Neural systems as nonlinear filters

Wolfgang Maass, Eduardo D. Sontag

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


Experimental data show that biological synapses behave quite differently from the symbolic synapses in all common artificial neural network models. Biological synapses are dynamic; their "weight" changes on a short timescale by several hundred percent in dependence of the past input to the synapse. In this article we address the question how this inherent synaptic dynamics (which should not be confused with long term learning) affects the computational power of a neural network. In particular, we analyze computations on temporal and spatiotemporal patterns, and we give a complete mathematical characterization of all filters that can be approximated by feedforward neural networks with dynamic synapses. It turns out that even with just a single hidden layer, such networks can approximate a very rich class of nonlinear filters: all filters that can be characterized by Volterra series. This result is robust with regard to various changes in the model for synaptic dynamics. Our characterization result provides for all nonlinear filters that are approximable by Volterra series a new complexity hierarchy related to the cost of implementing such filters in neural systems.

Original languageEnglish (US)
Pages (from-to)1743-1772
Number of pages30
JournalNeural computation
Issue number8
StatePublished - Aug 2000

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience


Dive into the research topics of 'Neural systems as nonlinear filters'. Together they form a unique fingerprint.

Cite this