I still remember when I trained my first recurrent network for Image Captioning. Within a few dozen minutes of training my first baby model (with rather arbitrarily-chosen hyperparameters) started to generate very nice looking descriptions of images that were on the edge of making sense. Sometimes the ratio of how simple your model is to the quality of the results you get out of it blows past your expectations, and this was one of those times. What made this result so shocking at the time was that the common wisdom was that RNNs were supposed to be difficult to train (with more experience I’ve in fact reached the opposite conclusion). Fast forward about a year: I’m training RNNs all the time and I’ve witnessed their power and robustness many times, and yet their magical outputs still find ways of amusing me.
We’ll train RNNs to generate text character by character and ponder the question “how is that even possible?”
What are RNNs anyway?
Recurrent Neural Networks Sequences. Depending on your background you might be wondering: What makes Recurrent Networks so special? A glaring limitation of Vanilla Neural Networks (and also Convolutional Networks) is that their API is too constrained: they accept a fixed-sized vector as input (e.g. an image) and produce a fixed-sized vector as output (e.g. probabilities of different classes). Not only that: These models perform this mapping using a fixed amount of computational steps (e.g. the number of layers in the model). The core reason that recurrent nets are more exciting is that they allow us to operate over sequences of vectors: Sequences in the input, the output, or in the most general case both. A few examples may make this more concrete:
Each rectangle is a vector and arrows represent functions (e.g. matrix multiply). Input vectors are in red, output vectors are in blue and green vectors hold the RNN's state (more on this soon). From left to right: (1) Vanilla mode of processing without RNN, from fixed-sized input to fixed-sized output (e.g. image classification). (2) Sequence output (e.g. image captioning takes an image and outputs a sentence of words). (3) Sequence input (e.g. sentiment analysis where a given sentence is classified as expressing positive or negative sentiment). (4) Sequence input and sequence output (e.g. Machine Translation: an RNN reads a sentence in English and then outputs a sentence in French). (5) Synced sequence input and output (e.g. video classification where we wish to label each frame of the video). Notice that in every case are no pre-specified constraints on the lengths sequences because the recurrent transformation (green) is fixed and can be applied as many times as we like.
As you might expect, the sequence regime of operation is much more powerful compared to fixed networks that are doomed from the get-go by a fixed number of computational steps, and hence also much more appealing for those of us who aspire to build more intelligent systems. Moreover, as we’ll see in a bit, RNNs combine the input vector with their state vector with a fixed (but learned) function to produce a new state vector. This can in programming terms be interpreted as running a fixed program with certain inputs and some internal variables. Viewed this way, RNNs essentially describe programs. In fact, it is known that RNNs are Turing-Complete in the sense that they can to simulate arbitrary programs (with proper weights). But similar to universal approximation theorems for neural nets you shouldn’t read too much into this. In fact, forget I said anything.
If training vanilla neural nets is optimization over functions, training recurrent nets is optimization over programs.
Sequential processing in absence of sequences. You might be thinking that having sequences as inputs or outputs could be relatively rare, but an important point to realize is that even if your inputs/outputs are fixed vectors, it is still possible to use this powerful formalism to process them in a sequential manner. For instance, the figure below shows results from two very nice papers from DeepMind. On the left, an algorithm learns a recurrent network policy that steers its attention around an image; In particular, it learns to read out house numbers from left to right (Ba et al.). On the right, a recurrent network generates images of digits by learning to sequentially add color to a canvas (Gregor et al.):
Character-Level Language Models Okay, so we have an idea about what RNNs are, why they are super exciting, and how they work. We’ll now ground this in a fun application: We’ll train RNN character-level language models. That is, we’ll give the RNN a huge chunk of text and ask it to model the probability distribution of the next character in the sequence given a sequence of previous characters. This will then allow us to generate new text one character at a time.
As a working example, suppose we only had a vocabulary of four possible letters “helo”, and wanted to train an RNN on the training sequence “hello”. This training sequence is in fact a source of 4 separate training examples: 1. The probability of “e” should be likely given the context of “h”, 2. “l” should be likely in the context of “he”, 3. “l” should also be likely given the context of “hel”, and finally 4. “o” should be likely given the context of “hell”.
A more technical explanation is that we use the standard Softmax classifier on every output vector simultaneously. The RNN is trained with mini-batch Stochastic Gradient Descent and I like to use RMSProp or Adam (per-parameter adaptive learning rate methods) to stablilize the updates.
Notice also that the first time the character “l” is input, the target is “l”, but the second time the target is “o”. The RNN therefore cannot rely on the input alone and must use its recurrent connection to keep track of the context to achieve this task.
At test time, we feed a character into the RNN and get a distribution over what characters are likely to come next. We sample from this distribution, and feed it right back in to get the next letter. Repeat this process and you’re sampling text! Lets now train an RNN on different datasets and see what happens.
To further clarify, for educational purposes I also wrote a minimal character-level RNN language model in Python/numpy. It is only about 100 lines long and hopefully it gives a concise, concrete and useful summary of the above if you’re better at reading code than text. We’ll now dive into example results, produced with the much more efficient Lua/Torch codebase.
We’ve learned about RNNs, how they work, why they have become a big deal, we’ve trained an RNN character-level language model on several fun datasets, and we’ve seen where RNNs are going. You can confidently expect a large amount of innovation in the space of RNNs, and I believe they will become a pervasive and critical component to intelligent systems.
Lastly, to add some meta to this post, I trained an RNN on the source file of this "readme.md" file. Unfortunately, at about this small amount characters I haven’t written enough data to properly feed the RNN, but the returned sample (generated with low temperature to get a more typical sample) is:
I've the RNN with and works, but the computed with program of the RNN with and the computed of the RNN with with and the code"