Do neural networks capture relationships between features?

Say we have a dataset that has several continuous features, 2 time features, and binary classes. I want to be clear, this isn't a time series dataset, but time snapshots of when each observation occurred is recorded. The dataset looks like this:

class    t1    t2    x1      x2      x3      x4      ...
0        735   311   0.345   0.123   -0.32   132
1        93    101   0.89    1.34    9.345   834
...      ...   ...   ...     ...     ...     ...     ...


with t1,t2 as time features and x1,...xn as the continuous features.

Uncaptured explicitly in the dataset, is the difference between times t1 and t2 (t1-t2). This metric is important because if the absolute difference t1-t2 is less than 20, the class will be 1 more than 90% of the time. In other words, the constructed feature t1-t2 is a very good indicator of an observations class.

Will a neural network classifier trained on the original, unchanged dataset above, capture the relationship between t1 and t2 to increase model accuracy?

More broadly speaking, do neural networks capture relationships between features?

I appreciate that in this hypothetical case, if I knew apriori about the time difference indicator, I would engineer a new feature that would be the absolute difference in time, and train the network on a dataset with this new feature. But for the sake of argument, say I do not know this in advance.

• Yes, neural nets finds the features that help to discriminate the classes. This is one of the main selling points of the approach: you can have a dataset with difficult to come up with all necessary heuristics/rules to carry out the classification task. A good example where neural nets have shown great success is image, video and time series data. Those are the areas where before researchers created features manually (sort of) or devised sophisticated techniques to guide discovery of those rules. The downside is that the neural net will not report a list of human readable rules. – Vladislavs Dovgalecs Jan 19 '18 at 17:28