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

audio audioduration (s) 0.62 28.4	text stringlengths 2 287
	heavily we know some of these explanations but not all of these explanations and thats
	a substantial part of what works i will also be working down on why it works and what are
	going through this whole route or if you have a different kind of a candidate search which
	in hand and thats what we will be doing from theory to experiments and eventually that
	you can do is get down any of these and then which which are really good except for lets
	place while we also have done the clustered axis given down for participants of this course
	so that you can get down access to an hpc so or you can obviously buy down this say
	tool boxes all of these are open source as of now so you can use any of this other than
	the one on matlab for which you will definitely have to pay for the licenses but the matlab
	can get this book and thats thats what we will be using as a major reading material
	to what we were doing in the earlier classes was that in the earlier classes while we were
	using feature extractors and feature descriptors which are hard coded functions over there
	neural network on the contrary today when we are going to do it
	so here is when a neutral network itself has to come down to be an end to end learning
	framework which means that input to the neural network itself is an image while the output
	from it is still a classification ah output so it can be a classification output it can
	again and then entering into the multi layer perceptron from there we enter into something
	is my input and my output related and what happens during the learning phase and this
	is a quite critical part over here
	since in the last lecture and the lab which we had done so you were introduced to the
	concept of error back propagation and from there we had a gradient descent based learning
	rule now what exactly happens in telling this as a error back propagation and why it happens
	of code is what we are going to explain you through this signal flow graph representation
	other transformations and cost functions also to exist and then eventually go down to the
	there were three inputs over here in the earlier case last week when we were doing it so these
	three different features but these three can be three pixels so you can consider just three
	space so each component itself is represented as one independent scalar value so your x
	one can be the red value of a pixel x two can be the green value of a pixel x three
	so let the decision associated with a particular pixel over here b p hat and now with the simple
	neuron model what would happen is that we will have a weighted combination of these
	inputs going down to a neuron and from there add down a bias take a summation out over
	them and this summation is what is has what has this form so its w naught plus w one x
	one plus w two x two plus w three x three where each of these weights w one w two and
	w three are three weights associated with each of the three values x one x two and x
	three and w naught is what is called as the bias or the one w naught can also be written
	down as one into b where say b is the weight over there and the constant input to this
	particular edge over there is what is one ok so in its linear algebra form which is
	in its matrix representation this is a form which you would be getting now so you get
	y is equal to the ah inner product or the dot product of two matrices
	one of them is the weight matrix where you have the weights and the bias taken together
	and the other matrix is a column matrix over there so thats why its x , one transpose
	of y tends towards plus infinity this value tends towards plus one as the value of y tends
	towards minus infinity this value tends towards zero and on the contrary with the tan hyperbolic
	now from taking down a perceptron to getting into a neural network formulation which is
	over there and i can map it down to again a different group of scalars so maybe my first
	everything to my p one hat now note over here that as we had also discussed in the earlier
	which you see with these weights one , two one , one one , three now the
	reasoning behind these weights is that the first subscript is to the target where its
	to my target which is called as p one so my first subscript is going to be the subscript
	it is connecting and thats the nomenclature which we are following now if i arrange all
	of these weights w one one w one two and w one three in a row matrix form then that is
	along with that i have my scalar value which is my bias w one zero or b one ok and accordingly
	dot product and then my non linearity applied similarly if i take down my second neuron
	on the output side of it and feed it appropriately
	so i would be getting down this second part of the partial network coming down and my
	called as w k , g and then put a impose non linearity on top of it and then taking
	which we see now if you look into this matrix of weights and biases which are come together
	so i arrange them in a column form in a call in a in a column major format which is that
	it is it just has k number of rows and just one column over there accordingly my bias
	can also be stacked one on top of the other because each is independent of the other one
	and now that would give me some sort of a rectangular matrix now if i clearly look into
	and then that gives me an output matrix over there and this output matrix is a column matrix
	my input matrix is also a column matrix
	so thats my y and then i have a non linearity applied on a matrix which means that each
	all of them together is what i get down as my target output so this was my very basic
	understanding of how a neural network works down as such and then this was what we had
	into the revision part over there so my error in prediction how it was different was that
	if i have one of these predictors p one then i get down one value of a scalar for another
	is the euclidean error over there so a euclidean error or the total error of the network is
	so whatever is my actual ground truth which is p and my predicted value p hat these two
	matrices are subtracted and then you take the amplitude of that or the l two norm of
	matrix is a of all of these scalar xs over there and one of these samples is x subscript
	one
	be getting down a predicted value which is p hat subscript one ok so similarly i take
	training data over there as i feed my last sample through my network over there my output
	i will be getting a different value of error but can we give some sort of a consolidated
	down and accordingly manipulating what happens to your predictions over there
	so because there there isnt anything else on which it can change see my input x is constant
	ah so that that will be different number of samples and across samples and across so between
	two samples it will be a different value thats always known but when i am training across
	over there the only reason why the prediction value bit of putting down the same sample
	my sample and i get down a predicted value p one hat i do all my updates and everything
	and then it comes to my second epoch which is epoch one in my epoch one i put down x
	the epoch one is very different from p one hat at epoch zero and the only reason why
	now that i have my cost function written down in terms of my weights my final point is that
	we need to come down to a point where to a point in the weight space such that my argument
	keep on changing the weights there will be one particular combination of these weights
	such that my error is minimum and thats the exact one which i would like to achieve now
	and how that achieved is through something called as the gradient descent learning rule
	so in this gradient descent learning rule what we do is basically that its an iterative
	your gradient of the weight space over there in terms of your cost function and that is
	a range of zero to one and then say my del del w of jw is in a range of ten power of
	going to be very less and in that case this factor over here comes to your rescue
	that value is something which will actually be impacting significantly how the value of
	w is changing over there
	so this learning rate basically is a fact way of mathematically modulating the gradient
	be in some way significantly impacting the change in w and thats how my w of k plus one
	will be revising at a much better rate then w of k would have if we did not have this
	till you are at the final conclusive step over there ok
	now this was one way of trying to visualize our learning in terms of its cost function

