Gradient Descent Explained Through Neural Networks
Key Points
- Gradient descent is likened to navigating a dark mountain, taking small steps in the direction that feels most downhill to eventually reach the lowest point, which mirrors how the algorithm iteratively reduces error.
- In neural networks, weights and biases determine how input data is processed, and training adjusts these parameters using labeled data so the model can correctly map inputs (e.g., shapes or house features) to desired outputs.
- The cost (or loss) function quantifies the mismatch between the network’s predictions and actual values; gradient descent minimizes this cost by moving opposite the gradient of the function.
- The size of each step in gradient descent is controlled by the learning rate, which must be chosen carefully to ensure steady convergence without overshooting.
- Real‑world examples—classifying drawn squiggles and predicting house prices—illustrate how the model’s predictions improve as gradient descent repeatedly updates weights and biases to lower the cost.
Sections
Full Transcript
# Gradient Descent Explained Through Neural Networks **Source:** [https://www.youtube.com/watch?v=i62czvwDlsw](https://www.youtube.com/watch?v=i62czvwDlsw) **Duration:** 00:07:02 ## Summary - Gradient descent is likened to navigating a dark mountain, taking small steps in the direction that feels most downhill to eventually reach the lowest point, which mirrors how the algorithm iteratively reduces error. - In neural networks, weights and biases determine how input data is processed, and training adjusts these parameters using labeled data so the model can correctly map inputs (e.g., shapes or house features) to desired outputs. - The cost (or loss) function quantifies the mismatch between the network’s predictions and actual values; gradient descent minimizes this cost by moving opposite the gradient of the function. - The size of each step in gradient descent is controlled by the learning rate, which must be chosen carefully to ensure steady convergence without overshooting. - Real‑world examples—classifying drawn squiggles and predicting house prices—illustrate how the model’s predictions improve as gradient descent repeatedly updates weights and biases to lower the cost. ## Sections - [00:00:00](https://www.youtube.com/watch?v=i62czvwDlsw&t=0s) **Untitled Section** - ## Full Transcript
gradient descent is like it's like
trying to find your way down a dark
Mountain you can't see where you're
going so you have to feel your way
around you take small steps in the
direction that feels the most downhill
eventually if you keep going you'll find
your way to the bottom that's gradient
descent let's get into it
so gradient descent is a common
optimization algorithm used to train
machine learning models and neural
networks by training on data these
models can learn over time and because
they're learning over time they can
improve their accuracy now you see a
neural network consists of connected
neurons
like this and these neurons are in
layers and those layers have weights and
biases which describe how we navigate
through this network
we provide the neural network with
labeled training data to determine what
we should set these weights and biases
to to figure something out so like for
example I could input a shape let's say
like that and then we could use the
neural network to learn that squiggle
as our input represents this output
for number three
after we train the neural network we can
provide it with more labeled data like
this squiggle and then we can see if it
could also correctly resolve that
squiggle to
the number six if it gets some of these
squiggles wrong the the weights and
biases here can be adjusted and then we
just try it again
now how can gradient descent help us
here well gradient descent is used to
find the minimum of something called a
cost
function
so what is
a cost function well it's a function
that tells us how far off our
predictions are from the actual values
so the idea is that we want to minimize
this cost function to get the best
predictions now to do this we take small
steps in the direction that reduces the
cost function the most if we think about
this on a graph we start here and we
keep going downhill reducing our cost
function as we go
the size of the steps that we take so
the size of the steps from here to here
and to here that's called The Learning
rate
let's think about another example let's
consider a neural network but instead of
dealing with squiggles predicts how much
a house will sell for so first we train
the network on a labeled data set let's
say that data has some information like
um like the location of a house let's
say the size of the house and then how
much it sold for
so with that we can then use our model
to train new labeled data so here's a
here's another example we've got a house
uh it's location let's do it by ZIP code
275 from three how big is it
uh 3 000 square feet input that into our
neural network so how much does this
house sell for well now our neural
network will make a forecast it says we
think
is sold for three hundred thousand
dollars
and we compare that
to the forecast of the actual sale price
which was
450
000 dollars
not a good guess we have a large cost
function weights and biases now need to
be adjusted and then the model can try
again and did it do any better over the
entire label data set or did it do worse
that's what gradient descent can help us
with
now there are three types of gradient
descent learning algorithms and let's
take a look at some of those
so first of all
we've got a gradient descent called
batch
this sums the entries for each point in
a training set updating the model only
after all the training examples have
been evaluated hence the term batch now
in terms of how well does this do well
computationally it is computationally
effective
you can give this a high rating
because we're doing things in one big
batch but what about processing time
well with processing time we can end up
with long processing times using batch
gradient descent because well we've got
large training data sets and it needs to
store all of that data in memory and
process it
so that's batch another option is
stochastic
gradient descent and this evaluates each
training example but one at a time
instead of in a batch since you only
need to hold one training example
they're easy to store in memory and get
individual responses much faster so in
terms of speed
that's
fast but in terms of computational
efficiency that's lower
now there is a happy medium and that is
called
mini batch and mini batch gradient
descent splits the training data set
into small batch sizes and performs
updates on each of those batches that is
a nice balance of computational
efficiency and of speed now gradient
descent does come with its own
challenges so for example it can
struggle to find the global minimum in
non-convex problems this was a nice
convex problem with a clearly defined
bottom
so when are the slope of the cost
function is close to zero or it's at
zero the model stops learning but if we
don't have this convex model here that
we have something like
this shape that's known as a saddle
point and it can mislead the gradient
descent because it thinks it's
at the bottom
before it really is this is going to
keep going down further
chord a subtle shape because it kind of
looks like a horse saddle I guess
another challenge is that in deeper
neural learning networks a gradient
descent can suffer from vanish
ingredients or exploding gradients so
Vanishing gradients are when the
gradient is too small and the earlier
layers in the network learn more slowly
than the later layers as we go through
this network here
exploding gradients on the other hand
are when the gradient is too large and
that can create an unstable model but
look despite those challenges gradient
descent is a powerful optimization
algorithm and it is commonly used to
train machine learning models and neural
networks today it's a clever way to get
you back down that mountain safely
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