# Emergence of optimal decoding of population codes through STDP

**S. Habenschuss, H. Puhr, and W. Maass**

### Abstract:

The brain faces the problem to infer reliable hidden causes from large
populations of noisy neurons, for example the direction of a moving object
from spikes in area MT. It is known that a theoretically optimal likelihood
decoding could be carried out by simple linear readout neurons if weights of
synaptic connections would be set to certain values that depend on the tuning
functions of sensory neurons. We show here that such theoretically optimal
readout weights emerge autonomously through STDP in conjunction with lateral
inhibition between readout neurons. In particular, we identify a class of
optimal STDP learning rules with homeostatic plasticity, for which the
autonomous emergence of optimal readouts can be explained on the basis of a
rigorous learning theory. This theory shows that the considered network motif
approximates Expectation Maximization for creating internal generative models
for hidden causes of high-dimensional spike inputs. Notably, we find that
this optimal functionality can be well approximated by a variety of STDP
rules beyond those predicted by theory. Furthermore we show that this
learning process is very stable, and automatically adjusts weights to changes
in the number of readout neurons, in the tuning functions of sensory neurons,
and in the statistics of external stimuli.

**Reference:** S. Habenschuss, H. Puhr, and W. Maass.
Emergence of optimal decoding of population codes through STDP.
*Neural Computation*, 25(6):1371-1407, 2013.