heavily we know some of these explanations but not all of these explanations and thats

a substantial part of what works i will also be working down on why it works and what are

going through this whole route or if you have a different kind of a candidate search which

in hand and thats what we will be doing from theory to experiments and eventually that

you can do is get down any of these and then which which are really good except for lets

place while we also have done the clustered axis given down for participants of this course

so that you can get down access to an hpc so or you can obviously buy down this say

tool boxes all of these are open source as of now so you can use any of this other than

the one on matlab for which you will definitely have to pay for the licenses but the matlab

can get this book and thats thats what we will be using as a major reading material

to what we were doing in the earlier classes was that in the earlier classes while we were

using feature extractors and feature descriptors which are hard coded functions over there

neural network on the contrary today when we are going to do it

so here is when a neutral network itself has to come down to be an end to end learning

framework which means that input to the neural network itself is an image while the output

from it is still a classification ah output so it can be a classification output it can

again and then entering into the multi layer perceptron from there we enter into something

is my input and my output related and what happens during the learning phase and this

is a quite critical part over here

since in the last lecture and the lab which we had done so you were introduced to the

concept of error back propagation and from there we had a gradient descent based learning

rule now what exactly happens in telling this as a error back propagation and why it happens

of code is what we are going to explain you through this signal flow graph representation

other transformations and cost functions also to exist and then eventually go down to the

there were three inputs over here in the earlier case last week when we were doing it so these

three different features but these three can be three pixels so you can consider just three

space so each component itself is represented as one independent scalar value so your x

one can be the red value of a pixel x two can be the green value of a pixel x three

so let the decision associated with a particular pixel over here b p hat and now with the simple

neuron model what would happen is that we will have a weighted combination of these

inputs going down to a neuron and from there add down a bias take a summation out over

them and this summation is what is has what has this form so its w naught plus w one x

