profile of the receptive field.

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You know all the cells are going to give a pretty similar uh response and also the shapes are the same center location, same kind of contrast and mean light levels, so those kind of low level cues are not going to be useful in telling them apart. It's really the the shape that that needs to be resolved here.

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Okay, so uh what does some of the data look like here? um Are uh kind of firing, kind of profiles of um three different ganglion cells, responding to one two, three different shapes, and so uh you can definitely see some selectivity here. So here uh you know for this: uh uh let's look at this game itself, so it doesn't fire at all to the x, but it requires a similar amount to these other two shapes.

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So it tells you something about whether the x is present, but you know the cell actually doesn't discriminate at all upside down in the bar. This one has a little bit of difference in firing, etc, etc. So you know when you look at individual cells, you see some selectivity, but of course uh you don't see any. You know perfect x, detectors or you know anything uh anything like that, there's just a little bit of selectivity per neuron.

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Of course you know the problem that the brain really has to solve is there's. You know one response. You know: 162 cells fire. This is what it looks like time.

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uh 162 cells, these are the spike trains, uh and so you know what the brain has to do is take this and you know classify um figure out what what the shape is. You know on a single trial, okay, so so so how do you? uh How do you sort of solve this uh decoding task?

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Okay, so, first of all, um what we're going to do here is we're going to treat one of the shapes as kind of the target stimulus that we want to recognize and we're going to lump all the rest of them together into the group of everything else or distractor, because remember we're not assuming ahead of time that we know that there are only two possible stimuli.

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So we're going to do this task of target versus all the rest of them as a distractor and then, of course, we'll we'll rotate and you know make each one of the shapes be the target stimulus. uh You know. uh One at a time is to kind of go through the analysis.

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Okay, so uh what you're gonna do is you're gonna kind of bend, your responses and concatenate the response of all n cells into kind of a single vector for the whole population, and then the idea is uh the optimal decision rule for kind of you know. uh Each one of these uh discriminations is too alternative. It's target versus everything else, and so the optimal decision rule uh is, is just going to be maximum likelihood. Okay.

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So if you observe a population response vector r, you want to know what's the probability of the target stimulus given that response, compare it to probability.