Lecture – 27 Learning : Neural Networks

Lecture – 27 Learning : Neural Networks


In the last lecture, we looked at decision
tree learning. Now, we will digress a little and look at kind of learning which comes under
statistical learning. So, specifically, we will look at learning using neural networks. I
will briefly introduce the structure and the basic definitions of a neural network and we will
see how we can use neural networks to learn different kinds of functions. So, a neural network consist of a set of nodes
which are neurons connected by links. Each of these nodes has very simple processing capability
and there are lots of them and they are connected links; each link has a numeric weight,
associated weight, each unit has a set of input links from other units. It has a set
of output links which goes into other units, it has a current activation level which I will define
shortly and has an activation function to compute the activation level in the next time
step. Now, when we talk about such nodes and etc.,
for the time being, we will assume that these are all done. This is just a model for computation.
It is not that we actually have a processor which is doing all this kind of stuff, it
is just that this is a model of computation that we are looking at, where we have set of nodes
having very limited computational capability and we have these interconnections. So, a typical
picture of a node is going to be like this- you see it clearly, right? These are the set of inputs that we have,
so, it is like, Aj is an input to this particular node or neuron; there is a weight associated
with every link. So, the weight from a neuron j to neuron i is given as Wji, so, this is directed
link from j to i and it has weight Wji. Then, we have a sigma function here, which
computes the total input that it receives from the other neurons. I will define what is the total
input and then, there is this activation function g, which is a function of the total
input that the neuron i receives. The sum function of this and that defines the activation
Ai of the neuron i. And then, this activation value is propagated through the output links
to other neurons. The total weight- the total weighted input-
is the sum of the input activations times their respective weights. What does that mean? It
means that if I have a neuron i- suppose this is our neuron i- and I have neuron j here feeding
into this, this has a weight of Wji. Then, the input that i receives from j is the activation
of j times Wji. This is the input that it receives from this. And if I want to compute
the total input that i receives from all of its neighbors- preceding neighbors- then, I sum
this over j, for all j which feed into this network, this node. And then, in each step, we compute the activation
ai which is a function of the total input. So, it is a function g of sigma of j Wji Aj.
Is this clear? Now, this function can be of different types; it can be a threshold function,
which says that Ai will be 1, if the total input exceeds some value. if the total input
is more than 0.7, then, Ai will become 1; if the total input is less than 0.7, then, Ai will
become 0. So, we could have something like that and so on. Now, let us see that how do we use a neural
network like this for learning. So, this is a single layer network. I have 1 layer of input
units here. These are the input units of the network and I have 1 layer of output units
of the network. These are nodes of the network. There is a Wji which is the weight of the
link from ij to the output i Oi. If the output for an output unit is O and the correct output
should be T, then, what do we mean by the correct output? So, what we are trying to do is, we
are trying to read; we are trying to learn a function from the inputs to the outputs. Again,
this structure of the neural network for a function which has 4 inputs and 3 outputs
is like this. Now, what will happen is that we will be given a set of training data set, just
like we had in the decision tree scenario. We will be given training sets; those training sets
will be valid input output pairs. So, it will be a set of a cases where we are given i1, i2,
i3, i4 and for a given value of i1, i2, i3, i4, what are the values of O1, O2 and O3? We will be given several such cases and the
objective is to make this network learn that function. That at the end of the training,
if I repeat any example from that, if I give the inputs corresponding to any of the sample
data sets, then, the correct output should be displayed in the output. Also, if I give some
inputs which was not there in the training set, then also, correct output should be displayed.
Now, again, just like the previous case also, we can never be 100 percent sure whether it
is giving the correct output for the others, but the objective is to make the neural network
to learn the function, so that it is able to extrapolate also correct values for the input
scenarios, which were not given in the training set. Obviously, we have to define an error term
and the objective will be to learn, so that this error is minimized. So, if the output for
an output units is O and remember that the output is actually a real valued stuff, because our
activation values that we have are real value; can be real value, it can be 0 and 1 also.
If we use a threshold function, then, the activation will be 0 or one. If you use some
other kind of function which gives real values as output, you can give that also, and then,
in case that case O will be a real and if the correct output is T, then, the error is given
by T minus O. Now, the weight adjustment rule is Wj tends Wj plus alpha into ij into Err. Now, let us see what- I will explain this
