Convolutional neural networks are very popular these days in computer vision. One of the things they do quite well is recognize objects with translation invariance. The way they do this is by "tying together" the strengths of certain synapses, so that they all change in the same way during learning. This is apparently not biologically plausible.
My question is this: what is known about how biological visual systems achieve translation invariance. For example, how is it that if we learn to recognize a new object with our left eye, we are automatically also able to recognize it with our right eye. What is the neuro-biological basis for this invariance? My field is mathematics/machine learning, not biology, so I would appreciate responses that are not overly technical (although I understand that might not be possible).