Detailed summary of all lectures and additional notes, explanations and examples for the course "Deep Learning" at Tilburg University which is part of the Master Data Science and Society. Course was given by G. Saygili during the first semester, block one of the academic year 2022 / 2023 (September...
Tilburg University
Study Program: Master Data Science and Society
Academic Year 2022/2023, Semester 1, Block 1 (September to October 2022)
Course: Deep Learning (880008-M-6)
Lecturer: G. Saygili
,Lecture 1: Introduction and the
Perceptron
Introduction
• Artificial Intelligence: hardcode
knowledge about the world in for-
mal languages, people struggle to
devise formal rules with enough
complexity to accurately describe
world knowledge
• Machine Learning: acquire their
own knowledge by extracting pat-
terns from raw data, performance
of simple ML algorithms depends
heavily on the representation of the
data (features)
• Representation Learning: use ML
not only to discover mappings from
representation to output but to learn the representation itself (example: autoencoder which
combined an encoder function with a decoder function)
• Deep Learning: Solves the problem representation learning because it introduces represen-
tations that are expressed in terms of other, simpler representations. This enables the com-
puter to build complex concepts out of simple ones. Depths enables the computer to learn a
multistep computer program.
History of Deep Learning
• 1940-1960: Cybernetics (early model of brain function, Perceptron by Rosenblatt)
• 1980-1990: Connectionism (distributed representation, backpropagation)
• Since 2006: Deep Learning
Artificial Neural Networks (ANNs)
• Proof by example that intelligent be-
havior is possible: reverse engineer
the computational principles behind
it and duplicate its functionality
• ML models hath help us understand
the principles that underlie human
intelligence
• In deep learning: more general principle of learning by multiple layers that create depth
o The next hidden layers identify are more complex structure based on the learnt fea-
tures from the previous layer(s). Each layer adds information and complexity.
CPU vs GPU
• CPU has multiple cores while GPU has hundreds of cores
,Deep Learning Frameworks
• TensorFlow: created by the Google Brain Team, first release in 2015
• Keras: runs on top of TensorFlow
• PyTorch: released in 2017, merged with Caffe2 and torch
The Perceptron
• Most basic single-layer
neural network
• typically used for bi-
nary classification
problems
• Data needs to be line-
arly separable (linear
decision boundary)
• input vector: 𝑋 =
𝑥1 , 𝑥2 , … , 𝑥𝑚
• weights vector: 𝑊 = 𝑤1 , 𝑤2 , … , 𝑤𝑚
• Summed input: ∑𝑖 𝑤𝑖 𝑥𝑖
• Activation function (step activation function):
∑𝑖 𝑤𝑖 𝑥𝑖 ≥ 𝑡 → 𝑦 ′ = 1 here the node fires
∑𝑖 𝑤𝑖 𝑥𝑖 < 𝑡 → 𝑦 ′ = 0 here the node doesn’t fire
• If there is no bias, the intersection with the y axis is always zero, the slope depends on the
weights. If a bias term is added, the line is shifted. The bias is a measure how easy it is to get
the perceptron to output a “1”.
• If the expected output is not equal the observed output, the weights (and bias) need to be
updated according to an update rule (𝛼 is the learning rate): 𝑤′𝑖 = 𝑤𝑖 + 𝛼𝑥𝑖 (𝑦 − 𝑦 ′ )
Matrix Multiplication
, Lecture 2: MLP and Back-Propagation Algorithm
Multilayer Perceptron
• MLP = Feedforward Network
• Dense or fully connected layers
• Goal: approximate some function and learn the
parameter values that lead to the best result
• The functions of the hidden layers and the output
layers are chained together: 𝑦 = 𝑓2 (𝑓1 (𝑥))
• The output of the network (y) is the output of the
last layer which is based on the previous outputs: At
each layer a weighted combination of the inputs plus
the bias term is calculated and an activation is ap-
plied. The result is forwarded to the next node.
• Activation functions are e.g., sigmoid, ReLu, leaky ReLu
• They can be the same per layer but also different within the network (hyperparameter)
Back-Propagation
• How the network optimizes its parameters
• Loss Function/Error Function/Cost Function
o Calculates the “cost”, or distance between the net-
work’s output and the expected one.
o Loss / cost: sum of errors over all training samples
o Error: sample wise
• Forward Propagation: Loss/error is calculated
• Backpropagation: Parameters (weights and biases) are updated
while minimizing the loss (with (stochastic) gradient descent)
• Backpropagate the prediction error from the loss function to
update the parameters.
• We often have thousands of parameters to update at once. We want to know how each indi-
vidual parameter contributes to the error so we can update them appropriately.
• This is done by taking the derivative of the error (cost function) with respect to each para-
meter (partial derivatives). Using the chain rule:
𝜕𝐿 𝜕𝐿 𝜕𝑎
if 𝐿 = 𝑓(𝑎) and 𝑎 = 𝑔(𝑧) then 𝜕𝑧 = 𝜕𝑎 ∗ 𝜕𝑧 which is the derivative of L with respect to z
𝜕𝑙𝑜𝑠𝑠 𝜕𝑙𝑜𝑠𝑠 𝜕𝑎 𝜕𝑢
• Example: We need to take the derivative to update our parameters 𝜕𝑤1
= 𝜕𝑎1
∗ 𝜕𝑢1 ∗ 𝜕𝑤1
1 1
• Exercise using the chain rule:
𝜕𝐿
o Expand 𝜕𝑊
o Use 𝑎 = 𝑓(𝑧) and 𝑧 = 𝑊 ∗ 𝑎 + 𝑏
o And assume that the loss L is a function of a
𝜕𝐿 𝜕𝐿 𝜕𝑎 𝜕𝑧
o Solution: 𝜕𝑊 = 𝜕𝑎 ∗ 𝜕𝑧 ∗ 𝜕𝑊
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