The neurons in the eyes pre-process a huge amount of information converting data from about 126M rods and cones to 1M ganglion cells - a pretty amazing amount of data compression.
From my limited understanding, CNNs seem to approximate this functionality in image processing tasks, where the convolution layers are akin to the retina extracting info (lines, shapes, etc) and compression (kernel striding and pooling), while the later fully-connected neural network works for categorization or whatnot.
That probably doesn't answer the question of how a bee's eyes work, though.
Ref: https://www.amazon.com/Visual-Thinking-Kaufmann-Interactive-...