LLM Chronicles #3.1: Loss Function and Gradient Descent (ReUpload)
Summary
TLDRThis episode delves into training a Multi-Layer Perceptron (MLP), focusing on parameter adjustments to optimize network performance. It explains the importance of preparing training data, including collecting samples and converting labels for classification tasks using one-hot encoding. The script also covers data normalization to ensure balanced feature importance and the division of data into training, validation, and testing sets. It introduces loss functions for regression and classification, emphasizing their role in guiding network training. The episode concludes with an overview of gradient descent, illustrating how it is used to minimize loss by adjusting weights and biases, and the concept of a computation graph for calculating gradients.
Takeaways
- 🧠 MLPs (Multi-Layer Perceptrons) can approximate almost any function, but the exact details of the function for real-world tasks like image and speech recognition are often unknown.
- 📚 Training an MLP involves tweaking weights and biases to perform a desired task, starting with collecting samples for which the function's values are known.
- 🏷 For regression tasks, the target outputs are the expected numerical values, while for classification tasks, labels need to be one-hot encoded into a numeric format.
- 📉 Normalization is an important step in preparing data sets to ensure that no single feature dominates the learning process due to its scale.
- 🔄 Data sets are partitioned into training, validation, and testing subsets, each serving a specific purpose in model development and evaluation.
- 📊 The training set is used to adjust the neural network's weights, the validation set helps in tuning parameters and preventing overfitting, and the testing set evaluates model performance on unseen data.
- ⚖️ Loss functions quantify the divergence between the network's output and the target output, guiding the network's performance; the choice of loss function depends on the problem's nature.
- 📉 Mean Absolute Error (L1) or Mean Squared Error (L2) are common loss functions for regression, while Cross-Entropy Loss is used for classification tasks.
- 🔍 Training a network is about minimizing the loss function by adjusting weights and biases, which is a complex task due to the non-linearity of both the network and its loss.
- 🏔 Gradient descent is an optimization approach used to minimize the loss by adjusting weights in the direction opposite to the gradient, which points towards the greatest increase in loss.
- 🛠️ A computation graph is built to track operations during the forward pass, allowing the application of calculus to compute the derivatives of the loss with respect to each parameter during the backward pass.
Q & A
What is the primary goal of training a Multi-Layer Perceptron (MLP)?
-The primary goal of training an MLP is to tweak the parameters, specifically the weights and biases, so that the network can perform the desired task effectively.
Why is it challenging to define the function for real-world tasks like image and speech recognition?
-It is challenging because these tasks involve complex functions that cannot be simply defined with a known formula due to the vast amount of possible data points.
What is the first step in training a neural network?
-The first step is to collect a set of samples for which the values of the function are known, which involves pairing each data point with its corresponding target label or output.
How are target outputs handled in regression tasks?
-In regression tasks, the target outputs are the expected numerical values themselves, such as the actual prices of houses in a dataset.
What is one hot encoding and why is it used in classification tasks?
-One hot encoding is a method of converting categorical labels into a binary vector of zeros and ones, where each position corresponds to a specific category. It is used because neural networks operate on numbers, not textual labels.
Why is normalization an important step in preparing datasets for neural networks?
-Normalization is important because it standardizes the range and scale of data points, ensuring that no particular feature dominates the learning process solely due to its larger magnitude.
What are the three distinct subsets that a dataset is typically partitioned into during model development and evaluation?
-The three subsets are the training set, the validation set, and the testing set, each serving specific purposes such as learning, tuning model parameters, and providing an unbiased evaluation of the model's performance.
How does a loss function help in training a neural network?
-A loss function quantifies the divergence between the network's output and the target output, acting as a guide for how well the network is performing and what adjustments need to be made.
What is gradient descent and why is it used in training neural networks?
-Gradient descent is an optimization approach that adjusts the network's parameters in the direction opposite to the gradient of the loss function, aiming to minimize the loss. It is used because it is an efficient way to find values that minimize the loss in complex networks.
How is the gradient computed in the context of gradient descent?
-The gradient is computed by building a computation graph that tracks all operations in the forward pass, and then applying the calculus chain rule during the backward pass to find the derivatives of the loss with respect to each parameter.
What is the purpose of the backward path in the context of training a neural network?
-The backward path is used to apply the calculus chain rule to compute the derivatives of the loss with respect to each parameter, which are then used to update the network's weights and biases in a way that reduces the loss.
