10 - The Algorithm that Put Paid to a Persistent Myth Flashcards
What did Minsky and Papert prove about single-layer perceptrons?
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.
Who is Geoffrey Hinton?
A key figure behind the modern deep learning revolution
Hinton became interested in neural networks in the mid-1960s.
What influenced Hinton’s interest in how brains learn?
A mathematician friend exploring how memories are stored in the brain
This led Hinton to study the mind and neural networks.
What did Hinton study at university?
Physics and physiology
However, he found the curriculum insufficient regarding understanding the brain.
What book deeply influenced Hinton?
The Organization of Behavior by Donald Hebb
This book impacted Hinton’s thinking on neural networks and learning.
What was Hinton’s doctoral focus?
Solving constrained optimization problems using neural networks
Hinton believed multi-layer networks could eventually learn.
What was the key limitation of single-layer perceptrons according to Minsky and Papert?
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.
What is back-propagation?
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.
What issue arises when initializing all weights in a neural network to zero?
All neurons produce the same output, leading to symmetry and ineffective learning
This problem prevents the network from detecting different features.
What did Rosenblatt suggest for updating weights in a neural network?
A stochastic process that introduces randomness to weight updates
This approach aimed to break symmetry in the network.
What was Hinton’s belief about the nature of neurons in neural networks?
Neurons had to be stochastic to ensure different learning outcomes
This belief was based on Rosenblatt’s argument about non-deterministic procedures.
What was Hinton’s experience in academia post-Ph.D.?
He faced rejection in the UK and eventually found a position in the US
This move was significant for his career in neural networks.
What is the gradient descent method?
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.
What is a major challenge with the error function in neural networks?
It is not convex and can have multiple local minima
This complexity makes finding the global minimum more difficult.
What phenomenon can occur with hill climbing algorithms?
The mesa phenomenon, where the algorithm gets stuck in flat regions of the error space
This can impede finding better solutions in optimization tasks.
What is the hill-climbing technique?
A method where performance must improve to a local optimum where no small change in controls yields improvement.
What phenomenon can hill climbing encounter according to Minsky and Selfridge?
The mesa phenomenon.
What is the mesa phenomenon?
A situation where small tweaks to parameters do not improve performance or lead to large performance changes.
What was Minsky and Papert’s view of multi-layer neural networks?
They had a dismal view, suggesting a deliberate sabotage of research into neural networks.
Who independently developed methods relevant to the backpropagation algorithm in 1960-61?
Henry J. Kelley and Arthur E. Bryson.
What contribution did Stuart Dreyfus make in 1962?
He derived formulas based on the chain rule to augment the Kelley-Bryson method.
Who demonstrated techniques for using stochastic gradient descent in 1967?
Shun’ichi Amari.
What did Seppo Linnainmaa develop in 1970?
The code for efficient backpropagation.
What was the title of Paul Werbos’s 1974 Ph.D. thesis?
Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences.
Who developed the modern version of the backpropagation algorithm in the early 1980s?
Rumelhart, Hinton, and Williams.
What does the equation y = wx + b represent?
The output of a neuron given a weight w, bias b, and scalar input x.
What is the delta rule used for?
Finding the weight and bias in a neuron.
What is the formula for calculating the error in the delta rule?
e = y - yhat.
What does loss represent in the context of the delta rule?
loss = (y - yhat)².
What does MSE stand for?
Mean Squared Error.
In the context of the delta rule, what is the learning rate denoted by?
α (alpha).
What happens to the weight and bias during the update process?
They are adjusted by a small fraction of the gradient.
What is a hyperplane in machine learning?
A line that separates different classes in a dataset.
What is the XOR problem in neural networks?
A classification problem where data points cannot be separated by a single linear line.
What is required to solve the XOR problem?
At least two layers of neurons.
What do the neurons in the first layer of a neural network for XOR do?
They find two lines to separate the data.
What is the output of a neuron that takes in two inputs x1 and x2?
y = w1x1 + w2x2 + b.
What is the purpose of the second layer in a neural network for XOR?
To create a weighted sum of the outputs of the first layer’s neurons.
What is the output of a simple linear neuron?
y = w1 * x1 + w2 * x2 + b
What is the role of the activation function in a neuron?
