Most theoretical and empirical studies of cortical population codes make the assumption that underlying neuronal activities is a unique and unambiguous value of an encoded quantity. We propose an alternative hypothesis, that neural populations represent, and effectively compute probabilities. Under this hypothesis, population activities can contain additional information about such things as multiple values of or uncertainty about the quantity. We discuss methods for recovering this extra information, and show how this approach bears on psychophysical and neurophysiological studies. A natural extension of this probabilistic interpretation hypothesis casts interacting populations as a belief network, a structure which permits the analysis of information propagation from one population to another. This novel framework for population codes opens up new avenues for studying a diverse set of problems, including cue combination, decision-making, and visual attention. 1 Introductio...

When the nervous system is presented with multiple simultaneous inputs of some variable, such as wavelength or disparity, they can be combined to give rise to qualitatively new percepts that cannot be produced by any single input value. For example, there is no single wavelength that appears white. Many models of decoding neural population codes have problems handling multiple inputs, either attempting to extract a single value of the input parameter or, in some cases, registering the presence of multiple inputs without synthesizing them into something new. These examples raise a more general issue regarding the interpretation of population codes. We propose that population decoding involves not the extraction of specific values of the physical inputs, but rather a transformation from the input space to some abstract representational space that is not simply related to physical parameters. As a specific example, a four-layer network is presented that implements a transformation from wavelength to a high-level hue-saturation color space.

To be published in Behavioral and Brain Sciences (in press)

Neural activity and perception are both affected by sensory history. The work presented here explores the relationship between the physiological effects of adaptation and their perceptual consequences. Perception is modeled as arising from an encoder-decoder cascade, in which the encoder is defined by the probabilistic response of a population of neurons, and the decoder transforms this population activity into a perceptual estimate. Adaptation is assumed to produce changes in the encoder, and we examine the conditions under which the decoder behavior is consistent with observed perceptual effects in terms of both bias and discriminability. We show that for all decoders, discriminability is bounded from below by the inverse Fisher information. Estimation bias, on the other hand, can arise for a variety of different reasons and can range from zero to substantial. We specifically examine biases that arise when the decoder is fixed, “unaware ” of the changes in the encoding population (as opposed to “aware ” of the adaptation and changing accordingly). We simulate the effects of adaptation on two well-studied sensory attributes, motion direction and contrast, assuming a gain change description of encoder adaptation. Although we cannot uniquely constrain the source of decoder bias, we find for both motion and contrast that an “unaware ” decoder that maximizes the likelihood of the percept given by the preadaptation encoder leads to predictions that are consistent with behavioral data. This model implies that adaptation-induced biases arise as a result of temporary suboptimality of the decoder.

Tuning curves are commonly used by the neuroscience community to characterise the response properties of sensory neurons to external stimuli. However, the interpretation of tuning curves remains an issue of debate. Do neurons most accurately encode stimuli located at the peak of their tuning curve, where they elicit maximal ring rates, and thus the response is most distinctive against background noise? Or do neurons most accurately encode stimuli in the high slope regions of their tuning curves, where small changes in the stimulus a ect the greatest change in response? Previous measures of encoding accuracy have either explicitly or implicitly assumed one of these two intuitions. Butts and Goldman (2006) [10] recently applied a new measure of encoding accuracy, the SSI, to the tuning curves of single neurons and a population of four neurons. The SSI predicts how the location of high encoding accuracy will shift from slope to peak regions of the tuning curve, dependent upon the level of neuronal variability and task speci city. Butts and Goldman (2006) stated that the...SSI is computationally constrained to small populations of neurons ([10] p.0644) and did not apply their measure for populations with more than four neurons. By utilising Monte Carlo integration techniques, this project presents a novel

Abstract: A variety of experimental studies suggest that sensory systems are capable of performing estimation or decision tasks at near-optimal levels. In this chapter, I explore the use of optimal estimation in describing sensory computations in the brain. I define what is meant by optimality and provide three quite different methods of obtaining an optimal estimator, each based on different assumptions about the nature of the information that is available to constrain the problem. I then discuss how biological systems might go about computing (and learning to compute) optimal estimates. The brain is awash in sensory signals. How does it interpret these signals, so as to extract meaningful and consistent information about the environment? Many tasks require estimation of environmental parameters, and there is substantial evidence that the system is capable of representing and extracting very precise estimates of these parameters. This is particularly impressive when one considers the fact that the brain is built from a large number of low-energy unreliable components, whose responses are affected by many extraneous factors (e.g., temperature, hydration, blood glucose and oxygen levels). The problem of optimal estimation is well studied in the statistics and engineering communities, where a plethora of tools have been developed for designing, implementing, calibrating and testing such systems. In recent years, many of these tools have been used to provide benchmarks or models for biological perception. Specifically, the development of signal detection theory led to widespread use of statistical decision theory as a framework for assessing performance in perceptual experiments. More recently, optimal estimation theory (in particular, Bayesian estimation) has been used as a framework for describing human performance in perceptual tasks.

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General case: computing log likelihood We first describe the general case of computing the log likelihood of a sensory parameter! that is encoded by the activity of N neurons. Each neuron’s tuning function is described by!i(!,S) where S represents the stimulus strength (e.g. contrast for gratings or coherence for random–dot motion) and fires ni spikes in response to the stimulus. The average number of spikes elicited is determined by the neuron’s mean firing rate (from the tuning function) multiplied by the stimulation time, t, and is subject to Poisson noise (equation (1)). Neurons are assumed to be statistically independent (equation (2)). Equation (3) describes the form of the log likelihood: p(n |!) = i " i (!,S).t ( ) n i n! i e # " i (!,S)t

Perceptual learning was used as a tool for studying motion perception. The pattern of transfer of learning of luminance- (LM) and contrast-modulated (CM) motion is diagnostic of how their respective processing pathways are integrated. Twenty observers practiced fine direction discrimination with either additive (LM) or multiplicative (CM) mixtures of a dynamic noise carrier and a radially isotropic texture modulator. The temporal frequency was 10 Hz, speed was 10 deg/s, and duration was 400 ms, with feedback. Group 1 pre-tested CM for 2 blocks, trained LM for 16 blocks, and post-tested CM for 6 blocks during 6 sessions on separate days. In Group 2, the LM and CM roles were reversed. The dVimproved almost twofold in both groups. There seemed to be full transfer from CM to LM but no significant transfer from LM to CM. The pattern of postswitch improvement was asymmetric as wellVno further learning during the LM post-test versus rapid relearning during the CM post-test. These strong asymmetries suggest a dual-pathway architecture with Fourier channels sensitive only to LM signals and non-Fourier channels sensitive to both LM and CM. We hypothesize that the channels tuned for the same motion direction but different carriers are integrated using a MAX operation.

Neural coding: computational and biophysical perspectives