10 - The Algorithm that Put Paid to a Persistent Myth

Question 1

What did Minsky and Papert prove about single-layer perceptrons?

Answer 1

They proved that single-layer perceptrons could not solve the XOR problem

This proof is often cited as a turning point in neural network research.

Question 2

Who is Geoffrey Hinton?

Answer 2

A key figure behind the modern deep learning revolution

Hinton became interested in neural networks in the mid-1960s.

Question 3

What influenced Hinton’s interest in how brains learn?

Answer 3

A mathematician friend exploring how memories are stored in the brain

This led Hinton to study the mind and neural networks.

Question 4

What did Hinton study at university?

Answer 4

Physics and physiology

However, he found the curriculum insufficient regarding understanding the brain.

Question 5

What book deeply influenced Hinton?

Answer 5

The Organization of Behavior by Donald Hebb

This book impacted Hinton’s thinking on neural networks and learning.

Question 6

What was Hinton’s doctoral focus?

Answer 6

Solving constrained optimization problems using neural networks

Hinton believed multi-layer networks could eventually learn.

Question 7

What was the key limitation of single-layer perceptrons according to Minsky and Papert?

Answer 7

They could not solve the XOR problem, which is a specific instance of a broader class of problems

This limitation led to skepticism about neural networks for some time.

Question 8

What is back-propagation?

Answer 8

A method for training multi-layer neural networks by propagating error corrections back through the network

Introduced by Rosenblatt in his work on neural networks.

Question 9

What issue arises when initializing all weights in a neural network to zero?

Answer 9

All neurons produce the same output, leading to symmetry and ineffective learning

This problem prevents the network from detecting different features.

Question 10

What did Rosenblatt suggest for updating weights in a neural network?

Answer 10

A stochastic process that introduces randomness to weight updates

This approach aimed to break symmetry in the network.

Question 11

What was Hinton’s belief about the nature of neurons in neural networks?

Answer 11

Neurons had to be stochastic to ensure different learning outcomes

This belief was based on Rosenblatt’s argument about non-deterministic procedures.

Question 12

What was Hinton’s experience in academia post-Ph.D.?

Answer 12

He faced rejection in the UK and eventually found a position in the US

This move was significant for his career in neural networks.

Question 13

What is the gradient descent method?

Answer 13

A technique to minimize error by updating weights in the opposite direction of the error gradient

Used in training neural networks to find optimal weight values.

Question 14

What is a major challenge with the error function in neural networks?

Answer 14

It is not convex and can have multiple local minima

This complexity makes finding the global minimum more difficult.

Question 15

What phenomenon can occur with hill climbing algorithms?

Answer 15

The mesa phenomenon, where the algorithm gets stuck in flat regions of the error space

This can impede finding better solutions in optimization tasks.

Question 16

What is the hill-climbing technique?

Answer 16

A method where performance must improve to a local optimum where no small change in controls yields improvement.

Question 17

What phenomenon can hill climbing encounter according to Minsky and Selfridge?

Answer 17

The mesa phenomenon.

Question 18

What is the mesa phenomenon?

Answer 18

A situation where small tweaks to parameters do not improve performance or lead to large performance changes.

Question 19

What was Minsky and Papert’s view of multi-layer neural networks?

Answer 19

They had a dismal view, suggesting a deliberate sabotage of research into neural networks.

Question 20

Who independently developed methods relevant to the backpropagation algorithm in 1960-61?

Answer 20

Henry J. Kelley and Arthur E. Bryson.

Question 21

What contribution did Stuart Dreyfus make in 1962?

Answer 21

He derived formulas based on the chain rule to augment the Kelley-Bryson method.

Question 22

Who demonstrated techniques for using stochastic gradient descent in 1967?

Answer 22

Shun’ichi Amari.

Question 23

What did Seppo Linnainmaa develop in 1970?

Answer 23

The code for efficient backpropagation.

Question 24

What was the title of Paul Werbos’s 1974 Ph.D. thesis?

Answer 24

Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences.

Question 25

Who developed the modern version of the backpropagation algorithm in the early 1980s?

Answer 25

Rumelhart, Hinton, and Williams.

Question 26

What does the equation y = wx + b represent?

Answer 26

The output of a neuron given a weight w, bias b, and scalar input x.

Question 27

What is the delta rule used for?

Answer 27

Finding the weight and bias in a neuron.

Question 28

What is the formula for calculating the error in the delta rule?

Answer 28

e = y - yhat.

Question 29

What does loss represent in the context of the delta rule?

Answer 29

loss = (y - yhat)².

Question 30

What does MSE stand for?

Answer 30

Mean Squared Error.

Question 31

In the context of the delta rule, what is the learning rate denoted by?

Answer 31

α (alpha).

Question 32

What happens to the weight and bias during the update process?

Answer 32

They are adjusted by a small fraction of the gradient.

Question 33

What is a hyperplane in machine learning?

Answer 33

A line that separates different classes in a dataset.

Question 34

What is the XOR problem in neural networks?

Answer 34

A classification problem where data points cannot be separated by a single linear line.

Question 35

What is required to solve the XOR problem?

Answer 35

At least two layers of neurons.

Question 36

What do the neurons in the first layer of a neural network for XOR do?

Answer 36

They find two lines to separate the data.

Question 37

What is the output of a neuron that takes in two inputs x1 and x2?

Answer 37

y = w1x1 + w2x2 + b.

Question 38

What is the purpose of the second layer in a neural network for XOR?

Answer 38

To create a weighted sum of the outputs of the first layer's neurons.

Question 39

What is the output of a simple linear neuron?