in a moment, so, what we are trying to do is, we are going to train the neural network in the following
weight. So, we will present it with some input value. Initially, the weights are randomly
assigned; they are all randomly assigned weights. I will give some input from the training
set and then, I will see what output it produces. Based on the output that it produces,
I will compute the error, because in the training set, the correct outputs are given,
which is T. So, I will compute the error and depending on the error, I will readjust the
weights on the inputs. Now, let us see in very crude terms, that what would that mean? Suppose I had- I will start by given a giving
an example where the inputs are all Booleans. So, let us say that I have these 3 inputs
and these 2 outputs and I have a complete connection, so, it represents a complete bi-partite
graph. Now, let us say that this is one, 2, 3; this is one, 2, so- this is i1, i2,
i3 and this is O1, O2. Now, I have given some value, let us say, 0, 1, and let us say that at this
point of time, this produces a value of 1, whereas this is our O and the value of O1
and actual value, which means the correct value, T1, should have been 0. That means that what we
need to do is- and let us say that the function that we are using here is a threshold function. So, it is a threshold function, which says
that if the total input is greater than 0.5, then, this is going to be high, otherwise, it is
going to be low. So, that means that V1- that the total input should be- for this case, should
be below 0.5, so that the unit remains at 0, the correct value. Now, how can we do that? What
we are going to do is, we are going to reduce the weights on the edges, which connect to the
1 values. So, we will pick up these 2 edges and reduce their weight. What effect is that going
to have? The input value will go down, because our input was sigma over j Wji times Aj. So,
Aj is 1 for these 2 and if we decrease Wji, then, the total input is going to go down. But at
the same time, if we unilaterally decrease the weights here, then, the total weight balance
is going to change. So, what we are going to do is, we are going
to reduce the weights on these and at the same time, increase the weight on this, so that
the total weight constitution remains fixed. It is just transferring weights from the ones which
we want to reduce to the ones where we want to increase it. If we do that, then, for this
case, we will move a little bit closer to the goal and we repeat this case over all the training
sets, with the hope that at the end of the training, we will be able to correctly classify
the samples and be able to produce the right kinds of outputs. Now, as it turns out, I
am going to come into the formal analysis in a moment, but as it turns out, that this kind
of a single layer of neural network is able to learn only functions which are linearly separable. Now, let us understand what is linearly separable;
linearly separable functions are ones where you can have a plane in the Euclidean space
which separates the positive cases from the negative cases; the yes answers from the no
answers. For example, if you look at say, an AND gate; suppose we want to learn the AND function.
This has 2 inputs; i1 and i2. If you look at the 2 dimensional plane with this being i1
and this being i2, then, if both are 0, then, we have 0. So, this is a no answer. If 1 of them
is 0; if i1 is 0, i2 is 1, then also, it is a no answer. If both- if i2 is 0 and i1 is 1, then
also, it is a no answer. If both are one- that is the only case where we have a yes answer. Now, this is linearly separable, because I
can have a plane which drives through this.Now, you might be wondering that what does this have
to do with the learning here. I will come to that in a moment. Let us look at the OR function.
If we have the OR function, then, what we will have is, this will be 0. So, I have i1, i2
here. Again, this will be 0 and these 3 will be 1. Again, this is linearly separable, because
we can have a plane like this in contrast. Let us look at the XOR function. So, for that, this
is going to be, 0 this is 1; this is 1 and this is 0. Now, there is no way that we can drive
a plane between yes cases and no cases. So, this is a case which our single layer network will
not be able to learn. It will not be able to learn the XOR function. Now, what has this got to do with our weight
adjustment, etc.? Why can it not learn this why? Can it learn the other ones? So, let us simply
look at the single layer network, where, if the total input is positive, we will switch on
the unit; if the total input is negative, we will switch off the unit. So, activation will be
1 if the total input is positive, activation will be 0 if the total input is negative. So then,
we have this sigma of j equal to 0 to n, where n is the set of inputs Wjxj, where xj is the
input. If this is greater than 0, then, the input switches on; otherwise, it switches off. Actually, the equation W dot x is greater
than 0, where W is the weight vector and x is the input vector. So when this happens, then only
we switch the unit on. Now, if you look at this function, this actually defines the hyper
plane; this defines a hyper plane- see this x. For 2 dimensions, this is going to be just a single
line; if you have multiple dimensions, it will become a hyper plane, because each of these
x can be k dimensional vector. So, this hyper plane is separating out- is acting as a threshold.
If that is greater than 0 is on the other side, anything which is less than 0 is on
this side. And so, because that is the decision for switching
the neuron on or off, so, that is the plane which separates the positive cases from the
