 
Summary: LINEARLY DECODABLE FUNCTIONS FROM NEURAL POPULATION
CODES
M. B. WESTOVER, C. ELIASMITH, C.H. ANDERSON
ABSTRACT. The population vector is a linear decoder for an ensemble of neurons,
whose response properties are nonlinear functions of the input vector. However,
previous analyses of this decoder seem to have missed the obsevation that the
population vector can also be used to estimate functions of the input vector. We
explore how to use singular value decomposition to delineate the class of functions
which are linearly decodable from a given population of noisy neural encoders.
1. INTRODUCTION
Many sensory systems utilize a large number of neurons to make measurements
on inherently low dimensional systems. Examples include the 1000 neurons in
the cricket cercal system that measure horizontal wind velocity [4]; and the much
larger hair cell population in the mamallian otolith that senses linear acceleration
of the head, a three dimensional vector [1]. Although the responses of the indi
vidual neurons are highly nonlinear and heterogeneous, a linear weighted sum
of these nonlinear measures often provides an exceptionally precise linear esti
mate of the underlying physical input. Linear or "population vector" decoding is
typically used to explore how neural systems might implement a communication
channel; that is, how downstream populations might reconstruct the value of an
