SPRINGLab/asr-task-data · Datasets at Hugging Face

audio audioduration (s) 0.62 28.4	text stringlengths 2 287
	versus epochs and this can be a typical graph so you would often be seeing that you start
	slightly then goes down it may keep on jittering and these are all aspects about whats happening
	be a very smooth transition which it will be getting if your value of is very high
	to the local minima and these are different issues which we would be tackling down through
	experimental processes and some more learning experiences subsequently now looking at the
	so here what i am doing is typically i am looking into two different plots so one is
	my plot of epoch versus cost function the other is my plot of weight space versus cost
	goes to the next one then to the next one and and finally to my convergence now if you
	you would be seeing that the error function over there form some sort of a very structure
	troughs present over there so as these points of my weights they keep on moving down they
	would always be encircling and coming down to my local minimum point as soon as possible
	and the way it comes down to this local minima is what is my learning which is happening
	is that we can actually initialize a network at any random point over there and based on
	that it can start converging and oscillating around any of these trucks and that definitely
	these non global minima positions but rather somehow escape into this from these small
	all of this what comes down to our mind is something interesting so you have seen that
	there is for any kind of a given network if i have three different scalar values over
	there then i can take in these scalar values and i can predict out one of these predicted
	that i have my weights w one w two and w three i take all of these weights together and then
	down to my output over there ok
	doing so in order to solve it out the best possible way is basically trying to look into
	something which is called as the chain rule of differentiation which you have done in
	so i can take a derivative of the cost function with respect to this output next is my output
	now be represented as a product of del del p of jw and del del y of p so together these
	of the cost function if you look into the second part of the gradient then you see that
	of the derivative thats a derivative of the linear network itself and these three things
	together are what will be helping me in finding out the gradient part for my whole network
	then enter into eventually the deep learning and how to train down these deep neural networks
	thank you and stay tuned for the next lecture
	so welcome and so in the ah we will be continuing down with the from where we left in the last
	lecture and thats on multi layer perceptrons to deep neural networks and this is where
	and a recap of the learning rules and how to create down this single model and then
	a single perceptron and then a whole collection of perceptrons in terms of its matrix and
	the matrix form of representing the data from there going down to the gradient and what
	it gets broken down into partial products over there and using these partial derivative
	last class so that was on the gradient computation part say i have three scalars x one x two
	and x three and then i would like to map it down to another predictor scalar which is
	is from x how to get down to p hat the question which we had raised is how to get down this
	to y which is the output from the summation block and you take a derivative of y with
	respect to w which is known as the derivative of the linear part of the network ok now and
	now the point is that this kind of a computation is what holds true for just one single neuron
	ok and the next point is that if it is not just one single neuron but you have a collection
	of neurons or something which is a deep neural network
	as a multi layer perceptron due to its multiple layers form over there so thats exactly what
	nodes over there that connects to another set of intermediate nodes and that subsequently
	to get down the derivative in its own way but then in order to get this one you see
	case is something tricky so lets look into this
	small part of the network so what we do is say that i am looking at one of my particular
	layer which is say called as the d th layer ok now for my a d th layer what will i will
	now that can be done as an extended product of del del w of y d which is output which
	is the linear part of summation which comes down to that particular plot now if i go down
	to my d minus one th layer so this is my w d which is just connecting down my output
	to the d th layer now if i go down to one layer before it now what we can see is that
	this linear part of this block with respect to the weights which are connecting these
	of the linear part of this one with respect to the block earlier it ok so this is my d
	this is my w of d minus one and thats where my expansion happens now and similarly i keep
	on repeating this whole thing together on the chain and finally what i would get down
	is on the final part which is del del w of y one which is my first output layer over
	it which is my x over here so this is a typical way in which we calculate now our whole networks
	gradient over there so if i want that my total network has to be solved out so this is exactly
	what i would be doing in terms of my calculations so you can typically look so now that i dont
	have what is my input coming from here so what i would be doing is i dont know exactly
	what values are over here so i will be again differentiating this with respect to this
	it stops is a del del w one of y one and thats equal to my input which is x ok so i i believe
	this part is quite clear to you guys and and quite intuitive actually not so hard to calculate
	down something like this now that i have this form going down so my first part of it is
	is what is called as a derivative of the network and finally is the input to the network which
	is my x ok so these together is what constitutes of any
	sort of a learning mechanism within a multi layer perceptron or any kind of a deep neural
	network so what you will have to do is you will have to find out what is my derivative
	of my cost function you will have to find out the derivative of the network which together
	and derivative of the perceptron together and you will have to find out what is that
	now by solving out this complete derivative over here is what we are able to get down
	as our neural network learning algorithm in terms of gradient descent and thats where
	criteria so what this essentially means is that in order for the total derivative of
	fraction of the derivative exists so every single part over there we were doing a chain
	rule of expansion so if every single component of the chain
	rule exists only in that case you would see that the total derivative of the network as
	which is lets take down these two cost functions so the first one is what is called as the
	you can do is quite simple i mean you can just take a del del w ah del del p of j over
	happen is definitely it does exist for the first case which is euclidean norm
	have the second one ok and this is where the fun is so do you think that the derivative
	of this one will exist as well or not just just take down a few seconds over here while
	at zero you see you have an l one norm or just a mod ok so mod of p minus p hat this
	one over there is basically a value which is always a nonzero value and this hat does
	of the rest part of the network and now over here one important point is that the derivative
	del del y of p that will not come into existence whereas del del y of z that does not have
	question is does the derivative of each of them exist or not so lets give you some time
	the derivative does exist and thats a perfectly differentiable function whereas look into
	the second part of that that again is something which is not differentiable because of the
	property so one property was definitely to make it bounded in some form ok but we also
	mentioned that the there are other properties and one of those important properties is that
	the cost function itself sorry not the cost function but the transfer function itself
	end over there until and unless a transfer function is differentiable the derivative
	function and thats the reason why these kind of functions cannot be made cannot be used
	through intermediate weights w one up to w d and ah go down to my final output which
	is p hat and the way of how we are doing down is something of this sort and the first step
	which is called as the forward pass of the network and this is something similar to what
	pass of this x in order to obtain your p hat now that you have your forward pass and you
	that i need to compute out my j which is my cost function the way of computing this j

