Here's a project idea.
Train two neural networks on the same data, but with different initial random weights. They will come out differently, but probably equally good at whatever classification task they are learning to do.
Come up with a way to determine that they were trained on the same data.
I expect that this finding will shed some light on how this might eventually work in brains. Neurally, your belief that 'a' is th first letter of 'apple' probably looks a lot different from mine.
I'm not a neural net scientist, so I'll probably never run this study. If you do, let me know.