  Networks are fundamental building blocks for representing data, and
computations. Remarkable progress in learning in structurally defined (shallow
or deep) networks has recently been achieved. Here we introduce evolutionary
exploratory search and learning method of topologically flexible networks under
the constraint of producing elementary computational steady-state input-output
operations.
  Our results include; (1) the identification of networks, over four orders of
magnitude, implementing computation of steady-state input-output functions,
such as a band-pass filter, a threshold function, and an inverse band-pass
function. Next, (2) the learned networks are technically controllable as only a
small number of driver nodes are required to move the system to a new state.
Furthermore, we find that the fraction of required driver nodes is constant
during evolutionary learning, suggesting a stable system design. (3), our
framework allows multiplexing of different computations using the same network.
For example, using a binary representation of the inputs, the network can
readily compute three different input-output functions. Finally, (4) the
proposed evolutionary learning demonstrates transfer learning. If the system
learns one function A, then learning B requires on average less number of steps
as compared to learning B from tabula rasa.
  We conclude that the constrained evolutionary learning produces large robust
controllable circuits, capable of multiplexing and transfer learning. Our study
suggests that network-based computations of steady-state functions,
representing either cellular modules of cell-to-cell communication networks or
internal molecular circuits communicating within a cell, could be a powerful
model for biologically inspired computing. This complements conceptualizations
such as attractor based models, or reservoir computing.