versus epochs and this can be a typical graph so you would often be seeing that you start

slightly then goes down it may keep on jittering and these are all aspects about whats happening

be a very smooth transition which it will be getting if your value of is very high

to the local minima and these are different issues which we would be tackling down through

experimental processes and some more learning experiences subsequently now looking at the

so here what i am doing is typically i am looking into two different plots so one is

my plot of epoch versus cost function the other is my plot of weight space versus cost

goes to the next one then to the next one and and finally to my convergence now if you

you would be seeing that the error function over there form some sort of a very structure

troughs present over there so as these points of my weights they keep on moving down they

would always be encircling and coming down to my local minimum point as soon as possible

and the way it comes down to this local minima is what is my learning which is happening

is that we can actually initialize a network at any random point over there and based on

that it can start converging and oscillating around any of these trucks and that definitely

these non global minima positions but rather somehow escape into this from these small

all of this what comes down to our mind is something interesting so you have seen that

there is for any kind of a given network if i have three different scalar values over

there then i can take in these scalar values and i can predict out one of these predicted

that i have my weights w one w two and w three i take all of these weights together and then

down to my output over there ok

doing so in order to solve it out the best possible way is basically trying to look into

something which is called as the chain rule of differentiation which you have done in

so i can take a derivative of the cost function with respect to this output next is my output

now be represented as a product of del del p of jw and del del y of p so together these

of the cost function if you look into the second part of the gradient then you see that

of the derivative thats a derivative of the linear network itself and these three things

together are what will be helping me in finding out the gradient part for my whole network

then enter into eventually the deep learning and how to train down these deep neural networks

thank you and stay tuned for the next lecture

so welcome and so in the ah we will be continuing down with the from where we left in the last

lecture and thats on multi layer perceptrons to deep neural networks and this is where

and a recap of the learning rules and how to create down this single model and then

