
.. _nan_tutorial:

=================
Dealing with NaNs
=================

Having a model yielding NaNs or Infs is quite common if some of the tiny
components in your model are not set properly. NaNs are hard to deal with
because sometimes it is caused by a bug or error in the code, sometimes it's
because of the numerical stability of your computational environment (library
versions, etc.), and even, sometimes it relates to your algorithm. Here we try
to outline common issues which cause the model to yield NaNs, as well as
provide nails and hammers to diagnose it. 


Check Superparameters and Weight Initialization
-----------------------------------------------

Most frequently, the cause would be that some of the hyperparameters, especially
learning rates, are set incorrectly. A high learning rate can blow up your whole
model into NaN outputs even within one epoch of training. So the first and
easiest solution is try to lower it. Keep halving your learning rate until you
start to get resonable output values.

Other hyperparameters may also play a role. For example, are your training
algorithms involve regularization terms? If so, are their corresponding
penalties set reasonably? Search a wider hyperparameter space with a few (one or
two) training eopchs each to see if the NaNs could disappear.

Some models can be very sensitive to the initialization of weight vectors. If
those weights are not initialized in a proper range, then it is not surprising
that the model ends up with yielding NaNs. 


Run in DebugMode
-----------------

If adjusting hyperparameters doesn't work for you, you can still get help from
Theano's DebugMode. Run your code in DebugMode with flag mode=DebugMode,
DebugMode.check_py=False. This will give you clue about which op is causing this
problem, and then you can inspect into that op in more detail. For a detailed
of using DebugMode, please refere to :ref:`debugmode`.

Theano's MonitorMode can also help. It can be used to step through the execution
of a function. You can inspect the inputs and outputs of each node being
executed when the function is called. For how to use that, please check
:ref:`faq_monitormode`. 


Numerical Stability
-------------------

After you have located the op which causes the problem, it may turn out that the
NaNs yielded by that op are related to numerical issues. For example, :math:
`1 / log(p(x) + 1)` may result in NaNs for those nodes who have learned to yield
a low probability p(x) for some input x.


Algorithm Related
-----------------

In the most difficult situations, you may go through the above steps and find
nothing wrong. If the above methods fail to uncover the cause, there is a good
chance that something is wrong with your algorithm. Go back to the mathematics
and find out if everything is derived correctly.