Outlines
📚 Training Data Preparation for MLP
This paragraph discusses the initial steps in training a Multi-Layer Perceptron (MLP), emphasizing the preparation of training data. MLPs can approximate complex functions, such as those involved in image and speech recognition, which are not easily defined by a formula. The first step involves collecting samples for which the function's values are known, like pairing images with their categories or speech clips with transcriptions. For regression tasks, the target outputs are the expected numerical values, while for classification tasks, labels must be converted into a numerical format using one-hot encoding. Normalization is also highlighted as an important step to ensure that no single feature dominates the learning process due to its scale. The paragraph concludes with an explanation of how data sets are partitioned into training, validation, and testing subsets, each serving a different purpose in model development and evaluation.
🔍 Understanding Loss Functions and Gradient Descent
The second paragraph delves into the concept of loss functions and the process of training a neural network using gradient descent. The loss function measures the discrepancy between the network's predictions and the actual values, serving as a guide for network performance. The choice of loss function depends on the problem type; mean absolute error (L1) or mean squared error (L2) for regression, and cross-entropy loss for classification tasks. The paragraph explains that training a network involves minimizing the loss function by adjusting the weights and biases, which is achieved through gradient descent. This optimization approach involves computing the gradient, which is the derivative of the loss with respect to each weight, and then updating the weights in the opposite direction of the gradient to reduce the loss. The paragraph also touches on the importance of building a computation graph to track operations and apply the chain rule for derivative calculations during the backward pass.
🔄 The Gradient Descent Training Loop
This paragraph, although brief, introduces the typical training loop for a neural network using gradient descent. It sets the stage for a detailed explanation of how the training process unfolds, which would likely involve iterating over the training data, making predictions, calculating the loss, performing backpropagation to compute gradients, and updating the network's weights and biases to minimize the loss. This iterative process is central to training neural networks and is essential for the network to learn from the data and improve its predictions.
Mindmap
Keywords
💡Multi-Layer Perception (MLP)
💡Weights and Biases
💡Training Data
💡Target Outputs
💡One-Hot Encoding
💡Normalization
💡Loss Function
💡Gradient Descent
💡Backpropagation
💡Training Loop
💡Overfitting
Highlights
Building a multi-layer perception (MLP) involves tweaking weights and biases.
MLPs can approximate almost any function, but often the exact function details are unknown.
Training a network requires collecting samples with known function values.
For regression tasks, the output is the expected numerical values.
For classification tasks, textual labels must be converted into a numerical format using one-hot encoding.
Normalization standardizes the range and scale of data points.
Data sets are partitioned into training, validation, and testing subsets.
The training set is used to train the model and adjust its weights.
The validation set helps in tuning model parameters and preventing overfitting.
The testing set provides an unbiased evaluation of the model's performance on unseen data.
The loss function quantifies the divergence between network output and target output.
Mean absolute error (L1) or mean squared error (L2) are used for regression tasks.
Cross-entropy loss function is used for classification tasks.
Training a network is about minimizing the loss function by adjusting parameters.
Gradient descent is an optimization approach used to minimize the loss.
The gradient is a vector that points in the direction of the greatest increase in loss.
A computation graph is built to compute the derivatives of the loss with respect to each weight.
The training loop for a neural network using gradient descent involves updating weights in the opposite direction of the gradient.
Transcripts
in the last episode we looked at how to
build a multi-layer perception and all
of the computations involved in the
forward pass in this episode we'll see
how to actually train an MLP which
essentially means how to tweak the
parameters the weights and the biases so
that the network performs the task we
want to start with let's look at how to
prepare the training data as we saw MLPs
can approximate almost any function and
the tasks we want the network to perform
can be thought of as functions however
we often don't know the exact details of
the function we're trying to mimic this
is because For Real World tasks such as
image and speech recognition these
functions are complex and cannot be
simply defined with a known formula in
other words we don't know the value of
the function for every possible data
part point so the first step to training
a network is to collect a set of samples
for which we know the values of the
function for every piece of data like an
image or speech recording we collect its
corresponding Target label or output
think of it as pairing an image with its
category or a speech clip with its
transcription these paired samples
become the training data for our MLP to
learn from
let's take a closer look at the Target
outputs for our data set for regression
tasks things are relatively
straightforward regression involves
predicting continuous values so the
output of our data set would typically
be the expected numerical values
themselves for example if we're building
a model to predict house prices based on
various features the target outputs
would be the actual prices of the houses
in the training data classification
tasks on the other hand require a
different approach here we are aiming to
categorize data into distinct classes
however neural networks fundamentally
operate on numbers not textual or
categorical labels so simply having
labels like apple banana Cherry wouldn't
suffice instead the textual labels need
to be converted into a format that the
network can work with
this is where one hot encoding comes
