# What does this gated recurrent unit notation mean?

I'm trying to replicate the algorithm found in this paper: http://arxiv.org/abs/1506.07285.

And I'm struggling to understand the notation of equation 3 on page 4, which is given as: Is z(c,m,q) a matrix of the individual vectors? That wouldn't make sense, though, because the last two elements look like they would be scalars. I've read the paper and it doesn't say much about this equation. Perhaps they aren't revealing the full function and are only listing used parameters? Any ideas? The equation is used for gating in a recurrent neural network.

Edit: I understand what the individual parameters mean, but I don't understand how to define z(c,m,q), which I will need to know before I can implement equation 4.

• What exactly do you mean by "this"? BTW, all these terms are described after equation (2) on the preceding page. – whuber Nov 2 '15 at 16:18
• You seem to have accidentally created two accounts - please follow these instructions to merge them. This will make it easier for you to do things like edit your own question as you will no longer need to wait for someone to approve your edit.. – Silverfish Nov 2 '15 at 17:24
• Accounts have been merged, thanks for heads up. And thanks whuber for the request for clarification -- question has been edited. – jstaker7 Nov 2 '15 at 19:09

## 1 Answer

I can't find a definitive answer, but the best guess I can come up with is that it is a concatenation of the individual vectors. This line in a Keras model is what prompted this guess:

model.add(Merge([sentrnn, qrnn], mode='concat')).

I've seen similar formatting here and there in other papers, sometimes like this:

sigma([vec1,vect2], vec3).

This would work for the equations above where the inner W(1) dimension equals the sum of the dimensions of the concatenated vectors.