XOR Revisited: Keras and TensorFlow

A few weeks ago, it was announced that Keras would be getting official Google support and would become part of the TensorFlow machine learning library. Keras is a collection of high-level APIs in Python for creating and training neural networks, using either Theano or TensorFlow as the underlying engine.

Given my previous posts on implementing an XOR-solving neural network in a variety of different languages and tools, I thought it was time to see what it would look like in Keras.

XOR can be expressed as a classification problem that is best illustrated in a diagram. The goal is to create a neural network that will correctly predict the values 0 or 1, depending on the inputs x1 and x2 as shown.

xor graph

The neural network that is capable of being trained to solve that problem looks like this:


If you’d like to understand why this is the case, have a look at the detailed explanation in the posts implementing the solution in Octave.

So how does this look in Keras? Well it’s rather simple. Assuming you’ve already installed Keras, we’ll start with setting up the classification problem and the expected outputs:

import numpy as np

x = np.array([[0,0], [0,1], [1,0], [1,1]])
y = np.array([[0], [1], [1], [0]])

So far, so good. We’re using numpy arrays to store our inputs (x) and outputs (y). Now for the neural network definition:

from keras.models import Sequential
from keras.layers import Dense, Activation

model = Sequential()
model.add(Dense(2, input_shape=(2,)))

The Sequential model is simply a sequence of layers making up the network. Our diagram above has a set of inputs being fed into two processing layers. We’ve already defined the inputs, so all we need to do is add the other two layers.

In Keras, we’ll use Dense layers, which simply means they are is fully connected. The parameters indicate that the first layer has two nodes and the second layer has one node, corresponding to the diagram above.

The first layer also has the shape of the inputs which in this case is a one-dimensional vector with 2 elements. The second layer’s inputs will be inferred from the first layer.

We then add an Activation of type ‘sigmoid’ to each layer, again matching our neural network definition.

Note that Keras looks after the bias input without us having to explicitly code for it. In addition, Keras also looks after the weights (Θ1 and Θ2). This makes our neural network definition really straightforward and shows the benefits of using a high-level abstraction.

Finally, we apply a loss function and learning mode for Keras to be able to adjust the neural network:

model.compile(loss='mean_squared_error', optimizer='sgd', metrics=['accuracy'])

In this example, we’ll use the standard Mean Squared Error loss function and Stochastic Gradient Descent optimiser. And that’s it for the network definition.

If you want to see that the network looks like, use:


The network should look like this:

>> model.summary()
Layer (type)                  Output Shape         Param # 
dense_1 (Dense)               (None, 2)            6 
activation_1 (Activation)     (None, 2)            0 
dense_2 (Dense)               (None, 1)            3 
activation_2 (Activation)     (None, 1)            0 
Total params: 9
Trainable params: 9
Non-trainable params: 0

Now we just need to kick off the training of the network.

model.fit(x,y, epochs=100000, batch_size=4)

All going well, the network weights will converge on a solution that can correctly classify the inputs (if not, you may need to up the number of epochs):

>>> model.predict(x, verbose=1)

4/4 [==============================] - 0s

array([[ 0.07856689],

       [ 0.91362464],

       [ 0.92543262],

       [ 0.06886736]], dtype=float32)


Clearly this network is on it’s way to converging on the original expected outputs we defined above (y).

So that’s all there is to a Keras version of the XOR-solving neural network. The fact that it is using TensorFlow as the engine is completely hidden and that makes implementing the network a lot simpler.



Using Xcode with Github

You’ve found a nice open-source project you want to play with on GitHub. You’ve cloned it to your own repository and use Xcode 7 as your development environment. How do you make Xcode and GitHub play nicely with each other?

Turns out that Xcode has some nice features built in so that you can work directly with your GitHub-based code. To get started, open up the Preferences pane under the Xcode menu. Select the “Source Control” tab:

Source Control Preferences

Make sure that the “Enable Source Control” option is checked. Then select the Accounts tab:

Github Accounts

Click on the “+” at the bottom of the pane on the left. Select “Add Repository”. The following pane has several fields that you need to fill in.

  • Address: This is the URL of the repository. You can get this by clicking on the green “Clone or Download” button on the GitHub website.
  • Type: Choose “Git”
  • Authentication: Choose “User Name and Password”
  • User Name: Enter your GitHub user name
  • Password: Enter your GitHub password

I’ve added Google’s Protobuf and my own clone of TensorFlow in the example above.

Close the Preferences pane and select the “Source Control” menu.

Source Control Menu

This menu contains the controls you need to manage branches, commits and Pull Requests as necessary.

Xcode also lets you compare versions of code. In the top right of the main editor window, there is an icon with two arrows. Click on that and select “Comparison”. Xcode will show you the current version of your code against one in a different branch. You can choose which branch to compare against by clicking on the branch symbol below each editor pane.

Xcode Compare

I’ve literally scratched the surface here with using GitHub in Xcode 7. But it looks like it’s a straightforward way to play with the many open-source projects hosted there.



Machine Learning for the masses: Google’s TensorFlow

Google TensorFlowThe Artificial Intelligence community was abuzz recently with the news that Google has open-sourced it’s machine learning framework, called TensorFlow. This system was created by the Google Brain Team, working in it’s Machine Intelligence Research group.

This is not the first open source machine learning framework. Within the Python environment in particular, there are frameworks such as scikit-learn, PyBrain and others that have been around for a good while. What’s different about this new framework is that it has the backing of one of the most advanced commercial machine learning organisations, Google. In committing the project to open-source, it is inviting researchers, commercial practitioners and hobbyists to contribute to the framework. With Google’s backing, it seems destined for a long life.

But back to today. The framework has both Python and C++ APIs, with the expectation that C++ will be slightly faster on certain tasks. The instructions for installing TensorFlow are straightforward, but immediately I ran into a problem. My (slightly ageing) MacBook was running Python 2.7.5 and running TensorFlow caused a segmentation fault. Updating to Python 2.7.10 fixed the problem and I was able to successfully run though some of the tutorials.

There seems to be a wide range of neural network capabilities already available within the framework which provides much opportunity for exploration and experimentation. The tutorials cover areas such as handwriting recognition, image classification (using convolutional neural networks) and language modelling (using recurrent neural networks).

What’s also interesting is that since it’s an open source framework, the underlying code behind all these machine learning techniques is available for anyone to download, examine, modify and improve.

What will be the long-term impact of this is hard to tell. However, it is clear that Google has already put in quite a bit of effort already effort into this framework, and now that it’s out in the open, there will be lots more improvement to come.

If you want to know more and perhaps even try it out yourself, you can download TensorFlow here.