The above animation depicts the state space of a discrete-time recurrent neural network (RNN) undergoing neuroevolution. Each new frame represents the discovery of an improvement over the previous best RNN.
The goal is to be able to classify the parity of a binary string, in this case, of length 10. The string is fed sequentially to the RNN, one bit per time step.
A few training examples:
0100110101 -> 1
1110001011 -> 0
0010000010 -> 0
The RNN I used for this particular experiment has a hidden layer of two neurons. This was done so that I could easily plot the state space in two dimensions. The x-axis represents the activation of the first neuron, the y-axis is the activation of the second. Each point within a given frame represents the 'state' of the RNN at the very end of processing a string. The number of points per frame corresponds to the number of training examples. The first few frames appear to have fewer points; this is just overlap. The points have been colored red and blue to denote whether the target output should have been even or odd parity; they are not representative of the actual output of the RNN.
As can be seen, over the course of evolution, the state space of the RNN rearranges itself so that the red and blue points become progressively more linearly separable. On the last frame, it has nearly achieved that goal (as shown below), and classification accuracy on unseen examples is roughly 99%.
For those who are interested, I created these visualizations using a combination of Processing and GIMP