Neural Networks and Deep Learning

Nielsen, Michael A.

Neural Networks and Deep Learning

What this book is about

On the exercises and problems

Using neural nets to recognize handwritten digits

Perceptrons

Sigmoid neurons

The architecture of neural networks

A simple network to classify handwritten digits

Learning with gradient descent

Implementing our network to classify digits

Toward deep learning

How the backpropagation algorithm works

Warm up: a fast matrix-based approach to computing the output from a neural network

The two assumptions we need about the cost function

The Hadamard product, $s \odot t$

The four fundamental equations behind backpropagation

Proof of the four fundamental equations (optional)

The backpropagation algorithm

The code for backpropagation

In what sense is backpropagation a fast algorithm?

Backpropagation: the big picture

Improving the way neural networks learn

The cross-entropy cost function

Overfitting and regularization

Weight initialization

Handwriting recognition revisited: the code

How to choose a neural network's hyper-parameters?

Other techniques

A visual proof that neural nets can compute any function

Two caveats

Universality with one input and one output

Many input variables

Extension beyond sigmoid neurons

Fixing up the step functions

Conclusion

Why are deep neural networks hard to train?

The vanishing gradient problem

What's causing the vanishing gradient problem? Unstable gradients in deep neural nets

Unstable gradients in more complex networks

Other obstacles to deep learning

Deep learning

Introducing convolutional networks

Convolutional neural networks in practice

The code for our convolutional networks

Recent progress in image recognition

Other approaches to deep neural nets

On the future of neural networks

Appendix: Is there a simple algorithm for intelligence?

Acknowledgements

Frequently Asked Questions

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