## Connectionist Temporal Classification (CTC) with Theano

This will be the first time I’m trying to present code I’ve written in an ipython notebook. The style’s different, but I think I’ll permanently switch to this method of presentation for code-intensive posts from now on. A nifty little tool that makes doing this so convenient is ipy2wp. It uses WordPress’ xml-rpc to post the HTML directly to the platform.

In any case, I’ve started working with the NUS School of Computing speech recognition group, and they’ve been using deep neural networks for classification of audio frames to phonemes. This requires a preprocessing step that aligns the audio frames to phonemes in order to reduce this to a simple classification problem.

CTC describes a way to compute the probability of a sequence of phonemes for a sequence of audio frames, accounting for all possible alignments. We can then define an objective function to maximise the probability of the phoneme sequence given the audio frame sequence from training data.

The end of this post had  a diagram showing the improvements of AdaDelta over standard SGD and AdaGrad, so I decided to look up what AdaGrad actually does. The details are written in the paper, including it’s “derivation”. It’s basically an improvement over AdaGrad, using rolling averages and also multiplying by the RMS of the rolling average of changes to the weight. Continue reading

## NLP with Neural Networks

Gave a presentation on neural networks at the NUS Web Information retrieval and NLP Group (WING). Idea was mainly to concretise my understanding of the topic and also to share some interesting concepts that have been introduced in neural networks research on NLP, while giving me some sorely needed experience doing public speaking.

Not sure how much of that I achieved, but here are the slides anyway.

## Dropout using Theano

A month ago I tried my hand at the Higgs Boson Challenge on Kaggle. I tried using an approach neural networks that got me pretty far initially, but other techniques seemed to have won out.

## Recursive Auto-encoders: Momentum

In the previous post, we wrote the code for RAE using the Theano library, but it wasn’t successful in performing the simple task of reversing a randomised sequence of 1 to 8. One of the tricks we can use for dealing with time sequence data is to use a small learning rate, along with momentum. I’ll be discussing what momentum is, and showing a simple way momentum can be implemented in Theano. Continue reading

## Recursive Auto-encoders: Example in Theano

Okay, time to get our hands dirty with some code! I’ve written an example in Theano that encodes a stream of one-hot encodings, and this is the example I’ll run through with this post.

As a quick recap of what was covered in the previous post, here’s a diagram:

## Recursive Auto-encoders: An Introduction

I’ve talked a little bit about recursive auto-encoders a couple of posts ago. In the deep learning lingo, an auto-encoder network usually refers to an architecture that takes in an input vector, and through a series of transformations, is trained to reproduce that input in its prediction layer. The reason for doing this is to extract features that describe the input. One might think of it as a form of compression: If the network is asked to be able to reproduce an input with after passing it through hidden layers with a lot less neurons than the input layer, then some sort of compression has to happen in order for it to be able to create a good reconstruction. So let’s consider the above network. 8 inputs, 8 outputs, and 3 in the hidden layer. If we feed the network a one-hot encoding of 1 to 8 (setting only the neuron corresponding to the input to 1), and insist that that input be reconstructed at the output layer, guess what happens? Continue reading

## “It’s like Hinton diagrams, but for the terminal.”

Which of the two matrix representations below would you rather be looking at?

Hinton diagrams are often used for visualising the learnt weights of neural networks. I’ve often found myself trying to imagine what the weights look like. And fortunately for me today, I remembered this project by GitHub’s Zach Holman.

Turns out, overriding the way NumPy represents numbers wasn’t too hard, so I hacked myself a cool little solution. The code’s here for the time being, until I spin it off into it’s own little repo.

Enjoy!

## Finding Maximum Dot (or Inner) Product

A problem that often arises in machine learning tasks is trying to find a row in a matrix that gives the highest dot product given a query vector. Some examples of such situations:

• You’ve performed some kind of matrix factorisation for collaborative filtering for say, a movie recommendation system, and now, given a new user, you want to be able to specify a couple of movies that your system would predict he would rate highly.
• A neural network where the final softmax predictive layer is huge (but you managed to train it, somehow).

In both these cases, the problem boils down to trying to search a collection of vectors to find the one that gives the highest (or the $k$ highest) dot product(s).

A simple way to do this would be to perform a matrix multiplication, and then to find the best scoring vector by scanning through the values. This is effectively performing $N$ dot product computations for a matrix with $N$ rows. Can we do better?