This course provides an introduction to basic computational methods for understanding what nervous systems do and for determining how they function. We will explore the computational principles governing various aspects of vision, sensory-motor control, learning, and memory. Specific topics that will be covered include representation of information by spiking neurons, processing of information in neural networks, and algorithms for adaptation and learning. We will make use of Matlab/Octave/Python demonstrations and exercises to gain a deeper understanding of concepts and methods introduced in the course. The course is primarily aimed at third- or fourth-year undergraduates and beginning graduate students, as well as professionals and distance learners interested in learning how the brain processes information.
2.1 What is the Neural Code?
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From the course by University of Washington
Computational Neuroscience
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From the lesson
What do Neurons Encode? Neural Encoding Models (Adrienne Fairhall)
This module introduces you to the captivating world of neural information coding. You will learn about the technologies that are used to record brain activity. We will then develop some mathematical formulations that allow us to characterize spikes from neurons as a code, at increasing levels of detail. Finally we investigate variability and noise in the brain, and how our models can accommodate them.
Meet the Instructors
Rajesh P. N. RaoProfessor
Computer Science & Engineering
Adrienne FairhallAssociate Professor
Physiology and Biophysics
[MUSIC]
Welcome to week two of computational neuroscience.
I'm Adrian Fairhall.
Last week's introduction gave you a high level overview of
some of the concepts we'll be covering in the course.
Today we're going to start on the subject of the
first half of the course which is neural coding.
As you know and heard last week brains do many, many different kinds of
things, but one of the best studied
is the representation and transformation of sensory information.
So the first part of this course will be an introduction to common concepts
that are used in thinking about and
quantifying the way that information is represented
in the brain, and how we can extract that information by monitoring brain activity.
Our ability to respond to the world and think about it purely
inside our head requires a transformation of information from one form to another.
Sensory signals or maybe written language are converted into physical
processes inside our brains that contain some version of that information.
A natural
way to talk about this is in terms of a code and our task is
to discover the form in which information
is represented in the activity inside our heads.
Today we'll be talking about how to go about cracking this code.
So, first we'll discuss some techniques for recording from the brain.
We'll then talk about tools for discovering how the brain
represents information and models that
express our understanding of this representation.
Next week we'll go on
to thinking about some methods for inferring what the brain is
doing based on recordings of acts, of it, of it's activity.
The following week we'll talk about, information theory
which is a method to quantify neural representations.
And finally in the fifth week we'll talk about the biophysical
basis of how the brain processes inputs and performs complex computations.
So the methods that we use to collect brain activity determine the ways that
we can analyze it and also the
kinds of information that that activity can contain.
So let's start by reviewing a few techniques
that are currently in use to peak inside brains.
We'll go from large scale to small scale, starting with some methods that
allow us to record activity from people, while those people are performing tasks.
So you've probably heard of functional magnetic resonance
imaging, as this is also used as a diagnostic
tool in hospitals.
This technique allows us to record from a persons brain while they're
performing some task, as long as that task does not require moving around.
The person is placed inside a scanner with
their head in the center of a large magnet.
The scanner measures spatial perturbations in the magnetic
field, which are caused by changes in blood oxygenation.
As different parts of the brain become active, blood
flows to those areas that support the underlying neural activity.
This provides a measure of activity over regions
of the scale of about a cubic millimeter.
Obviously this must represent the average activity of millions of neurons.
Here's an example of some images that one
can collect from fMRI, showing in color small regions
of the brains that respond differentially to some experimental
condition, in this case the viewing of some images.
While fMRI is a wonderful method for
discovering the approximate regions of neural activity, as
we've said the responses that are recorded are
averaged over many neurons and also they're slow.
The blood flow response to changes in neural activity
happens over timescales of seconds.
Another method that still relies on averaging over the responses of
many neurons but has a much
faster response time is EEG electroencephalography.
This method is faster because it captures the changes
in the electrical fields of the underlying neural circuits directly.
