Hyper-identity

An identity function is a function whose output is the same as input. This function works similar to a mirror, the only difference is that a mirror flips front to back (not left to right, as many expect). When we look into a mirror we think that we see ourselves, but actually we see our flipped versions, others see us differently and you can notice the difference by using a smart-phone in selfie mode and switching mirroring on and off.

If we wanted to create an artificial neural network (ANN) implementing an identity function of another ANN, what would we wanted to get? The first idea that comes to mind is that we would like to supply an ANN structure as input and get the same structure as output. And now look into a mirror and ask yourself if your appearance is what you are. Of course, you are much more than that. So, the second idea that comes to mind is that we would like to supply an ANN structure as input and get a different ANN doing the same things as the original ANN.

It’s trivial to create an identity ANN that just copies input structures to output structures, just shortwire input neurons to output neurons for that. But we are interested in creating a hyper-identity ANN, how could we fulfill this goal?

Let’s construct an ANN with randomly initialized synapses and start training it. Eventually it will start outputting hyper-identities with some level of error that we can tolerate. Note that for really useful tasks the level of error will never reach zero, because number of things, that an inputted ANN can do, is virtually infinite. In all those generated hyper-identities some may actually be improvements of their original ANNs, pity that percentage of these improved ANNs is so low… Wait! What if our hyper-identity ANN is fed with itself, can it output a better version of itself and increase the percentage? Can that better version be fed with itself as well?..

…This is how we may witness AI singularity, leading to emergence of AI. Of true AI - self-aware, identifying itself in a mirror, and capable to improve itself.