Transforms the weighted sum input into an output.
What is a threshold function?
A function that outputs 1 if z > 0 and 0 otherwise.
True or False: The threshold function is differentiable everywhere.
False
What is the sigmoid function used for?
To create a smooth, differentiable activation function.
As z tends to infinity, what does the sigmoid function approach?
1
As z tends to minus infinity, what does the sigmoid function approach?
0
What is the structure of a simple neural network for the XOR problem?
Three layers: input layer, hidden layer with two neurons, output layer with one neuron.
Fill in the blank: The output neuron takes a weighted sum of the outputs of the two hidden neurons and passes that through a _______.
sigmoid activation function
What is the loss function defined as in this context?
L = e^2, where e is the error (y - yhat).
What technique was developed for calculating partial derivatives in neural networks?
Backpropagation
Who were the key researchers in developing the backpropagation algorithm?
Werbos, Rumelhart, Hinton, Williams
What does backpropagation allow us to compute?
The gradients of the loss function with respect to weights and biases.
What is required for the chain rule to be applied in backpropagation?
Every operation must be differentiable.
What is the significance of breaking symmetry in neural networks?
To ensure that neurons learn different features and do not produce the same output.
How can symmetry be broken during the initialization of weights?
By setting initial weights to small random values.
What is the role of the output layer in a neural network for classifying digits?
It has one neuron for each digit class, firing the corresponding neuron for the detected digit.
What is a multi-layer perceptron?
A fully connected deep neural network.
What does a fully connected neural network mean?
Each neuron in a layer receives inputs from all neurons in the previous layer.
Fill in the blank: The first layer in a neural network for image recognition has _______ neurons, one for each pixel.
784
What type of activation function was initially used in binary threshold neurons?
Threshold activation function
What is the main advantage of using a sigmoid function over a threshold function?
It is differentiable everywhere.
What does the backpropagation algorithm enable networks to learn?
Interesting representations of data.
True or False: Neural networks require predefined features from the data.
False
What happens to the output of neurons in a well-trained network for digit recognition?
The correct digit neuron fires significantly more than others.
What is the primary challenge mentioned regarding complex networks with many layers?
Calculating partial derivatives becomes unrealistic.
What is the main advantage of neural networks over traditional algorithms like support vector machines?
Neural networks can learn to represent features internally without needing predefined features.
What are the features needed to separate circles from triangles in a two-dimensional dataset?
Nonlinear features such as [x1, x2, x1x2].
What is the role of hidden units in a neural network according to Rumelhart, Hinton, and Williams?
Hidden units represent important features of the task domain.
What distinguishes backpropagation from earlier methods like the perceptron-convergence procedure?
Backpropagation allows for the creation of useful new features automatically.
Who are the authors of the influential paper on backpropagation?
Rumelhart, Hinton, and Williams.
What significant event occurred in 1987 related to Rumelhart’s career?
Rumelhart moved to Stanford University.
What is the sigmoid function represented by?
u = 1 + e^{-z}
What must the output of each neuron in a neural network layer pass through?
An activation function.
Fill in the blank: The output of layer 1 after activation can be expressed as _______.
a1 = σ(z1)
What is the formula for calculating the error in a neural network?
e = (y - ŷ)
What is the loss function represented by in the context of a neural network?
L = e²
What is the purpose of calculating the gradient of the loss function?
To update the weights and biases in the neural network.
True or False: More hidden layer neurons always result in a rougher decision boundary.
False
What type of functions can be used as activation functions in neural networks?
Any differentiable function.
What does the term ‘gradient’ refer to in the context of neural networks?
The rate of change of the loss function with respect to weights and biases.
What is the output of the final layer in a simple neural network with one output neuron?
ŷ = σ(z4)
What condition must be satisfied for the activation function in a neural network?
It must be differentiable.
What is the significance of learning features automatically in neural networks?
It allows for more effective and flexible modeling of complex data.
Fill in the blank: The ability to create useful new features distinguishes _______ from earlier methods.
backpropagation
What does the term ‘delta rule’ refer to in neural networks?
A method used to update the weights based on the gradient.
Who independently developed an algorithm achieving similar results to backpropagation?
Yann LeCun.
What illness did Rumelhart suffer from before his retirement?
Pick’s disease.
