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How is the cost for a single training example calculated?
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By summing the squared differences between the network output and the desired output for that example.
What is the primary purpose of backpropagation in neural network learning?
To compute the gradient of the cost function and adjust weights and biases to minimize the cost.
What is Stochastic Gradient Descent (SGD) and why is it used?
SGD uses mini-batches of training data to perform gradient descent, resulting in faster but less precise optimization compared to using all training data.
Why is gradient descent important in neural networks?
It is a method used to minimize the cost function by adjusting the network's weights and biases.
Explain how backpropagation handles weight adjustments in the context of recognizing digit '2'.
Backpropagation adjusts weights by increasing activation for the target neuron (digit 2) and decreasing activations for other neurons.
How does using mini-batches in SGD compare to using all training data in terms of computation speed and precision?
Using mini-batches is faster because it approximates the gradient without calculating for all data, but it offers less precision in optimization.
What does a negative gradient of the cost function indicate?
It indicates the direction in which weights and biases should be adjusted to decrease the cost efficiently.
What future topic will be covered in the next video following the lecture on backpropagation?
The underlying calculus of backpropagation.
What role do hidden layers play in the neural network structure used for digit recognition?
Hidden layers process inputs through intermediate computations, allowing the network to learn complex patterns and representations.
Why is a large training dataset important in neural network training, as illustrated by the example of the MNIST database?
A large training dataset like MNIST helps in better generalization and more accurate training of the neural network.
Explain the concept of 'sensitivity' in the context of gradient descent in neural networks.
Sensitivity refers to how much the cost function responds to changes in weights and biases, where higher sensitivity leads to larger adjustments.
Describe the structure of a neural network used for handwritten digit recognition as noted in the class.
It consists of an input layer with 784 neurons, two hidden layers each with 16 neurons, and an output layer with 10 neurons.
What is meant by 'neurons that fire together, wire together' in the context of weight adjustment?
It means connections (weights) between neurons that are frequently activated together are strengthened.
What is the significance of averaging changes across all training examples for weight/bias adjustments?
It helps in finding an approximate gradient that represents the overall direction in which weights and biases should be adjusted for all training examples.
How do changes propagate through layers in backpropagation?
Changes propagate backwards from the output layer, where desired changes for one neuron influence preceding layers and aggregate changes from all output neurons inform adjustments in previous layers.
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