negative cases. Our objective is to learn the values of the weights, so that the the weight
vector that we construct along with the input vector will actually come to this plane; the
weight vector will coincide with this weight vector which separates these 2. That is intuitively
the objective that we are trying to do. Let me quickly derive this particular equation
for updating the rules, then, we will see some example cases of this learning and its applications
also. First, we define the error. For the error,
we are going to use the the root mean square error, RMS, which is the standard error that people
wish to minimize between functions. You have studied RMS error? What we are going to do
is, we are going to keep this as the error term. So, y minus this whole square where perceptron
is, the network is the simple network node that we talked about. It is the simple neural network
node that we talked about; it is popularly called perceptron. Now, our objective is to
update the weights in such a way that in each step, this error will reduce. What we are
going to do is, we are going to do gradient descent. You remember gradient decent? What does gradient
decent do? It has some objective function and we take steps, so that that objective function
gradually decreases. Of course, we have the problem of getting stuck in local minima;
we have the same problem here also, but let us see how can we do gradient descent to minimize
this error function. Every step is going to reduce the error and we want to do this monotonically;
that is why gradient descent- we want to monotonically reduce the weights. Remember
that we are going to put different training sets and each time, we are going to bring down
the error for the . To reduce this error, let us first see what
we have as delta E over delta Wj. I want to see that what is the change in error with respect
to a change in the weight that I receive from j. So, this is given by Err. What is Err? It
is half Err square. So, if I do this, then, it is Err times- see this- 2 and half will get cancelled
out, because of the differential. This 2 and half will get cancelled out and I will
have Err times delta Err by delta. I will have Err times- now, I substitute this out here. Delta
by delta Wj of g of y minus i; think I missed a g here, it should have been this- should be
a g here; this is g of g is the activation function of y minus- this is the total input-
j equal to 0 to n Wjxj. No, the difference, the error, is in terms of the output that we get. So, this comes to minus of Err into g dash
in, where in is this total input times xj and g dash is this derivative. See the other terms;
see this, besides xj, it has other terms also- xi, the ones which are non j. Now, those terms
are going to get eliminated, because this is a partial differential. So, the only term that
we will have out here is the 1 which corresponds to Xj and we will also have the derivative
of the whole thing. Now, could I make myself clear? No? This minus is getting propagated outside
this because this is a constant, it gets eliminated, so, I have this term. Now, is this clear? How we arrive at this?
See, this is a constant, so, it gets eliminated and then this g- because this is a function, it
becomes g dash of this whole thing- and then, the partial differential moves inside and when
it moves inside, then, everything which is non j gets eliminated and I am just left with xj.
Are you with me? This is the formula that tells us the weight updation rule. From this, what
we will get is- okay, so, let me write down what we have obtained so far. We have obtained delta
E. Yes- See, this is the- I think this is- wait, yes- Now, what is the confusion? The output
is g of the total input
and this is the incorrect input that we are getting, this is the correct
input that we should get and this is the incorrect input that we have got, because
our weights are not yet tuned. Yes, I think what we are trying to do here
is to minimize the error in the input, because if you are able to bring the total input to the
correct value, then, the output will obviously be the correct one. Let me reflect on this a
little more and I will clarify it. Maybe in the next lecture, because we are going to revisit good
part of this when we look at back propagation learning. So, for the time being, let us say
that we have obtained that delta E by delta Wj is given by minus of Err times g dash of in,
where in is the total input into the perceptron times xj. From this, we set Wj to be Wj plus alpha into
Err into g dash in into xj, where alpha is the is called the learning rate. See, rather than
adding this whole error term into Wj, we are adding only a fraction of it. So, we are not
just jumping into the same this thing, because that would amount- is something like you know,
quenching, but we do not want to do that; we just have to incrementally tune the weights,
so that over all the samples- we arrive at a set of steady state values of the weights. Therefore, this alpha is called the learning
rate and we just add a fraction of this error into Wj. Is it clear? And we do this for each
of the Wj. This was just computing delta E by delta Wj for 1 j and we do it for each of
the js, so that we have updated the weights into of all the links that are feeding into this.
Now, I will digress a little bit from this; we will come back to this analysis again when we look
at 2 layered networks, where we will study method called back propagation learning, where
instead of learning in just 2 layer networks, we will learn in multiple layer networks and
the interesting thing will be- what are the internal nodes? What do will they do? Here, we have just the output layer and the