a single perceptron and then a whole collection of perceptrons in terms of its matrix and

the matrix form of representing the data from there going down to the gradient and what

it gets broken down into partial products over there and using these partial derivative

last class so that was on the gradient computation part say i have three scalars x one x two

and x three and then i would like to map it down to another predictor scalar which is

is from x how to get down to p hat the question which we had raised is how to get down this

to y which is the output from the summation block and you take a derivative of y with

respect to w which is known as the derivative of the linear part of the network ok now and

now the point is that this kind of a computation is what holds true for just one single neuron

ok and the next point is that if it is not just one single neuron but you have a collection

of neurons or something which is a deep neural network

as a multi layer perceptron due to its multiple layers form over there so thats exactly what

nodes over there that connects to another set of intermediate nodes and that subsequently

to get down the derivative in its own way but then in order to get this one you see

case is something tricky so lets look into this

small part of the network so what we do is say that i am looking at one of my particular

layer which is say called as the d th layer ok now for my a d th layer what will i will

now that can be done as an extended product of del del w of y d which is output which

is the linear part of summation which comes down to that particular plot now if i go down

to my d minus one th layer so this is my w d which is just connecting down my output

to the d th layer now if i go down to one layer before it now what we can see is that

this linear part of this block with respect to the weights which are connecting these

of the linear part of this one with respect to the block earlier it ok so this is my d

this is my w of d minus one and thats where my expansion happens now and similarly i keep

on repeating this whole thing together on the chain and finally what i would get down

is on the final part which is del del w of y one which is my first output layer over

it which is my x over here so this is a typical way in which we calculate now our whole networks

gradient over there so if i want that my total network has to be solved out so this is exactly

what i would be doing in terms of my calculations so you can typically look so now that i dont

have what is my input coming from here so what i would be doing is i dont know exactly

what values are over here so i will be again differentiating this with respect to this

it stops is a del del w one of y one and thats equal to my input which is x ok so i i believe

this part is quite clear to you guys and and quite intuitive actually not so hard to calculate

down something like this now that i have this form going down so my first part of it is

is what is called as a derivative of the network and finally is the input to the network which

is my x ok so these together is what constitutes of any

sort of a learning mechanism within a multi layer perceptron or any kind of a deep neural

network so what you will have to do is you will have to find out what is my derivative

of my cost function you will have to find out the derivative of the network which together

and derivative of the perceptron together and you will have to find out what is that

now by solving out this complete derivative over here is what we are able to get down

as our neural network learning algorithm in terms of gradient descent and thats where

criteria so what this essentially means is that in order for the total derivative of

fraction of the derivative exists so every single part over there we were doing a chain

rule of expansion so if every single component of the chain

rule exists only in that case you would see that the total derivative of the network as

which is lets take down these two cost functions so the first one is what is called as the

you can do is quite simple i mean you can just take a del del w ah del del p of j over

happen is definitely it does exist for the first case which is euclidean norm

have the second one ok and this is where the fun is so do you think that the derivative

of this one will exist as well or not just just take down a few seconds over here while

at zero you see you have an l one norm or just a mod ok so mod of p minus p hat this

one over there is basically a value which is always a nonzero value and this hat does

of the rest part of the network and now over here one important point is that the derivative

del del y of p that will not come into existence whereas del del y of z that does not have

question is does the derivative of each of them exist or not so lets give you some time

the derivative does exist and thats a perfectly differentiable function whereas look into

the second part of that that again is something which is not differentiable because of the

property so one property was definitely to make it bounded in some form ok but we also

mentioned that the there are other properties and one of those important properties is that

the cost function itself sorry not the cost function but the transfer function itself

end over there until and unless a transfer function is differentiable the derivative

function and thats the reason why these kind of functions cannot be made cannot be used

through intermediate weights w one up to w d and ah go down to my final output which

is p hat and the way of how we are doing down is something of this sort and the first step

which is called as the forward pass of the network and this is something similar to what

pass of this x in order to obtain your p hat now that you have your forward pass and you

that i need to compute out my j which is my cost function the way of computing this j