  Common to all different kinds of recurrent neural networks (RNNs) is the
intention to model relations between data points through time. When there is no
immediate relationship between subsequent data points (like when the data
points are generated at random, e.g.), we show that RNNs are still able to
remember a few data points back into the sequence by memorizing them by heart
using standard backpropagation. However, we also show that for classical RNNs,
LSTM and GRU networks the distance of data points between recurrent calls that
can be reproduced this way is highly limited (compared to even a loose
connection between data points) and subject to various constraints imposed by
the type and size of the RNN in question. This implies the existence of a hard
limit (way below the information-theoretic one) for the distance between
related data points within which RNNs are still able to recognize said
relation.
