I thought I would write up some general tips and tricks that I have learned by experimenting with neural networks. My focus is on tips that apply to any problem and any neural network architecture, and in fact, some of these tips apply more generally to any machine learning algorithm. So what I have learned over the years?
Before doing anything else, you need to split the dataset into training and testing. But how much data should go into each split? This depends on your number of samples and the number of classes. For example, MNIST has only 10 digits with little variation in each digit, so the standard split is around 80% train and 20% test. ImageNet has over a million samples of 1000 diverse classes, so they use around 50% train and 50% test. So if you have an easy problem and/or a small dataset, I would suggest 80% train and 20% test. If you have a very tough problem and/or a large dataset, I would suggest 50% train and 50% test.
The test data should now be put in a lock box and only used on your final model.
Next you also should set aside some of the training data for validation which is used to determine generalization results when tuning hyperparameters. I would suggest around 20% of the training data to be used as a validation.
Finally, I do a little bit of cheating and I data snoop. I usually take a very tiny amount of the data, maybe 1-5% and play around with it. I will inspect the data to make sure that it looks good, and use the small number of samples to debug my initial code and very roughly tune the hyperparameters. This saves you the headache of doing a long training session only to find out that you had a bug in your code or grossly misunderstood where to start your hyperparameter search.
As a general rule, the data should be standardized by preprocessing. I’ll discuss some specific standardizations below, but a general issue is whether to standardize by the whole dataset, per sample, or per feature. I tend to default to per sample, but I don’t have a good scientific reason why that is the best. If you standardize by the whole dataset or per feature, you need to make sure you only use the training data to set the scales. If you standardize per feature, make sure that all of your features have significant variation before doing so (see MNIST for an example where per feature standardization can lead to weird results since many features have a standard deviation of zero).
All numerical data should be mean centered, no questions asked. If you classes can be robustly classified just by the mean difference, then you don’t need a neural network. You have a very simple problem and should just use a simple threshold discriminator.
I highly recommend scaling the data so that it is all order 1. This can speed up training because most initialization schemes of weights assume that the data is mean centered and has values around the size of 1. But there are two possible ways to scale your data: standard deviation or by the range. If you data looks normally distributed, then standard deviation makes sense. Otherwise I just divide by the maximum of the absolute value.
In theory, it can also be helpful to remove correlations between features by using PCA or ZCA whitening. However, in practice you may run into numerical stability issues since you will need to invert a matrix. So this is worth considering, but takes some more careful application.
More training data is always better, but obtaining that data can be expensive. So I always try hard to find a way to do data augmentation. However, the correct data augmentation is usually problem specific, so I won’t go into details here.
The no free lunch theorem of machine learning states that there is no general learning algorithm that will solve all problems. However, Geoff Hinton has pointed out that early stopping is as close to a free lunch as we can get. Early stopping is the easiest way for any machine learning algorithm to avoid overfitting, and you can read more about the technical justifications for it at Distill’s momentum article.
SGD vs Adam
In practice, all optimizers for neural networks involve some form of stochastic gradient descent (SGD). The only questions is whether you need to manually tune the learning rate and other parameters, or whether you use an adaptive version of SGD that automatically adjusts the learning rates. I think the best adaptive method is Adam (and Nadam when possible, see later subsection on momentum). So for me the choice is simple: either plain SGD or Adam/Nadam. For a more complete comparison of SGD variants, I highly recommend this blog post.
If you are using Adam, you will rarely need to tune the learning rate. But for SGD, the learning rate is by far the most important parameter to tune. A nice tip from Yoshua Bengio is this: the optimal learning rate is often an order of magnitude lower than the smallest learning rate that blows up the loss. So this means, start with a high learning rate and work your way down a half order of magnitude at a time (for example: 1, 0.3, 0.1, …). Then start your fine grained learning rate search about an order of magnitude below the last time the loss blew up.
Another useful tweak on the learning rate is to have it decay over the course of training. I find that this slightly improves the final performance, but more importantly leads to consistent training results. There are a variety of ways to implement the decay, but I’m not sure they make that much of a difference. My standard implementation is
where is the number of minibatches seen so far during training. I then set decay so that the final learning rate at the end of all the epochs is 1/10th the starting learning rate.
