Does the Brain Infer Invariance Transformations from Graph Symmetries?

The invariance of natural objects under perceptual changes is possibly encoded in the brain by symmetries in the graph of synaptic connections. The graph can be established via unsupervised learning in a biologically plausible process across different perceptual modalities. This hypothetical encoding scheme is supported by the correlation structure of naturalistic audio and image data and it predicts a neural connectivity architecture which is consistent with many empirical observations about primary sensory cortex.