Simple models for reading neuronal population codes.

Abstract

In many neural systems, sensory information is distributed throughout a population of neurons. We study simple neural network models for extracting this information. The inputs to the networks are the stochastic responses of a population of sensory neurons tuned to directional stimuli. The performance of each network model in psychophysical tasks is compared with that of the optimal maximum likelihood procedure. As a model of direction estimation in two dimensions, we consider a linear network that computes a population vector. Its performance depends on the width of the population tuning curves and is maximal for width, which increases with the level of background activity. Although for narrowly tuned neurons the performance of the population vector is significantly inferior to that of maximum likelihood estimation, the difference between the two is small when the tuning is broad. performance with the ML procedures. For direction estimation we focus on a network that computes a population vector by summing the preferred directions of the neurons weighted by their response magnitudes. Some experimental evidence for this scheme has been found in the generation of saccadic eye movements in primates (7). It has also been suggested as a code for the direction of arm movements (8) and as a model of visual orientation estimation (9-11).Here we study the performance of the population vector relative to the optimal ML estimation. An important outcome of our analysis of direction discrimination is that threshold linear models require adaptation to perform well. We calculate theoretical generalization curves for the amount of transfer of learning from a trained stimulus to novel stimuli. Testing these predictions by psychophysical measurements could shed light on the neuronal mechanisms involved in perception and perceptual learning (12-14). ML PROCEDURESPopulation of Direction Selective Neurons. We consider a population of neurons coding for direction in two dimensions, parametrized by 6 from 0 to 2Xr. For example, these could be simple cells in visual cortex coding the direction of motion of a bar stimulus. We characterize the response ofthe ith neuron by a single nonnegative integer ri, the total number of spikes generated by the neuron in a fixed time interval following the onset of the stimulus. Our starting point is the assumption that the response of a neuron to a sensory stimulus is stochastic-namely, that repeated presentations of the same stimulus 6 induce responses that vary in a random fashion. The response of a population of N neurons is described by a conditional probability distribution 9P(rJ6), where the vector notation r is used for the responses r1, . .. , rN.We model the responses {r,} of the population as independent Poisson random variables. The mean of the spike count of the ith neuron is denoted by (ri) = ff(6), where ( ... ) denotes an average with respect to 5P(rl 0). The variance of a Poisson process equals its mean-i.e., ((6r,)2) = f1(6)-where Sri = ri -(ri). A similar linear relationshi...

Population Response Profiles in Early Visual Cortex Are Biased in Favor of More Valuable Stimuli

“…5: Deneve et al 1999;Green and Swets 1966;Jazayeri and Movshon 2006;Ma et al 2006;Navalpakkam and Itti 2007;Pouget et al 2003;Seung and Sompolinsky 1993). In the present experiment, in which subjects had to discriminate between orientations sepa-FIG.…”

Insights from a Simple Expression for Linear Fisher Information in a Recurrently Connected Population of Spiking Neurons

“…In many population codes, the tuning curve of the neurons, that is, the average response as a function of a real-valued stimulus (denoted s), follows gaussian functions of s. Several studies have investigated how to optimize the parameters of these tuning curves, such as the height and width, when s is a scalar variable (Seung & Sompolinsky, 1993) as well as when s is a multidimensional vector (Zhang & Sejnowski, 1999). These studies have argued that for scalar s, the brain should use high-amplitude, narrow tuning curves to optimize information transmission and that learning should seek to reduce the width of the tuning curve as a way to improve behavioral performance (Somers, Nelson, & Sur, 1995;Spitzer, Desimone, & Moran, 1988;Murray & Wojciulik, 2004;Schoups, Vogels, Qian, & Orban, 2001;Teich & Qian, 2003).…”

Visual perception as retrospective Bayesian decoding from high- to low-level features

“…The assumption is also used in signal detection theory's definition of d′ (2) and thus the use of Fisher information to calculate d′ (3,4). Models based on the idea of relating tuning-curve slopes to discrimination (6,9,10) are no exception: after the absolute distributions are determined by tuning curves and a noise model, they are compared to calculate ordinal discriminability.…”

“…Typically, people choose model parameters to simulate observed ordinal discriminability without checking the relationship between absolute and relative/ordinal judgments (2)(3)(4)(5)(6). In particular, the assumption predicts that absolute-judgment distributions fully determine the corresponding relative-judgment distribution, yet no study measured distributions of both absolute and relative judgments to provide a strong test of the assumption.…”

“…Researchers have also studied decoding by using models to relate neuronal responses to perceptual estimation. Most models posit, explicitly or implicitly, that decoding follows the same low-to high-level hierarchy, often in the form of what we call the absolute-to-relative assumption (2)(3)(4)(5)(6). For example, these models may decode V1 responses to a line into a perceived orientation of, say 51.2°(or a distribution around it).…”