one plus w two x two plus w three x three where each of these weights w one w two and

w three are three weights associated with each of the three values x one x two and x

three and w naught is what is called as the bias or the one w naught can also be written

down as one into b where say b is the weight over there and the constant input to this

particular edge over there is what is one ok so in its linear algebra form which is

in its matrix representation this is a form which you would be getting now so you get

y is equal to the ah inner product or the dot product of two matrices

one of them is the weight matrix where you have the weights and the bias taken together

and the other matrix is a column matrix over there so thats why its x , one transpose

of y tends towards plus infinity this value tends towards plus one as the value of y tends

towards minus infinity this value tends towards zero and on the contrary with the tan hyperbolic

now from taking down a perceptron to getting into a neural network formulation which is

over there and i can map it down to again a different group of scalars so maybe my first

everything to my p one hat now note over here that as we had also discussed in the earlier

which you see with these weights one , two one , one one , three now the

reasoning behind these weights is that the first subscript is to the target where its

to my target which is called as p one so my first subscript is going to be the subscript

it is connecting and thats the nomenclature which we are following now if i arrange all

of these weights w one one w one two and w one three in a row matrix form then that is

along with that i have my scalar value which is my bias w one zero or b one ok and accordingly

dot product and then my non linearity applied similarly if i take down my second neuron

on the output side of it and feed it appropriately

so i would be getting down this second part of the partial network coming down and my

called as w k , g and then put a impose non linearity on top of it and then taking

which we see now if you look into this matrix of weights and biases which are come together

so i arrange them in a column form in a call in a in a column major format which is that

it is it just has k number of rows and just one column over there accordingly my bias

can also be stacked one on top of the other because each is independent of the other one

and now that would give me some sort of a rectangular matrix now if i clearly look into

and then that gives me an output matrix over there and this output matrix is a column matrix

my input matrix is also a column matrix

so thats my y and then i have a non linearity applied on a matrix which means that each

all of them together is what i get down as my target output so this was my very basic

understanding of how a neural network works down as such and then this was what we had

into the revision part over there so my error in prediction how it was different was that

if i have one of these predictors p one then i get down one value of a scalar for another

is the euclidean error over there so a euclidean error or the total error of the network is

so whatever is my actual ground truth which is p and my predicted value p hat these two

matrices are subtracted and then you take the amplitude of that or the l two norm of

matrix is a of all of these scalar xs over there and one of these samples is x subscript

one

be getting down a predicted value which is p hat subscript one ok so similarly i take

training data over there as i feed my last sample through my network over there my output

i will be getting a different value of error but can we give some sort of a consolidated

down and accordingly manipulating what happens to your predictions over there

so because there there isnt anything else on which it can change see my input x is constant

ah so that that will be different number of samples and across samples and across so between

two samples it will be a different value thats always known but when i am training across

over there the only reason why the prediction value bit of putting down the same sample

my sample and i get down a predicted value p one hat i do all my updates and everything

and then it comes to my second epoch which is epoch one in my epoch one i put down x

the epoch one is very different from p one hat at epoch zero and the only reason why

now that i have my cost function written down in terms of my weights my final point is that

we need to come down to a point where to a point in the weight space such that my argument

keep on changing the weights there will be one particular combination of these weights

such that my error is minimum and thats the exact one which i would like to achieve now

and how that achieved is through something called as the gradient descent learning rule

so in this gradient descent learning rule what we do is basically that its an iterative

your gradient of the weight space over there in terms of your cost function and that is

a range of zero to one and then say my del del w of jw is in a range of ten power of

going to be very less and in that case this factor over here comes to your rescue

that value is something which will actually be impacting significantly how the value of

w is changing over there

so this learning rate basically is a fact way of mathematically modulating the gradient

be in some way significantly impacting the change in w and thats how my w of k plus one

will be revising at a much better rate then w of k would have if we did not have this

till you are at the final conclusive step over there ok

now this was one way of trying to visualize our learning in terms of its cost function