Download Topology - UCSB Physics

The topology of the central nervous system has been, and remains today a topic of
considerable study. It is known that for humans, the central nervous system starts in the
embryo as a plate, eventually deforming into a tube, one end of which thickens to become
the brain (the remainder being the spinal chord). The cerebral cortex, which houses much
of the machinery of intelligence, is a sheet with six layers, and numerous small columns
running perpendicular to the layers. Neurons in these columns often seem to fire together
in distinct patterns (Tsodyks et al 1999). Certain regions of the cortex have the same,
identifiable function in all humans (e.g. the area “V1” does very basic visual processing,
and is located in the same place in all humans). Thus structure in the cortex, or in the
wiring to the cortex seems to be at least partially responsible for function.
Visible and large-scale topology in the brain can be misleading, as the network
topology of the wiring is more important than physical location. The exact wiring in the
cortex is not known, because there are far too many connections (thousands per neuron)
and the connections themselves are small, but may follow a convoluted path over long
distance. Fortunately, it may be unnecessary to follow the exact plan of the cortex: birds
lack a cortex, yet have displayed some intelligent behavior, such as tool-making (Weir et
al 2002). Instead, some general design principles, may be more important. The human
brain uses hierarchy (e.g. V1 sends its output to a region called V2) and feedback (V2
sends predictions back down to V1) in sensory systems, and even planning (Dehaene et al
1997). Any theoretical approach to understanding cognition must incorporate those basic
principles, and any realistic topology should be consistent with them. Thus it is
necessary to move beyond simple feed-forward networks with a few layers.
The necessity of moving to more complex network topologies also places
restrictions on neuron models. Static neurons that are either activated for all time, or
never at all, will not work with feedback. Similarly, learning cannot be implemented via
back-propagation to update synapse weights, as there is no logical starting or stopping
point. Instead, more biologically plausible techniques must be used, like Hebbian
learning, where neurons that fire together with appropriate timing will have their
connections strengthened. Thus network topology and neuron models are connected and
must be implemented in a complimentary manner.