How does seeing a human as "neural activities which in turn are caused by sensory input and noise" contradict an idea of free will? The neural activity is obviously so complicated that it can make "sense" of the sensory input and the noise, and make intelligent decisions based on past experience, on it's own generatlizations of experience, on external ideas, etc. etc.

There are obviously some mechanisms for creating new information and action, based on past experience as well (thus also creating new unforeseen behavior). These mechanisms can clearly be implemented on the neural machine of the brain, since it's evident that it can even already be approximated in Google Deep Dream to create new unforeseen images based on previous inputs.

Whether the human can always verbally describe the decision tree (or whatever other decision mechanism is used), is another question. But even if it cannot describe, so what? The decision is done somewhere deep in the net, and the verbal processor does not have access to it. It's still the network making a decision...

So what makes you say that free will is an "illusion"? Our brains obviously soak up the information and then make future decisions based on that information (subject to effectiveness of learning, etc...).