  This work proposes a Neural Network model that can control its depth using an
iterate-to-fixed-point operator. The architecture starts with a standard
layered Network but with added connections from current later to earlier
layers, along with a gate to make them inactive under most circumstances. These
``temporal wormhole'' connections create a shortcut that allows the Neural
Network to use the information available at deeper layers and re-do earlier
computations with modulated inputs. End-to-end training is accomplished by
using appropriate calculations for a numeric iterate-to-fixed-point operator.
In a typical case, where the ``wormhole'' connections are inactive, this is
inexpensive; but when they are active, the network takes a longer time to
settle down, and the gradient calculation is also more laborious, with an
effect similar to making the network deeper. In contrast to the existing
skip-connection concept, this proposed technique enables information to flow up
and down in the network. Furthermore, the flow of information follows a fashion
that seems analogous to the afferent and efferent flow of information through
layers of processing in the brain. We evaluate models that use this novel
mechanism on different long-term dependency tasks. The results are competitive
with other studies, showing that the proposed model contributes significantly
to overcoming traditional deep learning models' vanishing gradient descent
problem. At the same time, the training time is significantly reduced, as the
``easy'' input cases are processed more quickly than ``difficult'' ones.
