LLM Chronicles #3.1: Loss Function and Gradient Descent (ReUpload)

Summary

This 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

00:00

📚 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.

05:01

🔍 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.

10:01

🔄 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.

Keywords

💡Multi-Layer Perception (MLP)

A Multi-Layer Perception (MLP) is a type of artificial neural network. It contains at least three layers of nodes: an input layer, one hidden layer, and an output layer. MLPs are the simplest type of feedforward neural network and are used for various tasks such as classification and regression. In the video, MLP is the primary focus, as the host discusses how to build and train one to perform a task by tweaking its parameters.

💡Weights and Biases

Weights and biases are parameters in a neural network that are adjusted during training to minimize the loss function. Weights determine the strength of the connection between nodes, while biases are added to the weighted sum before applying the activation function. In the context of the video, tweaking these parameters is essential for training the MLP to perform the desired task effectively.

💡Training Data

Training data is a set of samples used to train a machine learning model. It includes input data and the corresponding target labels. The video emphasizes the importance of preparing training data by collecting samples and their target outputs, which the MLP will learn from. For instance, in image recognition, training data would consist of images paired with their correct labels.

💡Target Outputs

Target outputs are the expected results or labels corresponding to each piece of input data in the training set. They represent the values the model is aiming to predict. The video explains that for regression tasks, target outputs are numerical values, while for classification tasks, they are often one-hot encoded vectors representing categories.

💡One-Hot Encoding

One-hot encoding is a representation method used to convert categorical labels into a format that can be provided to machine learning algorithms. It involves representing each category by a binary vector where all elements are zero except for one that is one, indicating the presence of that category. The video uses the example of fruit categories to illustrate how one-hot encoding allows neural networks to work with categorical data.

💡Normalization

Normalization is the process of scaling data to a common range or scale. It is an important step in preparing data for machine learning models as it helps to ensure that no single feature dominates the learning process due to its scale. The video mentions that normalizing features like age and income, which can have vastly different scales, allows the network to focus on learning relationships rather than being biased by the magnitude of the data.

💡Loss Function

A loss function is a measure of how well the neural network's predictions match the actual target outputs. It quantifies the divergence between the network's output and the target output. The video explains that the loss function is crucial for training a model as it guides the optimization process. Different loss functions are used depending on the task, such as mean absolute error (L1) or mean squared error (L2) for regression, and cross-entropy for classification.

💡Gradient Descent

Gradient descent is an optimization algorithm used to minimize the loss function by adjusting the network's parameters. It involves computing the gradient of the loss function with respect to each parameter and updating the parameters in the opposite direction of the gradient. The video uses the analogy of moving down a hill to illustrate how gradient descent allows the network to find the optimal weights and biases that minimize the loss.

💡Backpropagation

Backpropagation is the process of computing the gradient of the loss function with respect to each parameter in the network by applying the chain rule of calculus. It is a crucial part of the training loop in neural networks, as it allows for the calculation of the derivatives needed for gradient descent. The video mentions building a computation graph to keep track of operations during the forward pass, which is then used for backpropagation.

💡Training Loop

A training loop is the iterative process used to train a neural network. It involves passing the training data through the network, calculating the loss, performing backpropagation to compute the gradients, and updating the network's parameters using gradient descent. The video describes a typical training loop as an essential part of the network's training process.

💡Overfitting

Overfitting occurs when a machine learning model learns the training data too well, including its noise and outliers, to the extent that it negatively impacts the model's performance on new, unseen data. The video discusses the role of a validation set in preventing overfitting by providing a way to tune model parameters and make decisions about when to stop training.

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