Answer 39

y = w1 * x1 + w2 * x2 + b

Question 40

What is the role of the activation function in a neuron?

Answer 40

Transforms the weighted sum input into an output.

Question 41

What is a threshold function?

Answer 41

A function that outputs 1 if z > 0 and 0 otherwise.

Question 42

True or False: The threshold function is differentiable everywhere.

Answer 42

False

Question 43

What is the sigmoid function used for?

Answer 43

To create a smooth, differentiable activation function.

Question 44

As z tends to infinity, what does the sigmoid function approach?

Answer 44

1

Question 45

As z tends to minus infinity, what does the sigmoid function approach?

Answer 45

0

Question 46

What is the structure of a simple neural network for the XOR problem?

Answer 46

Three layers: input layer, hidden layer with two neurons, output layer with one neuron.

Question 47

Fill in the blank: The output neuron takes a weighted sum of the outputs of the two hidden neurons and passes that through a _______.

Answer 47

sigmoid activation function

Question 48

What is the loss function defined as in this context?

Answer 48

L = e^2, where e is the error (y - yhat).

Question 49

What technique was developed for calculating partial derivatives in neural networks?

Answer 49

Backpropagation

Question 50

Who were the key researchers in developing the backpropagation algorithm?

Answer 50

Werbos, Rumelhart, Hinton, Williams

Question 51

What does backpropagation allow us to compute?

Answer 51

The gradients of the loss function with respect to weights and biases.

Question 52

What is required for the chain rule to be applied in backpropagation?

Answer 52

Every operation must be differentiable.

Question 53

What is the significance of breaking symmetry in neural networks?

Answer 53

To ensure that neurons learn different features and do not produce the same output.

Question 54

How can symmetry be broken during the initialization of weights?

Answer 54

By setting initial weights to small random values.

Question 55

What is the role of the output layer in a neural network for classifying digits?

Answer 55

It has one neuron for each digit class, firing the corresponding neuron for the detected digit.

Question 56

What is a multi-layer perceptron?

Answer 56

A fully connected deep neural network.

Question 57

What does a fully connected neural network mean?

Answer 57

Each neuron in a layer receives inputs from all neurons in the previous layer.

Question 58

Fill in the blank: The first layer in a neural network for image recognition has _______ neurons, one for each pixel.

Answer 58

784

Question 59

What type of activation function was initially used in binary threshold neurons?

Answer 59

Threshold activation function

Question 60

What is the main advantage of using a sigmoid function over a threshold function?

Answer 60

It is differentiable everywhere.

Question 61

What does the backpropagation algorithm enable networks to learn?

Answer 61

Interesting representations of data.

Question 62

True or False: Neural networks require predefined features from the data.

Answer 62

False

Question 63

What happens to the output of neurons in a well-trained network for digit recognition?

Answer 63

The correct digit neuron fires significantly more than others.

Question 64

What is the primary challenge mentioned regarding complex networks with many layers?

Answer 64

Calculating partial derivatives becomes unrealistic.

Question 65

What is the main advantage of neural networks over traditional algorithms like support vector machines?

Answer 65

Neural networks can learn to represent features internally without needing predefined features.

Question 66

What are the features needed to separate circles from triangles in a two-dimensional dataset?

Answer 66

Nonlinear features such as [x1, x2, x1x2].

Question 67

What is the role of hidden units in a neural network according to Rumelhart, Hinton, and Williams?

Answer 67

Hidden units represent important features of the task domain.

Question 68

What distinguishes backpropagation from earlier methods like the perceptron-convergence procedure?

Answer 68

Backpropagation allows for the creation of useful new features automatically.

Question 69

Who are the authors of the influential paper on backpropagation?

Answer 69

Rumelhart, Hinton, and Williams.

Question 70

What significant event occurred in 1987 related to Rumelhart's career?

Answer 70

Rumelhart moved to Stanford University.

Question 71

What is the sigmoid function represented by?

Answer 71

u = 1 + e^{-z}

Question 72

What must the output of each neuron in a neural network layer pass through?

Answer 72

An activation function.

Question 73

Fill in the blank: The output of layer 1 after activation can be expressed as _______.

Answer 73

a1 = σ(z1)

Question 74

What is the formula for calculating the error in a neural network?

Answer 74

e = (y - ŷ)

Question 75

What is the loss function represented by in the context of a neural network?

Answer 75

L = e²

Question 76

What is the purpose of calculating the gradient of the loss function?

Answer 76

To update the weights and biases in the neural network.

Question 77

True or False: More hidden layer neurons always result in a rougher decision boundary.

Answer 77

False

Question 78

What type of functions can be used as activation functions in neural networks?

Answer 78

Any differentiable function.

Question 79

What does the term 'gradient' refer to in the context of neural networks?

Answer 79

The rate of change of the loss function with respect to weights and biases.

Question 80

What is the output of the final layer in a simple neural network with one output neuron?

Answer 80

ŷ = σ(z4)

Question 81

What condition must be satisfied for the activation function in a neural network?

Answer 81

It must be differentiable.

Question 82

What is the significance of learning features automatically in neural networks?

Answer 82

It allows for more effective and flexible modeling of complex data.

Question 83

Fill in the blank: The ability to create useful new features distinguishes _______ from earlier methods.

Answer 83

backpropagation

Question 84

What does the term 'delta rule' refer to in neural networks?

Answer 84

A method used to update the weights based on the gradient.

Question 85

Who independently developed an algorithm achieving similar results to backpropagation?

Answer 85

Yann LeCun.

Question 86

What illness did Rumelhart suffer from before his retirement?

Answer 86

Pick’s disease.