Developing structural constraints on connectivity for biologically embedded neural networks
- 151 Downloads
In this article, we analyse under which conditions an abstract model of connectivity could actually be embedded geometrically in a mammalian brain. To this end, we adopt and extend a method from circuit design called Rent’s Rule to the highly branching structure of cortical connections. Adding on recent approaches, we introduce the concept of a limiting Rent characteristic that captures the geometrical constraints of a cortical substrate on connectivity. We derive this limit for the mammalian neocortex, finding that it is independent of the species qualitatively as well as quantitatively. In consequence, this method can be used as a universal descriptor for the geometrical restrictions of cortical connectivity. We investigate two widely used generic network models: uniform random and localized connectivity, and show how they are constrained by the limiting Rent characteristic. Finally, we discuss consequences of these restrictions on the development of cortex-size models.
KeywordsNeural networks Rent’s Rule Network connectivity Multi-point nets Network analysis
Unable to display preview. Download preview PDF.
- Beiu V, Madappuram B, Kelly P, McDaid L (2009) On two-layer brain-inspired hierarchical topologies—a Rent’s Rule approach. In: LNCS transactions on high-performance embedded architecture and compilers, vol 4(4), pp 1–22Google Scholar
- Braitenberg V, Schüz A (1998) cortex: statistics and geometry of neuronal connectivity. Springer, New YorkGoogle Scholar
- Changizi M (2007) Scaling the brain and its connections. In: Kaas J (ed) Evolution of nervous systems. Elsevier, OxfordGoogle Scholar
- Häusler S, Schuch K, Maass W (2009) Motif distribution, dynamical properties, and computational performance of two data-based cortical microcircuit templates. J Physiol 103: 73–87Google Scholar
- Partzsch J, Schüffny R (2009) On the routing complexity of neural network models—Rent’s Rule revisited. In: ESANN, pp 595–600Google Scholar
- Schemmel J, Brüderle D, Grübl A, Hock M, Meier K, Millner S (2010) A wafer-scale neuromorphic hardware system for large-scale neural modeling. In: ISCAS, pp 1947–1950Google Scholar
- Stroobandt D, Kurdahi F (1998) On the characterization of multi-point nets in electronic designs. In: 8th Great Lakes symposium on VLSI, pp 344–350Google Scholar
- Young M, Scannell J, Burns G (1995) In: Landes RG (ed) The analysis of cortical connectivity. Springer, New YorkGoogle Scholar