Here, one of our former grad students, Kai Miller, is wearing
a cap covered by electrodes that are making contact with his scalp.
The downside of EEG is it tends to be a very noisy signal,
since there are many contributions to the recorded signal.
Still, methods like fMRI and EEG
are very exciting because, although they're limited,
they're non-invasive and so they can be used on healthy, awake human subjects.
Ideally, of course, we'd like to have access to the activity of single neurons.
In cases when we have direct access to neural tissue, one
can use devices such as I'm showing here: a multi-electrode array.
This one developed by physicist Alan Litke.
Most of the device that you see consists of electronics and
amplifiers for amplifying the tiny voltage signals extracted from individual neurons.
At the center, down here, is the array itself,
blown up on the picture here.
Each electron is about 10 microns across, roughly the size of
a single neuron, and this array has 512 such electrodes spaced
60 microns apart, so one can record from many neurons simultaneously,
as is being done here with the slice of the hippocampus.
The multi-electrode array shown before is great when it's possible to lay the
tissue directly on the array surface, for example in experiments using brain slices.
But generally one would like to penetrate into the brain to see
what neurons are doing when the organism is carrying out normal behavior.
This rather scary looking electrode is
actually only about, about two millimeters long.
The tip of each prong is an active electrode.
In newer versions of such electrodes, that are being
developed by groups at MIT and elsewhere, these electrodes can
be moved, individually, into tissue, allowing one to find active cells.
Other electrodes also have multiple contact points along them
so that one can record at different depths simultaneously.
Another beautiful technique for recording for
many individual cells is through calcium imaging.
Here, cells contain a calcium indicator that changes
its florescent properties when calcium binds to it.
Thus, the fluorescent light intensity is an indicator
of the amount of calcium inside the cell.
Since calcium enters the cell during action potentials this signal
acts as a record of the firing activity of the neuron.
This technique
is being used to record, like here,
for many neurons at once, possibly even thousands.
It's also possible to use fiber optics to be able to
open windows like this, our neural activity deep within the brain.
The electrical techniques mentioned so far look at the changes in the
electric field outside the cell caused
by signals that the cells generate internally.
It's also very interesting to look inside the
cell to learn how these signals are being generated.
To do this, we can use patch
electrodes, which the experimenter clamps onto the cell
membrane, and can use to make a direct
electrical contact with the inside of the cell.
So now we've seen some examples of the kind of data we have to work with.
Let's move on to talk about the neural code itself.
Let's start out discussion with some example experimental data which we'll
take from a very important part of the brain, the retina.
Your eyes are an outlying but very vital part of your brain.
The retina is a sheet of cells at the back of your eyeball that
take light that's focused through the lens
and converts those light signals into electrical signals.
So by looking at these signals we can get
our first look at the language of the brain.
Here's a rough cartoon of the experiment.
A retina is dissected from an eye and placed
on top of one of those multi-electrode arrays that
we already saw, and it's kept in some fluid
that will help to keep it alive and active.
A movie is projected down onto the retina and
the neurons of the retina respond to the movie.
So let's zoom in a little on the retina itself,
which is an excuse, really, to show you a beautiful image
drawn by Ramon y Cajal, a master Spanish anatomist
who was active at the turn of last century.
This is an example of very early connectomics.
Well, in real life, the cells in the retina are very densely packed, here
they're drawn schematically in this image to get a sense of the circuit wiring.
So this image shows you the cells that capture light,
here at the photoreceptors, both rods, here, and columns here,
and the successive layers of cells that accumulate and process the
information from the photoreceptors, until they finally reach the output cells, here,
the retinal ganglion cells, whose axons join the optic tack in
heading out of the eye and into the rest of the brain.
Here's a typical way that we look at responses of a single neuron.
This is called a raster plot.
Every tiny red dot here is an action potential or a spike.
When we play the movie once, time goes this way, the
neuron fires at some particular times, marked by those red dots.
