As a student of neuroscience, I have never heard of computational neural networks. I guess you mean artificial neural networks. I can just speak for myself.
Many theorists believe there is a link between ANN, DL and brains, but to most neuroscientists only believe what evidence tell them. There is not much proof showing ANN and deep learning are how brains work.
The connection between ANNs and brains are nearly non-exsitent. The fact is that ANNs and DL only looks like real neural network from a layman’s perspective. There’s nothing they are alike when you scrutinize the details. For example, the ‘cell’ in ANNs stores values. However, in real cells there are just electrical potentials and the information are full of noises. Besides, the connections in our brains are quite random, and full of recurrent loops in different levels, while in DL the network structures are feed-forward and fixed. In another words, it seems the more successful the ANNs, the less it resembles real neural networks. Even many vision scientists use probabilistic models for visual cortex, it is not explained how a global cost-function minimization, back propagation are achieved neurologically. For deep learning such as deep belief networks, the training is not on-line but off-line (batch training, 2 phase training), which is also very different from our brains.
On the other hand, neuroscientists have fairly clear idea of how grid cells and place cells in hippocampus work to encode spacial memory based on experiments, and the machenism is very different from ANNs. Other successful models for cerebellum are very different from ANNs, either. If ANNs and DL are generic models of brains, then the mechanisms should not be so different.