Momentum is very useful for neural networks, but in practice I spend minimal time tuning the momentum rate because I have a few default settings that I strongly recommend.
First, I really only consider three possible momentum values: 0.5, 0.9, and 0.99. Since the maximum effect of momentum is , my default values are roughly spaced by an order of magnitude. I always start with 0.9 and go from there.
Also, I always choose Nesterov momentum whenever possible. Most packages, like Keras, have Nesterov as an option for SGD, and Keras also has Nadam, which is Adam with Nesterov momentum. For more details on Nesterov, see here. The short explanation is that it leads to the same maximum effect of , but it does so in a more gradual manner. In practice, this means that while standard momentum gets very unstable above 0.9, Nesterov momentum can be safely set to 0.99.
Another useful tip is to set the momentum to a smaller value (say half your standard value) for the final few epochs (maybe the last 5-10% of epochs). The intuition for why this is helpful is that hopefully by the end of training, the neural network is close to good weights, but it might be rocking back and forth around the optimal weights. Since the neural network weight space is highly non-convex, by tuning down the momentum, you force the neural network to settle down into these non-convex “valleys” that may contain the best weights.
The final tip, originally suggested here, is to exponentially ramp up and down the momentum anytime you want to change the momentum rate during training. This gives the weights updates time to adjust to the new momentum rates. I personally have found this gives a very slight improvement in performance, but more importantly it leads to consistent training results.
Summary of my momentum tips:
- Peak momentum values of: 0.5, 0.9, or 0.99
- Always choose Nesterov momentum if possible
- Start momentum initially at half the desired peak value and exponentially ramp up
- Towards the end of training, exponentially ramp down momentum to half the desired peak value.
- Train for 5-10% of epochs at the desired smaller momentum.
All weights should be initialized to an orthogonal matrix. This is extremely important for recurrent neural networks (as explained here), but I have also found it to be useful for all neural networks.
The standard is that all hidden layers are ReLUs unless you need the hidden layers to be a valid probability, in which case you should use a sigmoid.
Choosing the right loss function is very problem dependent, so I will leave that for another day. However, whatever loss function you do choose, make sure the output layer activation function is complimentary to that loss, see Michael Nielsen’s book for details on why sigmoid outputs and crossentropy losses are complimentary.
Weight regularization is almost always a requirement to prevent overfitting and to get good generalization. The two main choices are L1 or L2 regularization. L1 will ensure that small weights are set to zero, and hence will lead to a sparser set of weights. L2 prevents weights from becoming too large, but does not sparsify the weights. Personally, rather than choosing between the two, I tend to default to both. I set L1 to be very small so that I at least get slightly sparser weights, but then I mainly focus on tuning L2 to control overfitting.
Dropout and batch normalization are not regularizers in the traditional sense, but in practice they help reduce overfitting by controlling the activation outputs. Additionally, it is extremely difficult to train very deep neural networks without using either dropout or batchnorm. Dropout was the standard for several years, but now it is usually replaced by batchnorm.
Neural networks have a lot of interdependent hyperparameters to tune, so picking which ones to tune first is kind of a chicken and the egg problem. Personally, I start off with an adaptive optimizer (like Adam or Nadam) and then tune the architecture. Next I will roughly tune the regularization. Once that leads to acceptable results, I will switch the optimizer to SGD and only focus on tuning the learning rate. If SGD seems promising, I will then tune other parameters like decay and momentum. Hopefully by this point, you are achieving pretty good results. I will then use this neural network as the starting point for a systematic hyperparameter search to truly find the best results.
Don’t take my word for anything, try it out yourself! I strongly recommend experimenting with every option you can find in Keras and see for yourself what actually will work. I also suggest getting opinions from as many people as possible (see Yoshua Bengio’s tips). I think that about 90% of the advice will overlap, but everyone has their own bias. So hopefully be reading enough independent sources, you can average out all our mistakes. Good luck!