Joel and I were playing around with TensorFlow, the deep learning library that Google recently released and that you have no doubt heard of. We had put together a little autoencoder implementation and were trying to get a handle on how well it was working.
An autoencoder can be viewed as a neural network where the final layer, the output layer, is supposed to reconstruct the values that have been fed into the input layer, possibly after some distortion of the inputs (like forcing a fraction of them to be zero, dropout, or adding some random noise). In the case with corrupted, it’s called a denoising autoencoder, and the purpose of adding the noise or dropout is to make the system discover more robust statistical regularities in the input data (there is some good discussion here).
An autoencoder often has fewer nodes in the hidden layer(s) than in the input and is then used to learn a more compact and general representation of the data (the code or encoding). With only one hidden layer and linear activation functions, the encoding should be essentially the same as one gets from PCA (principal component analysis), but non-linear activation functions (e g sigmoid and tanh) will yield different representations, and multi-layer or stacked autoencoders will add a hierarchical aspect.
Some references on autoencoders:
Anyway, we were trying some different parametrizations of the autoencoder (its training performance can depend quite a lot on how the weights are initialized, the learning rate and the number of hidden nodes) and felt it was a bit boring to just look at a single number (the reconstruction error). We wanted to get a feel for how training is progressing across the input data matrix, so we made the script output for each 1000 rounds of training a colored block of text in the terminal where the background color represents the absolute difference between the target value and the reconstructed value using bins. The “best” bin (bin 0) is dark green and represents that the reconstruction is very close to the original input; the “bad” bins have reddish colors. If the data point has been shifted t0 a new bin in the last 1000 rounds (i e the reconstruction has improved or deteriorated noticeably), a colored digit indicating the new bin is shown in the foreground. (This makes more sense when you actually look at it.) We only show the first 75 training examples and the first 75 features, so if your data set is larger than that you won’t see all of it.
The code is on GitHub. There are command-line switches for controlling the number of hidden nodes, learning rate, and other such things. There are probably many aspects that could be improved but we thought this was a fun way to visualize the progress and see if there are any regions that clearly stand out in some way.
Here are a few screenshots of an example execution of the script.
As the training progresses, the overall picture gets a bit greener (the reconstruction gets closer to the input values) and the reconstructions get a bit more stable (i e not as many values have a digit on them to indicate that the reconstruction has improved or deteriorated). The values under each screenshot indicates the number of training cycles and the mean squared reconstruction error.