What is num_units in tensorflow BasicLSTMCell?

Question

From this brilliant article

num_units can be interpreted as the analogy of hidden layer from the feed forward neural network. The number of nodes in hidden layer of a feed forward neural network is equivalent to num_units number of LSTM units in a LSTM cell at every time step of the network.

See the image there too!

The number of hidden units is a direct representation of the learning capacity of a neural network -- it reflects the number of learned parameters. The value 128 was likely selected arbitrarily or empirically. You can change that value experimentally and rerun the program to see how it affects the training accuracy (you can get better than 90% test accuracy with a lot fewer hidden units). Using more units makes it more likely to perfectly memorize the complete training set (although it will take longer, and you run the risk of over-fitting).

The key thing to understand, which is somewhat subtle in the famous Colah's blog post (find "each line carries an entire vector"), is that X is an array of data (nowadays often called a tensor) -- it is not meant to be a scalar value. Where, for example, the tanh function is shown, it is meant to imply that the function is broadcast across the entire array (an implicit for loop) -- and not simply performed once per time-step.

As such, the hidden units represent tangible storage within the network, which is manifest primarily in the size of the weights array. And because an LSTM actually does have a bit of it's own internal storage separate from the learned model parameters, it has to know how many units there are -- which ultimately needs to agree with the size of the weights. In the simplest case, an RNN has no internal storage -- so it doesn't even need to know in advance how many "hidden units" it is being applied to.

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• A good answer to a similar question here.
• You can look at the source for BasicLSTMCell in TensorFlow to see exactly how this is used.

Side note: This notation is very common in statistics and machine-learning, and other fields that process large batches of data with a common formula (3D graphics is another example). It takes a bit of getting used to for people who expect to see their for loops written out explicitly.

The argument n_hidden of BasicLSTMCell is the number of hidden units of the LSTM.

As you said, you should really read Colah's blog post to understand LSTM, but here is a little heads up.

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If you have an input x of shape [T, 10], you will feed the LSTM with the sequence of values from t=0 to t=T-1, each of size 10.

At each timestep, you multiply the input with a matrix of shape [10, n_hidden], and get a n_hidden vector.

Your LSTM gets at each timestep t:

• the previous hidden state h_{t-1}, of size n_hidden (at t=0, the previous state is [0., 0., ...])
• the input, transformed to size n_hidden
• it will sum these inputs and produce the next hidden state h_t of size n_hidden

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From Colah's blog post:

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If you just want to have code working, just keep with n_hidden = 128 and you will be fine.

An LSTM keeps two pieces of information as it propagates through time:

A hidden state; which is the memory the LSTM accumulates using its (forget, input, and output) gates through time, and The previous time-step output.

Tensorflow’s num_units is the size of the LSTM’s hidden state (which is also the size of the output if no projection is used).

To make the name num_units more intuitive, you can think of it as the number of hidden units in the LSTM cell, or the number of memory units in the cell.

Look at this awesome post for more clarity

Since I had some problems to combine the information from the different sources I created the graphic below which shows a combination of the blog post (http://colah.github.io/posts/2015-08-Understanding-LSTMs/) and (https://jasdeep06.github.io/posts/Understanding-LSTM-in-Tensorflow-MNIST/) where I think the graphics are very helpful but an error in explaining the number_units is present.

Several LSTM cells form one LSTM layer. This is shown in the figure below. Since you are mostly dealing with data that is very extensive, it is not possible to incorporate everything in one piece into the model. Therefore, data is divided into small pieces as batches, which are processed one after the other until the batch containing the last part is read in. In the lower part of the figure you can see the input (dark grey) where the batches are read in one after the other from batch 1 to batch batch_size. The cells LSTM cell 1 to LSTM cell time_step above represent the described cells of the LSTM model (http://colah.github.io/posts/2015-08-Understanding-LSTMs/). The number of cells is equal to the number of fixed time steps. For example, if you take a text sequence with a total of 150 characters, you could divide it into 3 (batch_size) and have a sequence of length 50 per batch (number of time_steps and thus of LSTM cells). If you then encoded each character one-hot, each element (dark gray boxes of the input) would represent a vector that would have the length of the vocabulary (number of features). These vectors would flow into the neuronal networks (green elements in the cells) in the respective cells and would change their dimension to the length of the number of hidden units (number_units). So the input has the dimension (batch_size x time_step x features). The Long Time Memory (Cell State) and Short Time Memory (Hidden State) have the same dimensions (batch_size x number_units). The light gray blocks that arise from the cells have a different dimension because the transformations in the neural networks (green elements) took place with the help of the hidden units (batch_size x time_step x number_units). The output can be returned from any cell but mostly only the information from the last block (black border) is relevant (not in all problems) because it contains all information from the previous time steps.