  The primate brain contains a hierarchy of visual areas, dubbed the ventral
stream, which rapidly computes object representations that are both specific
for object identity and relatively robust against identity-preserving
transformations like depth-rotations. Current computational models of object
recognition, including recent deep learning networks, generate these properties
through a hierarchy of alternating selectivity-increasing filtering and
tolerance-increasing pooling operations, similar to simple-complex cells
operations. While simulations of these models recapitulate the ventral stream's
progression from early view-specific to late view-tolerant representations,
they fail to generate the most salient property of the intermediate
representation for faces found in the brain: mirror-symmetric tuning of the
neural population to head orientation. Here we prove that a class of
hierarchical architectures and a broad set of biologically plausible learning
rules can provide approximate invariance at the top level of the network. While
most of the learning rules do not yield mirror-symmetry in the mid-level
representations, we characterize a specific biologically-plausible Hebb-type
learning rule that is guaranteed to generate mirror-symmetric tuning to faces
tuning at intermediate levels of the architecture.