input layer and we are tuning the weights between the output and input layer, so that the output
layers come closer to the desired values- the weights become closer to the desired values,
so that it is able to give the proper output for all the training examples and others. Now,
let us look at slightly different problem- we will look at the problem of recognizing text. Let
us say that we are given a matrix of dots. This is the matrix of dots that is given to us and on this matrix, we can have different
letters by setting these to 1 and 0. For example, if
we set this to 1, this t 1, then, that gives us A. Similarly, you can have B, C, D, whatever. Now, what we want to do is that if somebody
writes A slightly differently- maybe instead of writing it this way, it writes it that instead
of lighting this dot, it lights this dot; slightly different, this 1 is off and this
1 is on. We should be able to classify all those cases. I will train it with a set of different
A, B, C, D, etc., and then, it should be able to make out a slightly different perturbed
A, it should be able to make out the slightly perturbed B and so on, and be able to say
that yes, this is still an A, this is still a B and so on. Now, how do we model this into a neural
network framework? 1 option is that we create a neural network where these are the inputs;
each of these dots is an input which can take a value 0 or one. And I have a set of output nodes and each
of these inputs will be feeding into those outputs. I will be receiving these output nodes, receive
inputs from each of these elements; so, I have again that 2 layer kind of complete network
that we have. So, it is that complete bi-partite graph that we have here as well. What we are
going to do is, we are going to- this is going to have at least twenty 6, could have more also;
at least twenty 6. Then, we are going to train this network, so that whenever we have A,
1 of these glows; wherever we have B, some other 1 of these glows; whenever we have C, some third
1 glows, and the others remain off. Now, 1 way of doing this which was suggested,
was doing what is called competitive learning. Competitive learning sets up a competition
between these nodes and whichever is the winner is the 1 which will be declared as the value.
Which means that whenever we give yes, there should be 1 particular node which should become the
winner for all As and 1 particular node should become the winner for all Bs. Which 1 of these
will classify the As and which 1 of these will correspond to Bs? We still do not know. So,
initially, all weights are random. How the learning will progress initially- all weights
are random, so, when I present it with the first A, 1 of these will win. Let us say that this
1 wins for A. Now, what we want is that in future, whenever we present A, even with slight
perturbations, this is the 1 which should win. So, what we will do is, we will strengthen
this so that its activation value will further increase when we present an A. How do we do
that? When you have an A, then, there are some when you presented it with an A, then, some
of these units were one, which means that there are some of these links which correspond to
the ones and some of the links which correspond to the 0s of the input. We will do that weight
transferring, so, we will take a fraction of the weights from the 0 ones and transfer that
weight and distribute it equally to the ones that we have here. What we are going to have here
is that the total weight will always be one, so, for every unit, the total weight of the edges
incident on that sum of the weight will be one. Whenever we redistribute the weights, the
total weight will still remain one. But now, we have moved weight away from the 0 inputs to the
links corresponding to the 1 input. So, next time, when we give A that activation of this, the
total input to this will be more. So, it will stand a larger chance of winning. On the other
hand, what do we do with the ones which had loosed the competition? For the ones which
loosed the competition, we will do the same, but a much lesser fraction for the winner; the fraction
of weight that we transfer will be larger than compared to the losers. For the losers,
we will take out weight from the 1 inputs and transfer it to the 0 inputs, but the fraction
of weights that we transfer will be much lesser. Having done this weight adjustment, we then
again present it with another sample and repeat the procedure. And the idea is that our expectation
is that eventually, these nodes will start classifying some particular letter. There will be 1 which will always come up
for A one, which will always come up for B one, will always come up for C and so on. But just like-
this is also gradient descent. Why? Because if you take any particular node, it is being
dragged on to something. What is it being dragged on? So, 1 view of looking at this is that
each of these is a vector; this is a vector, this is a Boolean vector and it has so many different
dimensions. If there are some twenty dots here, then, is a twenty dimensional vector. Let
us think of the twenty dimensional hyper plane. you look at the twenty dimensional hyper plane,
then, in that plane, each of these samples is a point, because every vector is a point in
that twenty dimensional hyper plane. I have the A as 1 of the points in this hyper
plane, so, just remember that this is just not a circle; it is actually a hyper plane and this
is 1 point which corresponds to the A. Then, similarly, we may have another point on the
hyper plane that corresponds to B and another plane which corresponds to P. The 1 which
