The above model is what really helped me understand the implementation of convolutional neural networks, so based on that, I've got a tricky hypothesis that I want to find more about, since actually testing it would involve developing an entirely new training model if the concept hasn't already been tried elsewhere.
I've been building a machine learning project for image recognition and thought about how at certain stages we flatten the input after convoluting and max pooling, but it occurred to me that by flattening the data, we're fundamentally losing positional information. If you think about how real neurons process information based on clusters, it seems obvious that proximity of the biological neurons is of great significance rather than thinking of them as flat layers, by designing a neural network training model that takes neuron proximity into account in deciding the structure by which to form connections between neurons, so that positional information can be utilized and kept relevant, it seems that it would improve network effectiveness.
Edit, for clarification, I made an image representing the concept I'm asking about:
Basically: Pixels 1 and 4 are related to each other and that's very important information. Yes we can train our neural network to know those relationships, but that's 12 unique relationships in just a 3x3 pixel grid that our training process needs to successfully teach the network to value, whereas a model that takes proximity of neurons into consideration, like the real world brain would maintain the importance of those relationships since neurons connect more readily to others in proximity.
My question is: Does anyone know of white papers / experiments closely related to the concept I'm hypothesizing? Why would or would that not be a fundamentally better model?