One problem with understanding ANNs is that the weight matrix carries a lot of spurious interactions. Running perturbation analysis you can see that many of the interactions do not contribute to the information processing of the circuit. This is the same for Gene Regulatory Networks. I wrote a paper published in Nature&#x27;s &quot;Systems Biology&quot; entitled Survival of the Sparsest Gene Networks are Parsimonious. It&#x27;s been cited ~130 times. There I represent an algorithm to evolve the connectivity of the network. What you find if that a network will tend to remove spurious interactions if the system is allowed to evolve. Because there will be very few network topologies that are both sparsely connected and functionally equivalent (think of how many ways you could create a minimally complex 8-bit added) there is likely only a small handful of non-isomorphic network topologies for any given function. With these sparse networks we should get a better grasp on the functional circuits that drive them. When the networks appear fully connected, at least in each layer, that circuitt does not reveal itself.