corresponds to R is going to be close to P and so on. And where are our vectors here? Each of
these vectors- the weight vectors that we have- they also correspond to points in this plane.
So, I will have some vector here. Initially, say 1 is here, 1 is here, 1 is here, 1 is here.
So, what is happening is that when I present an A, let us say that this fellow wins. So, the
weight adjustment rule is moving it towards A and for B- if this 1 wins, this is going to move
towards B. And also, the weight adjustment rule is going to take to a much smaller extent
the ones which are here to slightly away. As we were saying, that the ones which are-
Yes, now, why do we move them away? We move them away because of certain scenario. This part
is clear? That the weight adjustment is actually taking it closer to this, to the vectors that
correspond to the actual thing and when you move it closer, if you give a slight perturbation
of A; if you give a slight perturbation of A, let us say A dash, which is here or even if A
double dash, which is here or even if A double dash, which is here, then, it is more likely that
this fellow will win once it moves closer to it. This vector will not only have learned the
A that you presented but also learn As which are close to them. That is a good thing about
this. There can be some problematic situations for which we have the other kinds of roots. Suppose
we have A here and I have say, B here, and incidentally, it turns out that both of these
are pretty close to this one. Now, what is happening is that every time this 1 wins-
okay let me not; not this case, forget about this case. I have xB here, sorry, B here and then,
I have A here and other ones here. And now, see, the problem is that every time you present
A, it is this 1 which is going to win and it is going to move slightly towards this direction. And every time you present B, it is this only
which is winning, because this is absolutely opposite way. And if this 1 again wins, then,
that means that this is going to again be dragged on to this side. So, it is going to
oscillate between these 2, whereas there is another vector which is not being used at
all. So, whenever you have a losing one, whenever you present A: this 1 wins, this 1 loses.
So, you push this away slightly, then, that is going to have the effect in the long term of moving
this slowly around, so that at some point of time, it is going to come pretty close to
B. Yes, B is also going to push it away. So, if you have a scenario where you are presenting A
and B alternately, then, again, you would have a bit of a problem. You have to mix up your training in such a
way that it eventually starts classifying. The intuitive idea of moving it away is this:
to move away those vectors which were not being used at all, which are not winning on any cases.
If we can move them away slightly, then, maybe somewhere down the line, they will move close
enough to some 1 else and actually start participating in the classification. Having
vectors- having outputs- which are not winning in any case is not useful, right? As you can
still imagine, that there will be cases where we will get stuck in local minima and you will
have 1 vector which is moving around between 2 of them. But in many cases, we will be able to do this
and if we put in more vectors, more outputs, then, it is more likely that we will- another
option is that if you have a particular output which is not playing a role, you randomize
the weights to that, so that it now moves into a entirely different place and maybe starts
participating. So, this is 1 paradigm of learning that we have learned today. In the next class,
we will be talking about learning algorithm called back propagation learning. In the last, we had started off with neural
networks and we had seen how, by using very simple processing units called neurons, we attempt
to learn different kinds of functions. The model that we looked at in the last lecture
was what is called a perceptron and a perceptron is a single layer network. Where we have neurons which are simple processing
units and we had a set of input units feeding into the neuron. Each neuron was like
this and we had actually, a collection of other neurons also and each of these other neurons
would also receive inputs from the same set of input lines. This was the simple form of a
single layer network that we had looked at in the last class. And then, we wanted to see that
how to compute the weight learning function. Initially, all the weights are randomized
and we want to learn the weight learning function, so that after we have learned the weights
and we are presented with the inputs, the neuron outputs are the activation values of the neurons,
should have the correct output value. For example, 1 way of the these neurons can
have different kinds of function that they can compute, of which 1 is where you compute the
total input into the unit i as sigma W j i, over all the inputs j times the input that you
receive from j. This was defined as the total input. And then, we define the activation function
as some g of this input and that is the output that this neuron is going to have. And we
saw that there can be different kinds of functions for g, of which the 2 most common ones are
the sigmoid function, which looks like this, where the input changes gradually or it could be
a threshold function, which means that the moment you reach the threshold, it will simply switch
on. So, it is off- when you reach the threshold, it switches on. Yes. There-. These
ones- they are the input units, they are the inputs to your neuron. So, a neural network
will have a several layers of neurons like this and will have 1 layer at the bottom of input
units.

