This is where the training happens, by calling model.
To get the label, we have to find out which probability is the highest.
Do not forget to use the lr_decay_callback you have created.
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However, there is a type of neural network that can take advantage of shape information: convolutional networks.
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The sigmoid activation function is actually quite problematic in deep networks.
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Handwritten digits are made of shapes and we discarded the shape information when we flattened the pixels.
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We now have a dataset of pairs (image, label).
This is a tiny dataset so it will work.
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The dropout technique shoots random neurons at each training iteration.
Indeed, as you add layers, neural networks have more and more difficulties to converge.
The depth of the output (nb of channels) is adjusted by using more or fewer filters.
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You would be dropping your predicted probabilities.
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You will find useful code snippets below.
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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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That was a really bad idea.
Noise reappears (unsurprisingly given how dropout works).
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You can add dropout after each intermediate dense layer in the network.
This is a fairly disappointing result.
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Input can be used to define it.
By default, Keras runs a round of validation at the end of each epoch.
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.
Look how it behaves on the sides: it gets flat.
It squashes all values between 0 and 1 and when you do so repeatedly, neuron outputs and their gradients can vanish entirely.
In Keras, you can do this with the tf.
We keep softmax as the activation function on the last layer because that is what works best for classification.
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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Generally speaking, you always need lots of data to train neural networks.
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Not bad, but you will now improve this significantly.
The number of neurons in them can be anything between 784 (the number of input pixels) and 10 (the number of output neurons).
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Remember how we are using our images, flattened into a single vector?
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Keras offers the very nice model.
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We could go back to our previous speed but there is a better way.
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The learning algorithm works on training data only and optimises the training loss accordingly.
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The input comes from softmax which is essentially an exponential and an exponential is never zero.
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The model seems to be converging nicely now.
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The art of initializing weights biases before training is an area of research in itself, with numerous papers published on the topic.
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And the validation accuracy went down a bit.
This is what our model expects.
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Once the model is trained, we can get predictions from it by calling model.
Here we have prepared a set of printed digits rendered from local fonts, as a test.
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The validation dataset is prepared in a similar way.
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.
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Sequential style to create them.
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Then retrain the model.
Different neurons will be dropped at each training iteration.
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Configuring the model is done in Keras using the model.
We are now ready to define a model and use this dataset to train it.
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Why is the sigmoid problematic?
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.
And that means its derivative there is close to zero.
Convolutional neural networks apply a series of learnable filters to the input image.
The relu on the other hand has a derivative of 1, at least on its right side.
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Keras does this automatically, so all you have to do is add a tf.
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It should be 10x better!
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The training curves are really noisy and look at both validation curves: they are jumping up and down.
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.
Do not add dropout after your softmax layer.
To improve the recognition accuracy we will add more layers to the neural network.
Remember how the training progresses, by following the gradient, which is a vector of derivatives.
In Keras, it is possible to add custom behaviors during training by using callbacks.
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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.
That is how the dynamically updating training plot was implemented for this workshop.
There is nothing for you to do since Keras already does the right thing.
The impact of this little change is spectacular.
It has 10 neurons because we are classifying handwritten digits into 10 classes.
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This operation is then repeated across the entire image using the same weights.
The image is not compressed so the function does not need to decode anything (decode_raw does basically nothing).
Basic overfitting happens when a neural network has too many degrees of freedom for the problem at hand.
The loss seems to have shot through the roof too.
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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.
This means that we are going too fast.
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It is important that training data are well shuffled.
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