When we repeat the movie, we can plot the responses in
that second repetition, and in some cases, they're almost the same.
We can repeat
it again and again.
The responses for different repetitions are staggered upward by a little
so that each horizontal strip represents one repetition of the movie.
So now we're looking at the neural activity of a group
of about 20 retinal ganglion cells while the movie was played repeatedly.
In fact, many times, as you can see from the
number of repetitions in one of these individual raster plots.
So what you can see hear is that each cell
responds every time at specific sudden points in the movie.
Sometimes the responses are strong.
Maybe here, and sometimes they're weak, here.
There are some repeats of the movie, where the cell doesn't fire at all.
What I hope you can see from this is something extremely beautiful
and exciting, each neuron is encoding some feature or features of the movie.
And each neuron is responsible for
a different set of features, sometimes overlapping.
For example, Cell R and Cell P have a
lot of features in common, but sometimes they're very different.
So our questions are, how do we use these responses
to determine what in the stimulus is making that cell fire.
Looking at this picture one also wonders
how should we think about this concerted activity?
Does every neuron signal its own message or is
the population responding as a whole in some complex code?
Well, we'll not answer that question.
We will be discussing models that, that
describe single neuron and population level responses.
So the questions we'll be addressing over the next
few weeks involve how we read out this code.
There are two ways of looking at it that are of course quite related.
We can consider the end-coding problem.
How does a stimulus cause a pattern of responses?
This leads us in the direction of building quasi-mechanistic models
of our neural system that allow us to predict it's response.
We can also remain agnostic about the system
and simply ask what do the responses that we
observe tell us about what the stimulus was?
This is the approach one might see at work in
say a neural prosthetic used to drive a robot arm whose
job would be to read some measure of neural data
and activate the arm to move in that person's intended direction.
So our goal will be to build models of this type.
Because neural systems are noisy or may contain information about aspects
that we don't control, we think about the model as inherently probabilistic.
We would like to know the probability of a response, given a stimulus.
This is a conditional probability distribution.
Conversely, in decoding, we'd like to know the probability of the,
of a stimulus having been shown, given the response that we recorded.
What we'll have to define and ultimately discover
is what is the appropriate measure of response?
What is the right way of thinking about the stimulus?
And what's the relationship between them that's embodied by our coding model?
So here's an example of neural representation of information.
We'd like to find some stimulus parameter, along which the neural response varies.
So we have stimulus parameter, in everything that
follows I'm going to call my stimulus parameter S.
And the meaning of S is going to change from slide to slide.
And neural response, the simplest way we can be think about this, and the
approach that we will be taking today, is that the neural response is some
kind of average firing rate or probability of generating a spike.
So here are a couple of classic examples of what we call tuning curves.
Here's data from a neuron in primary visual cortex, V1.
Such neurons respond to oriented bars of white, here,
passing through a sudden location in the visual field.
As the orientation of the bar is charged, say from almost horizontal
to almost vertical, this particular neuron at first does not respond at all,
but then starts to fire with a higher and higher rate.
And then less again, as the orientation moves away from that preferred one.
If you count up the spikes in a time
bend of say, 100 milliseconds, and pluck those number
of spikes as a function of the orientation, you'll
get a curve like this, which looks like a Gaussian.
Here's another example, this time from the motor cortex.
Now, as the animal in these experiments, a monkey,
makes an arm movement in a certain angle relative
to his body the firing rate of this neuron
is large for some angles and small for other.
And this time the plot of firing rate
versus movement direction is more like a cosine curve.
It turns out the neurons in primary visual
cortex are sensetive to many input features and
often the sensitivity to those features is distributed
in an orderly way, across the cortical sheet.
So what you're seeing here is an image of
a piece of cortex, a piece of visual cortex.
The color indicates the value of a particular feature to
which the neuron or neurons in that location respond most strongly.
This picture of response as a function
of location in cortex is called a funcitonal map.
This is an example of some functional maps in cat
and bush baby, and these classic what's called pinwheel structures.
