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In what sense is backpropagation a fast algorithm? How to choose a neural network’s hyper-parameters? Why are deep neural networks hard to train? What’s causing the vanishing gradient problem? Appendix: Is there a simple algorithm for intelligence? If you benefit from the book, please make a small donation. 5, but you can choose the amount.

Thanks to all the supporters who made the book possible, with especial thanks to Pavel Dudrenov. Thanks also to all the contributors to the Bugfinder Hall of Fame. When a golf player is first learning to play golf, they usually spendmost of their time developing a basic swing. Only gradually do theydevelop other shots, learning to chip, draw and fade the ball,building on and modifying their basic swing.

In a similar way, up tonow we’ve focused on understanding the backpropagation algorithm. It’s our “basic swing”, the foundation for learning in most work onneural networks. Of course, we’re only covering a few of the many, many techniqueswhich have been developed for use in neural nets. The philosophy isthat the best entree to the plethora of available techniques isin-depth study of a few of the most important.

Mastering thoseimportant techniques is not just useful in its own right, but willalso deepen your understanding of what problems can arise when you useneural networks. That will leave you well prepared to quickly pick upother techniques, as you need them. Most of us find it unpleasant to be wrong. Soon after beginning tolearn the piano I gave my first performance before an audience.

I wasnervous, and began playing the piece an octave too low. Yet while unpleasant, we also learn quickly whenwe’re decisively wrong. You can bet that the next time I playedbefore an audience I played in the correct octave! Is this what happens in practice? To answer thisquestion, let’s look at a toy example. Of course, this is such a trivial taskthat we could easily figure out an appropriate weight and bias byhand, without using a learning algorithm. However, it turns out to beilluminating to use gradient descent to attempt to learn a weight andbias.

So let’s take a look at how the neuron learns. These are generic choices used as aplace to begin learning, I wasn’t picking them to be special in anyway. Indeed, for thefirst 150 or so learning epochs, the weights and biases don’t changemuch at all. This behaviour is strange when contrasted to human learning. As Isaid at the beginning of this section, we often learn fastest whenwe’re badly wrong about something. But we’ve just seen that ourartificial neuron has a lot of difficulty learning when it’s badlywrong – far more difficulty than when it’s just a little wrong. What’s more, it turns out that this behaviour occurs not just in thistoy model, but in more general networks.


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