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