Error-Based Analysis of Optimal Tuning Functions Explains Phenomena Observed in Sensory Neurons

Biological systems display impressive capabilities in effectively responding to environmental signals in real time. There is increasing evidence that organisms may indeed be employing near optimal Bayesian calculations in their decision-making. An intriguing question relates to the properties of optimal encoding methods, namely determining the properties of neural populations in sensory layers that optimize performance, subject to physiological constraints. Within an ecological theory of neural encoding/decoding, we show that optimal Bayesian performance requires neural adaptation which reflects environmental changes. Specifically, we predict that neuronal tuning functions possess an optimal width, which increases with prior uncertainty and environmental noise, and decreases with the decoding time window. Furthermore, even for static stimuli, we demonstrate that dynamic sensory tuning functions, acting at relatively short time scales, lead to improved performance. Interestingly, the narrowing of tuning functions as a function of time was recently observed in several biological systems. Such results set the stage for a functional theory which may explain the high reliability of sensory systems, and the utility of neuronal adaptation occurring at multiple time scales

Optimal Population Coding, Revisited

Cortical circuits perform the computations underlying rapid perceptual decisions within a few dozen milliseconds with each neuron emitting only a few spikes. Under these conditions, the theoretical analysis of neural population codes is challenging, as the most commonly used theoretical tool – Fisher information – can lead to erroneous conclusions about the optimality of different coding schemes. Here we revisit the effect of tuning function width and correlation structure on neural population codes based on ideal observer analysis in both a discrimination and reconstruction task. We show that the optimal tuning function width and the optimal correlation structure in both paradigms strongly depend on the available decoding time in a very similar way. In contrast, population codes optimized for Fisher information do not depend on decoding time and are severely suboptimal when only few spikes are available. In addition, we use the neurometric functions of the ideal observer in the classification task to investigate the differential coding properties of these Fisher-optimal codes for fine and coarse discrimination. We find that the discrimination error for these codes does not decrease to zero with increasing population size, even in simple coarse discrimination tasks. Our results suggest that quite different population codes may be optimal for rapid decoding in cortical computations than those inferred from the optimization of Fisher information

Allocation of Computational Resources in the Nervous System.

The nervous system integrates past information together with predictions about the future in order to produce rewarding actions for the organism. This dissertation focuses on the resources underlying these computations, and the task-dependent allocation of these resources. We present evidence that principles from optimal coding and optimal estimation account for overt and covert orienting phenomena, as observed from both behavioral experiments and neuronal recordings. First, we review behavioral measurements related to selective attention and discuss models that account for these data. We show that reallocation of resources emerges as a natural property of systems that encode their inputs efficiently under non-uniform constraints. We continue by discussing the attentional modulation of neuronal activity, and showthat: (1) Modulation of coding strategies does not require special mechanisms: it is possible to obtain dramatic modulation even when signals informing the system about fidelity requirements enter the system in a fashion indistinguishable from sensory signals. (2) Optimal coding under non-uniform fidelity requirements is sufficient to account for the firing rate modulation observed during selective attention experiments. (3) The response of a single neuron cannot bewell characterized by measurements of attentional modulation of only a single sensory stimulus. (4) The magnitude of the activity modulation depends on the capacity of the neural circuit. A later chapter discusses the neural mechanisms for resource allocation, and the relation between attentional mechanisms and receptive field formation. The remainder of the dissertation focuses on overt orienting phenomena and active perception. We present a theoretical analysis of the allocation of resources during state estimation of multiple targets with different uncertainties, together with eye-tracking experiments that confirm our predictions. We finish by discussing the implications of these results to our current understanding of orienting phenomena and the neural code