Author: Kevin Mason

47 thoughts on “Lecture – 27 Learning : Neural Networks

  1. The mathematics of this lecture are way above the average YouTube user.

    The typical YouTuber is interested in girls shaking their asses around. Those are the vids that get millions of views.

    But for those that care about machine learning, this is roughly equivalent to an upper year computer science lecture.

    Valuable academic content in this video, but could have been more professionally presented and edited.

    4 stars.

  2. Can you speak loudly? I dont understand single words..please bag ur pardon…Here question arises that why did you post this video if its voice quality lower..

  3. I very much like these lectures from India Universities.

    Interesting to see how students got confused when he did calculations for error-minimizatin. Using x as multiplication sign and as a variable is certainly not helpful in writing equations.

  4. Excellent, excellent training video. One thing I noticed however, is that the error function is demonstrating method of least squares and not root mean square, if I'm not mistaken. Thank you for the very informative lecture.

  5. you are right..
    Please visit this lecture from MIT for visualization of Least Squre Mathod..

    Lec 21 | MIT 18.086 Mathematical Methods for Engineers II

  6. Nice Tutorial!!….Its very great to see our IITs coming out with such good initiatives in the times when engineering youth do nothing except jerking all the time 😛 ….Prof Dasgupta, though a bit confused, really rocks in the video!!….In fact, IIT profs are rocking in their own way!!

  7. Amazing video … great examples.. love NN!!!… saved me a lot of time reading the lecture slides 😉 way to go IIT!!!

  8. Yes, I am an idiot!
    My point is to let him know that he is wasting paper and think of some alternative ways to save paper. No wonder our world is doomed because of such mindset.

  9. Hows this a waste? That is what paper is intended to do. He can't use the back since he is using marker and it would show through. Also these drawings are being used by thousands of people who have now watched the video. So each sheet of paper is useful for thousands of people. Now think about a student in this guys class taking down notes, only that student will use his or her notes. So in essense each of these pages is orders of magnitude more useful than students taking notes. stop them

  10. You may be affirmative.
    I've heard that Mahatma Gandhi used to write on the free space of letters which used to come to him. Imagine how dirty those letters would have been since they used to come from afar and Mahatma still used to write on them. That's why he is the Mahatma and is still respected.
    Nevermind, I will not get into more arguments but ways have to be found out to save our environment as best as possible. Even one paper is important.

