# The Wire-Length Complexity of Neural Networks

### Abstract:

The ability of our nervous system to rapidly process and react on the huge
amount of sensory input data is grounded on its massively parallel
architecture. Arguably, physical cost for communication, that is to say the
space needed for wires, is the most severe bottleneck in biological as well
as in artificial architectures of this type. In this thesis the complexity of
wiring in biological and artificial neural networks, the implications of
wiring constraints to models for brain circuits, and the implementation of
wire-efficient circuit designs in hardware are studied. We present a simple
mathematical framework that allows us to study the wiring complexity of
neural circuits in a formal and general manner. In this model, the complexity
of a circuit is measured by the total length of wires needed to implement the
circuit, a complexity measure that is one of the most salient ones if
real-world constraints of implementations in hardware or ``wetware'' are
considered.Furthermore, we study the layout of general computational
structures like tree computations. We give tight upper and lower bounds on
the wire length of constrained tree layouts and show efficient layout
strategies for prefix computations.

**Reference:** R. A. Legenstein.
*The Wire-Length Complexity of Neural Networks*.
PhD thesis, Graz University of Technology, 2002.