papers on neural coding

• Previous message: Mark E. Nelson: "Postdocs: Comp. Neurosci. / Sensory Neuroethology"
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I would like to draw your attention on two recent papers exploring
the coding of multi-dimensional correlates with mixed continuous and
discrete features by populations of neurons in cortex.
In particular the model studied refers to the case of movement coding
in the motor cortex of behaving monkeys. Yet it is equally applicable
to other correlates.

"A theoretical model of neuronal population coding of stimuli
with both continuous and discrete dimensions"

Valeria Del Prete and Alessandro Treves,
SISSA, cognitive neuroscience sector, Trieste, Italy

Phys.Rev.E 64(2) 021912, (2001).
AVAILABLE AT: http://babbage.sissa.it/ps/cond-mat/0103286

                             ABSTRACT
In a recent study the initial rise of the mutual information between
the firing rates of N neurons and a set of p discrete stimuli has
been evaluated, under the assumption that neurons fire independently of
one another to each stimulus and that each conditional distribution of
firing rates is gaussian. Yet real stimuli or behavioural correlates are
high-dimensional, with both discrete and continuously varying features.
Moreover, the gaussian approximation implies negative firing rates,
which is biologically implausible. Here, we generalize the analysis to
the case where the stimulus or behavioural correlate has both a discrete
and a continuous dimension, like orientation and shape could be in a
visual stimulus, or type and direction in a motor action. The functional
relationship between the firing patterns and the continuous correlate is
expressed through the tuning curve of the neuron, using two different
parameters to modulate its width and its flatness. In the case of large
noise we evaluate the mutual information up to the quadratic approximation
as a function of population size. Then we consider a more realistic
distribution of firing rates, truncated at zero, and we prove that the
resulting correction, with respect to the gaussian firing rates, can be
expressed simply as a renormalization of the noise parameter. Finally, we
demonstrate the effect of averaging the distribution across the discrete
dimension, evaluating the mutual information only with respect to the
continuously varying correlate.

"Replica symmetric evaluation of the information transfer in a two-layer
network in presence of continuous+discrete stimuli"

Valeria Del Prete and Alessandro Treves,
SISSA, cognitive neuroscience sector, Trieste, Italy

Submitted to Phys.Rev.E
AVAILABLE AT: http://babbage.sissa.it/ps/cond-mat/0107587

                                   ABSTRACT

In a previous report we have evaluated analytically the mutual information
between the firing rates of N independent units and a set of multi
dimensional continuous+discrete stimuli, for a finite population size and
in the limit of large noise. Here, we extend the analysis to the case of
two interconnected populations, where input units activate output ones via
gaussian weights and a threshold linear transfer function. We evaluate the
information carried by a population of M output units, again about
continuous+discrete correlates. The mutual information is evaluated
solving saddle point equations under the assumption of replica symmetry,
a method which, by taking into account only the term linear in N of the input
information, is equivalent to assuming the noise to be large. Within this
limitation, we analyze the dependence of the information on the ratio M/N,
on the selectivity of the input units and on the level of the output
noise. We show analytically, and confirm numerically, that in the limit of a
linear transfer function and of a small ratio between output and input noise,
the output information approaches asymptotically the information carried in
input. Finally, we show that the information loss in output does not depend
much on the structure of the stimulus, whether purely continuous, purely
discrete or mixed, but only on the position of the threshold nonlinearity,
and on the ratio between input and output noise.

Valeria Del Prete
SISSA via Beirut 2-4 Trieste Italy
cognitive neuroscience sector
tel. +39 40 3787 531
e-mail delprete@sissa.it
http://www.sissa.it/~delprete/

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