  11. He did a great work. It is an amazing source of knowledge. Stop commenting on trivial stuff (his writing or paper sheets) and please please don't abuse the right of commenting by doing this.

  12. @bubach85 lol, man you idiot, he probably plays a string instrument (guitar or sitara), i know you know that ppreciate your ahumour tho

  13. I used to teach that 20 years ago, but with a more visual method, using color interactive graphics (not as developed as now, but still quite helpful) to understand the different steps and show the convergence over time.

    regarding BIAS: it does NOT matter whether you use + or -, as long as you are consistent throughout the learning and operation phase.

  14. Seems like that the professor is very confused… He's also skipping topics by making excuse "i will tell in a mo" n then forget. Not good for newbies 🙁 . One must read book to learn basics before watching this video.

  15. This video is average quality. The relatively archaic explanation methods and strong mathematical bias place burdens on the learner to be good at math and able to follow the topics in an order thats not necessarily the easiest.

  16. @venkatarun95

    Typical 3rd world mentality. Middle east schools are similar in that they focus only on the harder sciences and stupidly think those are the only ones that matter.

    Indians are forgetting their intellectual history of a broad spectrum of ideas.

    To properly understand learning in general, you need to understand psychology, and neuroscience, and cognitive science before you can fully grasp backpropagation being just one way of doing it.

    You know you're not that bright.

  17. @Norman60Fahrer

    How many times did (do) you confuse between gas pedal and break pedal when you are driving @ high speeds?

  18. What are you even talking about? I would say I'm living proof that knowing the flaws of back-propagation from a purely mathematical perspective is possible (this shouldn't be hard to believe). Please stop calling people names and complaining about math. The math in this video is of a trivial nature.

  19. I am saying that a mathematics student trying to improve upon back-propagation will only do so from the view of viewing it as a differential mathematical machine. They will not know or understand its relationship to whats gone on before, nor what its intended to model, which is parallel distributed processing in brains. Stupid approaches led to dead ends like perceptrons and newer support vector machines, which are mathematical circle jerks by people who don't know brain science.

  20. And what I am saying is that I understand all of that, but if you cannot tolerate even baby math, there are many things which you won't understand on this topic (including, in particular, the very subjects you raised). If you do not mind that, then so be it, but a lot of people assume at least a marginally mathematical mindset.

  21. You think chain rule calculus is baby math? To a mathematician it obviously is, but to most people, even those that might have degrees but don't use calculus everyday will get rusty. I doubt you could derive the chain rule from first principles, even if you know how to use it in a mechanical way. But the key conceptual ideas of understanding the power of backprop have to do with the nonlinear sigmoid and its differentiability in relation to credit assignment problem and functional superposition

  22. To finish up. A lazy, or arrogant or useless teacher is the kind that throws only abstract math at the students. A *good* teacher can use metaphor and analogy to help the student picture in their minds what the math is expressing. I've seen this before in programming courses and in math courses. People may be able to use the tools, but they don't gain an intuitive feel for the stuff without different views both mathematical and non-mathematical of the subject matter.

  23. Wonderful video for understanding Intelligent Character Recognition (ICR) module.. Nice Classical music in the end sums up all 🙂

  24. I like this lecture, the proffessor seems to be an owl in disguise.

    Error should be 0.5*(y – g(<x,w>))^2 for y the correct answer.

  25. great lecture! thank you. I think the second equation at 29:07 should be

    dE/dWj = Err * d(y – g(Summation of W, Ij))/dWj

    because g is the activation function, and is what is applied to the weighted sum of inputs to have output that is subtracted from y(expected or correct output).
    It evaluates to the same thing though

  26. It is more natural to define neuron in first layer with i and j for the second layer why not facilating the understanding !!!!!!!

Leave a Reply

Your email address will not be published. Required fields are marked *