Introduction to debugging neural networks

The following advice is targeted at beginners to neural networks, and is based
on my experience giving advice to neural net newcomers in industry and at
Stanford. Neural nets are fundamentally harder to debug than most programs,
because most neural net bugs don't result in type errors or runtime errors.
They just cause poor convergence. Especially when you're new, this can be very
frustrating! But an experienced neural net trainer will be able to
systematically overcome the difficulty in spite of the ubiquitous and
seemingly ambiguous error message:

  Performance Error: your neural net did not train well.

To the uninitiated, the message is daunting. But to the experienced, this is a
great error. It means the boilerplate coding is out of the way, and it's time
to dig in!

How to deal with NaNs

By far the most common first question I get from students is, "Why am I
getting NaNs." Occasionally, this has a complicated answer. But most often,
the NaNs come in the first 100 iterations, and the answer is simple: your
learning rate is too high. When the learning rate is very high, you will get
NaNs in the first 100 iterations of training. Try reducing the learning rate
by a factor of 3 until you no longer get NaNs in the first 100 iterations. As
soon as this works, you'll have a pretty good learning rate to get started
with. In my experience, the best heavily validated learning rates are 1-10x
below the range where you get NaNs.

If you are getting NaNs beyond the first 100 iterations, there are 2 further
common causes. 1) If you are using RNNs, make sure that you are using "gradient
clipping", which caps the global L2 norm of the gradients. RNNs tend to
produce gradients early in training where 10% or fewer of the batches have
learning spikes, where the gradient magnitude is very high. Without clipping,
these spikes can cause NaNs. 2) If you have written any custom layers
yourself, there is a good chance your own custom layer is causing the problems
in a division by zero scenario. Another notoriously NaN producing layer is
the softmax layer. The softmax computation involves an exp(x) term in both the
numerator and denominator, which can divide Inf by Inf and produce NaNs. Make
sure you are using a stabilized softmax implementation.

What to do when your neural net isn't learning anything

Once you stop getting NaNs, you are often rewarded with a neural net that runs
smoothly for many thousand iterations, but never reduces the training loss
after the initial fidgeting of the first few hundred iterations. When you're
first constructing your code base, waiting for more than 2000 iterations is
rarely the answer. This is not because all networks can start learning in
under 2000 iterations. Rather, the chance you've introduced a bug when coding
up a network from scratch is so high that you'll want to go into a special
early debugging mode before waiting on high iteration counts. The name of the
game here is to reduce the scope of the problem over and over again until you
have a network that trains in less than 2000 iterations. Fortunately, there
are always 2 good dimensions to reduce complexity.

1) Reduce the size of the training set to 10 instances. Working neural nets
can usually overfit to 10 instances within just a few hundred iterations. Many
coding bugs will prevent this from happening. If you're network is not able to
overfit to 10 instances of the training set, make sure your data and labels
are hooked up correctly. Try reducing the batch size to 1 to check for batch
computation errors. Add print statements throughout the code to make sure
things look like you expect. Usually, you'll be able to find these bugs
through sheer brute force. Once you can train on 10 instances, try training on
100. If this works okay, but not great, you're ready for the next step.

2) Solve the simplest version of the problem that you're interested in. If
you're translating sentences, try to build a language model for the target
language first. Once that works, try to predict the first word of the
translation given only the first 3 words of the source. If you're trying to
detect objects in images, try classifying the number of objects in each image
before training a regression network. There is a trade-off between getting 
a good sub-problem you're sure the network can solve, and spending the
least amount of time plumbing the code to hook up the appropriate data.
Creativity will help here.

The trick to scaling up a neural net for a new idea is to slowly relax the
simplifications made in the above two steps. This is a form of coordinate
ascent, and it works great. First, you show that the neural net can at least
memorize a few examples. Then you show that it's able to really generalize to
the validation set on a dumbed down version of the problem. You slowly up the
difficulty while making steady progress. It's not as fun as hotshotting it
the first time Karpathy style, but at least it works. At some point, you'll
find the problem is difficult enough that it can no longer be learned in 2000
iterations. That's great! But it should rarely take more than 10 times the
iterations of the previous complexity level of the problem. If you're finding
that to be the case, try to search for an intermediate level of complexity.

Tuning hyperparameters

Now that your networks is learning things, you're probably in pretty good
shape. But you may find that your network is just not capable of solving the
most difficult versions of your problem. Hyperparameter tuning will be key
here. Some people who just download a CNN package and ran it on their dataset
will tell you hyperparameter tuning didn't make a difference. Realize that
they're solving an existing problem with an existing architecture. If you're
solving a new problem that demands a new architecture, hyperparameter tuning
to get within the ballpark of a good setting is a must. You're best bet is
to read a hyperparameter tutorial for your specific problem, but I'll list
a few basic ideas here for completeness.

Conclusion

Debugging neural nets can be more laborious than traditional programs because
almost all errors get projected onto the single dimension of overall network
performance. Nonetheless, binary search is still your friend. By alternately
1) changing the difficulty of your problem, and 2) using a small number of
training examples, you can quickly work through the initial bugs.
Hyperparameter tuning and long periods of diligent waiting will get you the
rest of the way.