into play using a fruit example instead
of the textual labels we represent each
fruit as a binary Vector of zeros and
ones in this format each position in the
vector corresponds to a specific fruit
category A1 denotes the presence of that
category for a given data point while
zero indicates its substance by
converting our labels into this numeric
format we ensure that our Network can
effectively learn to classify data
points into the correct
categories once we've prepared our data
sets we often also want to perform an
additional step
normalization this refers to the process
of standardizing the range and scale of
the data points in our data set imagine
a data set that contains age ranging
from zero to 100 and income possibly
ranging from thousands to Millions these
two features have vastly different
scales if we feed these directly into
our Network the model might give undue
importance to income just because its
values are larger even if age might be
more relevant for the
prediction by normalizing we are
essentially Transforming Our data so
that all input features regardless of
their original scale have a consistent
range often between between 0o and one
or a mean of zero and a standard
deviation of one this ensures that no
particular feature dominates the
learning process solely due to its
larger
magnitude during training we typically
partition our data set into distinct
subsets each serving a specific purpose
in the life cycle of model development
and
evaluation as the name suggests the
training set is used to train our model
this is the data on which our neural
network algorithm practices and adjusts
its weights the validation set plays an
important role in the model building
process while the training set helps the
model learn the validation set assists
in tuning model parameters and
preventing overfitting that will cover
later it provides a platform to validate
the model's performance during training
and helps in making decisions like when
to stop training training or which model
architecture is the most promising once
our model is trained and validated we
need a final measure of its performance
and that's where the testing set comes
in the data set provides an unbiased
evaluation of the model's performance on
unseen data giving us an idea of how our
model might perform in real world
scenarios all right we have the data
ready and we pass it through our Network
which we have initialized with ROM
weights now to train the network we
first need to establish how off our
Network's predictions are from the
actual values and we do this with the
loss
function the loss function quantifies
the Divergence between the network
output and the target output acting as a
guide for how well are networks
performing choosing the right loss
function is instrumental in training a
successful model and the choice often
hinges on the nature of the problem at
hand when we are predicting continuous
values such as the price of a house this
is simple we can actually calculate the
error as the mean difference between the
predicted value and the True Values this
is called mean absolute error or L1 we
could also use the mean squared error or
L2 which simply squares these
differences which tends to amplify large
errors and is more sensitive to outliers
classification is a bit more complex
here we are assigning data points to
specific categories and our models
output is essentially a probability
distribution across these categories for
instance in classifying an image as a
cat or a dog the model might output
probabilities like 90% cat and 10% dog
to measure the difference between the
predicted probabilities and the actual
labels we typically use the cross
entropy loss function we won't delve
into the mathematical details here but
for reference keep in mind that cross
entropy is related to KL Divergence
which measures the difference between
two probability
distributions so far we have a set of
training data with inputs and the
desired outputs or labels and the loss
function tells us how of our networks
predictions are from the actual labels
so now we can Define the problem of
training a network in terms of
minimizing the loss
function a key Point here is that the
loss is essentially a function of the
Network's parameters weights and biases
so training a network can be seen as
Trying to minimize the loss by adjusting
these parameters in other words we want
to find values for the weights and
biases that make the loss small reducing
the error of our Network and increasing
it its performance but since both the
network and its loss are complex
functions finding values that minimize
the loss is not straightforward a na
approach could be to randomly try
different weights and hope to get lucky
and stumble on a set of Weights that
minimizes the loss effectively however
this is like finding a needle in a high
stock and won't work in practice for
real large networks instead we apply an
optimization approach called gradient
descent imagine you are on a hilly
terrain and your objective is to reach
the lowest point instead of wandering
aimlessly you'd probably feel the ground
slope with your feet and move downwards
this slope is analogous to the gradient
or derivative the derivative tells us
the influence of a weight on the loss
specifically the derivative of the loss
with respect to a weight tells us how
much a minute in increment to that
weight will affect the loss if we add a
small amount to this weight will the
loss grow or Shrink by how much the
intuition is that once we know the
derivative of a weight we are in a
position to update the value of the
weight in the opposite direction of the
derivative which will make the loss go
down this is the key idea of gradient
descent to compute the derivative of the
loss with respect to each weight we we
need to build a computation graph
keeping track of all of the operations
that we performed in the forward pass
then in the so-called backward path we
can apply calculus chain rule to compute
the derivatives of the loss with respect
to each parameter all of these
derivatives together form the gradient
which is a vector that points in the
direction in which the loss function
increases the
most now that we understand what the
gradient of the loss means we can take a
look at a typical training Loop for a
neural network using gradient
descent
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