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