In Chapter 15, Goodfellow et al. consider representation learning, focussing on unsupervised pre-training. Specifically, they discuss when and why unsupervised pre-training may help the subsequent supervised task. The two discussed interpretations are:
Regarding the first interpretation, it was originally assumed to help optimization by avoiding poor local minima. However, Goodfellow et al. emphasize that it is known by now that local minima aren't a significant problem in deep learning. That may also be one of the reasons why unsupervised pre-training isn't as popular anymore (especially compared to supervised pre-training or various forms of transfer learning). However, unsupervised pre-training may make optimization more deterministic. Goodfellow et al. specifically argue that unsupervised pre-training causes deep learning to consistently reach the same "solution". This suggests that unsupervised pre-training reduces the variance of the learned estimator. It is hard to say when unsupervised pre-training is beneficial when using this interpretation.
The second interpretation gives more clues about when unsupervised pre-training may be beneficial. For example, if the initial representation is poor. Goodfellow et al. name the example of word representations and also argue that there is less benefit for vision tasks as discrete images already represent an appropriate representation of the data. When thinking of unsupervised pre-training (or semi-supervised training) as identifying the underlying causes of the data, success may depend on the causal factors involved and the data distribution. For example, assumptions such as sparsity or independence may or may not be present regarding the causes. Furthermore, from a uniform data distribution, no useful representation can be learned. From a highly multi-modal distribution, unsupervised pre-training may already identify the different modes without knowing the semantics.
Overall, the chapter gives a good, high-level discussion of unsupervised pre-training and representation learning in general without going into algorithmic details. Two important takeaways are the two presented interpretations that can be used to reason about unsupervised pre-training.