R Huerta

RA Jortner

Thomas Nowotny

BMC Neuroscience

Springer - Publisher Connector

Divergence alone cannot guarantee stable sparse activity patterns if connections are dense

Thomas Nowotny (4462033)

Sussex Research Online

BioMed CentralBMC Neuroscience
ssOpen AccePoster presentation
Divergence alone cannot guarantee stable sparse activity patterns 
if connections are dense
Thomas Nowotny
Address: Informatics Department, University of Sussex, Falmer, Brighton, BN1 9QJ, UK
Email: Thomas Nowotny - t.nowotny@sussex.ac.uk
Introduction
It is quite well known, and we have recently confirmed it
for the olfactory system in insects [1], that sparse activity
is necessary for efficient pattern recognition and memory
formation. In many brain centers, including the olfactory
system, strongly divergent connections with high-thresh-
old post-synaptic neurons are believed to generate these
sparse patterns. We have shown in a generic model that
this interpretation rests on the assumptions that the con-
nections are not only divergent but also sparse. However,
in locusts the connections from the antennal lobe to the
mushroom bodies have been found to be not sparse. To
the contrary, experimental observations seem to imply
connectivities with 50% of all-to-all connections [2]. Our
generic model elucidates how such dense connections
lead to instabilities with respect to noise and fluctuations
in the incoming signals. We then suggest a hypothesis
how the original coding idea can be rescued by appropri-
ate feed-forward gain control mechanisms.
Results
There are three minimal requirements for a successful
sparse coding strategy: (1) The response patterns should
be sparse for the whole range of expected input patterns,
(2) different input patterns should not elicit identical
responses (confusion), and (3) the baseline activity of
input neurons should not trigger any responses. To inves-
tigate these requirements we formalized the idea of a
divergent layered neuronal system with a set of minimal
assumptions. We then investigated for which combina-
tions of two crucial parameters, the density of connections
from Eighteenth Annual Computational Neuroscience Meeting: CNS*2009
Berlin, Germany. 18–23 July 2009
Published: 13 July 2009
BMC Neuroscience 2009, 10(Suppl 1):P188 doi:10.1186/1471-2202-10-S1-P188
<supplement> <title> <p>Eighteenth Annual Computational Neuroscience Meeting: CNS*2009</p> </title> <editor>Don H Johnson</editor> <note>Meeting abstracts – A single PDF containing all abstracts in this Supplement is available <a href="http://www.biomedcentral.com/content/files/pdf/1471-2202-10-S1-full.pdf">here</a>.</note> <url>http://www.biomedcentral.com/content/pdf/1471-2202-10-S1-info.pdf</url> </supplement>
This abstract is available from: http://www.biomedcentral.com/1471-2202/10/S1/P188
© 2009 Nowotny; licensee BioMed Central Ltd. 
Regions where our criteria 1–3 are fulfilledFigure 1
Regions where our criteria 1–3 are fulfilled. Dark blue: 
none are fulfilled, blue: (3) is true, light blue: (2) is true, cyan: 
(2) and (3) are true, yellow: (1) and (3) are true, orange: (1) 
and (2) are true, and red: all three are true. Note that for no 
gain control (A), the red region is located between pc = 0.1 
and pc = 0.3 and is very thin. It then moves to higher pc with 
increasing gain control (B), (C) and (D), where it disappears. 
The strings of white dots in each of the panels mark the locus 
of the minimum of the probability of confusion with respect 
to the threshold KC for each given value of pc Depending on 
the density of connections, a different degree of gain control 
is necessary to be able to fulfill all three criteria for a suitable 
sparse activity.Page 1 of 2
(page number not for citation purposes)
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pc and the firing threshold KC, these conditions can be ful-
filled. Without additional mechanisms of gain control all
three conditions cannot be fulfilled simultaneously for
dense connections (Figure 1A) while an appropriate gain
control mechanism allows it (Figure 1C).
Acknowledgements
TN acknowledges helpful discussions with Falk Hildebrand. This work was 
partially funded by the Biotechnology and Biological Sciences Research 
Council (grant number BB/F005113/1).
References
1. Huerta R, Nowotny T, Garcia-Sanchez M, Abarbanel HDI, Rabinovich
MI: Learning classification in the olfactory system of insects.
Neural Comput 2004, 16:1601-1640.
2. Jortner RA, Farivar SS, Laurent G: A simple connectivity scheme
for sparse coding in an olfactory system.  J Neurosci 2007,
27:1659-1669.Page 2 of 2
(page number not for citation purposes)


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Divergence alone cannot guarantee stable sparse activity patterns if connections are dense

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