If deep-learning learns features, aren't we saying it can learn association rules?
Finding valuable association rules is defined base on their support and confidence. ANN is not proper for these kinds of specifications. 
Hence, if we use ANN for learning association rules, we can't guarantee the specified support and confidence are satisfied.

Anyhow, there are other machine learning methods to learn association rules such as decision tree. Although, that methods not such that proper to find rules with specified support and confidence. You can know more about this in this article.