In this case, the neurons prefer an
angle encoded by color, changes systematically in space.
The lower two panels show a map of preferred spatial frequency
again in cat and bush baby that is the width of lines
in a grating, to which these neurons have a strong response.
Again, this shows an orderly pattern across cortex.
FMRI studies show that there are localized regions in the temporal
lobe that are responsive to semantic categories, for example, faces or houses.
So the notion of a stimulus that drives a neuron maximally can get quite complex.
And the idea of being able to draw a tuning curve
as a function of some meaningful stimulus parameter becomes quite difficult.
As we can see here in these famous experiments.
So this group recorded from single
neurons, in the parahypocampal area in humans.
This is normally not something one can do, but here the experiment
has worked with patients who are undergoing surgery for epilepsy and had
agreed to participate in experiments.
What you're seeing here is the response of a particular neuron to different images,
where here the number of the image is not arranged in any particular order.
It is on the x-axis.
So, clearly there are few images that drive this neuron particularly well.
If we now look at the images that correspond to those large responses.
It was found that these have a common property, they all turn out
to be images of Brad Pitt and Jennifer Aniston.
So interestingly this neuron did not fire to images of either of
them separately, so see for example this response of Jennifer Aniston by herself.
Well, its true that because these experiments were done a long time
ago it's likely that not too many people have this neuron type anymore.
Maybe some of you, who, unlike me, refuse to read magazine covers
in the checkout line at the supermarket are a little bit younger,
some of you may never have had a neuron of this type.
So here's another intriguing example.
Again, some particularly large responses to some subset of those images.
Now when we look at which images those were, we see
that they all have a common property, in this case, Pamela Anderson.
But interestingly, they're not just photographs of Pamela Anderson,
here and here, but also drawings of Pamela Anderson.
And although
you probably can't see it on your screen, there's also a
case of a picture of Pamela Anderson's name written in text.
So in later experiments, this group has also showed that
such neurons also respond to audio clips of that person's name.
So we can think about neurons like this as embodying a concept.
So what's emerging from all this, is a pictgure
of brain regions having increasing complexity of stimulus representations,
starting from more geometric and becoming more semantic, here
down in the retina and the thalamus, lateral geniculate nucleus.
We see very simple forms of receptive fields.
As we go to V1, we see oriented edges.
As we move up to V4, we see conjunctions of edges that form contours.
And higher up into the, into the brain
where we see semantic categories such as houses and
maybe specific houses, such as The White House.
It's tempting to think about this as a progression of
features being agglomerated into more and more specific and complex features.
This also leads to increasing in variance.
Higher order areas are less sensitive to details,
such as color or location in the visual field.
So this idea of hierarchical features being assembled in a feed
forward way is the basis for many powerful and important models,
including ones that are enjoying a lot of success in Machine Vision.
What makes the true computation very interesting
is that these regions are massively interconnected.
For example, while the thalamus generally is thought of as a relay
station that takes in information as represented in sensory receptors, like the
retina, and distributes it to various other regions of the brain, in
fact it receives a massive amount of feedback from all of these areas.
And this suggests that these representations also feed back to
control what information is coming through in the first place.
So this is how semantics, the meaning or the value of the context
of an image, can end up influencing its initial representation in V1 or V4.
So here where there's a role for learning and for expectation.
What you think you're looking at can shape what you actually see.
Here's maybe a
nice example of such top down effects.
You might find it hard, at first, to figure out what this is a picture of.
Once you've seen it, whenever you see this picture again, which will be regularly,
if you go into the field of
visual neuroscience, you'll always see it instantly.
And while the role of these top-down effects is
very interesting and quite an open area that we've
love to talk about more in this course, I'm
primarily going to stick with these lower level, geometric representations.
While later in the course, Roger will tell you more about how networks
can learn to maintain memories, which presumably
form the basis of these semantic expectations.
In the next section, we're going to talk
about how we go about constructing these response models.
Let's take a break and be back for the next section.
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