With sigmoid activation, especially if there are many layers, the gradient can become very small and training get slower and slower.
We define a function for doing so.
This is a tiny dataset so it will work.
The theory is that neural networks have so much freedom between their numerous layers that it is entirely possible for a layer to evolve a bad behaviour and for the next layer to compensate for it.
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This is a fairly disappointing result.
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This means that your neural network, in its present shape, is not capable of extracting more information from your data, as in our case here.
It has 10 neurons because we are classifying handwritten digits into 10 classes.
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This is what our model expects.
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To get the label, we have to find out which probability is the highest.
And the validation accuracy went down a bit.
And that means its derivative there is close to zero.
We are now ready to define a model and use this dataset to train it.
You would be dropping your predicted probabilities.
You can add dropout after each intermediate dense layer in the network.
Basic overfitting happens when a neural network has too many degrees of freedom for the problem at hand.
The learning algorithm works on training data only and optimises the training loss accordingly.
This operation is then repeated across the entire image using the same weights.
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Different neurons will be dropped at each training iteration.
Sequential style to create them.
To improve the recognition accuracy we will add more layers to the neural network.
This means that we are going too fast.
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The input comes from softmax which is essentially an exponential and an exponential is never zero.
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Then retrain the model.
There is nothing for you to do since Keras already does the right thing.
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It adds a bias and feeds the sum through an activation function, just as a neuron in a regular dense layer would.
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Indeed, as you add layers, neural networks have more and more difficulties to converge.
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The training curves are really noisy and look at both validation curves: they are jumping up and down.
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The loss seems to have shot through the roof too.
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The validation dataset is prepared in a similar way.
The art of initializing weights biases before training is an area of research in itself, with numerous papers published on the topic.
The model seems to be converging nicely now.
In Keras, you can do this with the tf.
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Look how it behaves on the sides: it gets flat.
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Handwritten digits are made of shapes and we discarded the shape information when we flattened the pixels.
We now have a dataset of pairs (image, label).
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Keras does this automatically, so all you have to do is add a tf.
The sigmoid activation function is actually quite problematic in deep networks.
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This is where the training happens, by calling model.
It squashes all values between 0 and 1 and when you do so repeatedly, neuron outputs and their gradients can vanish entirely.
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These are points that are not local minima but where the gradient is nevertheless zero and the gradient descent optimizer stays stuck there.
It is important that training data are well shuffled.
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That is how the dynamically updating training plot was implemented for this workshop.
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The number of neurons in them can be anything between 784 (the number of input pixels) and 10 (the number of output neurons).
The relu on the other hand has a derivative of 1, at least on its right side.
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The image is not compressed so the function does not need to decode anything (decode_raw does basically nothing).
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Generally speaking, you always need lots of data to train neural networks.
Once the model is trained, we can get predictions from it by calling model.
Why is the sigmoid problematic?
Imagine we have so many neurons that the network can store all of our training images in them and then recognise them by pattern matching.
It should be 10x better!
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That was a really bad idea.
Noise reappears (unsurprisingly given how dropout works).
It turns out that deep neural networks with many layers (20, 50, even 100 today) can work really well, provided a couple of mathematical dirty tricks to make them converge.
The impact of this little change is spectacular.
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In Keras, it is possible to add custom behaviors during training by using callbacks.
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The dropout technique shoots random neurons at each training iteration.
Input can be used to define it.
Here we have prepared a set of printed digits rendered from local fonts, as a test.
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By default, Keras runs a round of validation at the end of each epoch.
We keep softmax as the activation function on the last layer because that is what works best for classification.
Convolutional neural networks apply a series of learnable filters to the input image.
Remember how we are using our images, flattened into a single vector?
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The depth of the output (nb of channels) is adjusted by using more or fewer filters.
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Do not add dropout after your softmax layer.
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We could go back to our previous speed but there is a better way.
However, there is a type of neural network that can take advantage of shape information: convolutional networks.
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Do not forget to use the lr_decay_callback you have created.
You will find useful code snippets below.
Configuring the model is done in Keras using the model.
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Remember how the training progresses, by following the gradient, which is a vector of derivatives.
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It never sees validation data so it is not surprising that after a while its work no longer has an effect on the validation loss which stops dropping and sometimes even bounces back up.
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Not bad, but you will now improve this significantly.
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