Probability density methods for smooth function approximation and learning in populations of tuned spiking neurons

Adaptive Tuning Curve Widths Improve Sample Efficient Learning

Natural brains perform miraculously well in learning new tasks from a small number of samples, whereas sample efficient learning is still a major open problem in the field of machine learning. Here, we raise the question, how the neural coding scheme affects sample efficiency, and make first progress on this question by proposing and analyzing a learning algorithm that uses a simple reinforce-type plasticity mechanism and does not require any gradients to learn low dimensional mappings. It harnesses three bio-plausible mechanisms, namely, population codes with bell shaped tuning curves, continous attractor mechanisms and probabilistic synapses, to achieve sample efficient learning. We show both theoretically and by simulations that population codes with broadly tuned neurons lead to high sample efficiency, whereas codes with sharply tuned neurons account for high final precision. Moreover, a dynamic adaptation of the tuning width during learning gives rise to both, high sample efficiency and high final precision. We prove a sample efficiency guarantee for our algorithm that lies within a logarithmic factor from the information theoretical optimum. Our simulations show that for low dimensional mappings, our learning algorithm achieves comparable sample efficiency to multi-layer perceptrons trained by gradient descent, although it does not use any gradients. Furthermore, it achieves competitive sample efficiency in low dimensional reinforcement learning tasks. From a machine learning perspective, these findings may inspire novel approaches to improve sample efficiency. From a neuroscience perspective, these findings suggest sample efficiency as a yet unstudied functional role of adaptive tuning curve width.

Evolution of neural computations: Mantis shrimp and human color decoding

Mantis shrimp and primates both possess good color vision, but the neural implementation in the two species is very different, a reflection of the largely unrelated evolutionary lineages of these creatures. Mantis shrimp have scanning compound eyes with 12 classes of photoreceptors, and have evolved a system to decode color information at the front-end of the sensory stream. Primates have image-focusing eyes with three classes of cones, and decode color further along the visual-processing hierarchy. Despite these differences, we report a fascinating parallel between the computational strategies at the color-decoding stage in the brains of stomatopods and primates. Both species appear to use narrowly tuned cells that support interval decoding color identification.

Risk-aware control

Human movement differs from robot control because of its flexibility in unknown environments, robustness to perturbation, and tolerance of unknown parameters and unpredictable variability. We propose a new theory, risk-aware control, in which movement is governed by estimates of risk based on uncertainty about the current state and knowledge of the cost of errors. We demonstrate the existence of a feedback control law that implements risk-aware control and show that this control law can be directly implemented by populations of spiking neurons. Simulated examples of risk-aware control for time-varying cost functions as well as learning of unknown dynamics in a stochastic risky environment are provided.

Computational properties of networks of synchronous groups of spiking neurons

We demonstrate a model in which synchronously firing ensembles of neurons are networked to produce computational results. Each ensemble is a group of biological integrate-and-fire spiking neurons, with probabilistic interconnections between groups. An analogy is drawn in which each individual processing unit of an artificial neural network corresponds to a neuronal group in a biological model. The activation value of a unit in the artificial neural network corresponds to the fraction of active neurons, synchronously firing, in a biological neuronal group. Weights of the artificial neural network correspond to the product of the interconnection density between groups, the group size of the presynaptic group, and the postsynaptic potential heights in the synchronous group model. All three of these parameters can modulate connection strengths between neuronal groups in the synchronous group models. We give an example of nonlinear classification (XOR) and a function approximation example in which the capability of the artificial neural network can be captured by a neural network model with biological integrate-and-fire neurons configured as a network of synchronously firing ensembles of such neurons. We point out that the general function approximation capability proven for feedforward artificial neural networks appears to be approximated by networks of neuronal groups that fire in synchrony, where the groups comprise integrate-and-fire neurons. We discuss the advantages of this type of model for biological systems, its possible learning mechanisms, and the associated timing relationships.

Decoding movement intent from human premotor cortex neurons for neural prosthetic applications

Primary motor cortex (M1), a key region for voluntary motor control, has been considered a first choice as the source of neural signals to control prosthetic devices for humans with paralysis. Less is known about the potential for other areas of frontal cortex as prosthesis signal sources. The frontal cortex is widely engaged in voluntary behavior. Single-neuron recordings in monkey frontal cortex beyond M1 have readily identified activity related to planning and initiating movement direction, remembering movement instructions over delays, or mixtures of these features. Human functional imaging and lesion studies also support this role. Intraoperative mapping during deep brain stimulator placement in humans provides a unique opportunity to evaluate potential prosthesis control signals derived from nonprimary areas and to expand our understanding of frontal lobe function and its role in movement disorders. This study shows that recordings from small groups of human prefrontal/premotor cortex neurons can provide information about movement planning, production, and decision-making sufficient to decode the planned direction of movement. Thus, additional frontal areas, beyond M1, may be valuable signal sources for human neuromotor prostheses.

Information processing in a neuron ensemble with the multiplicative correlation structure

The present study investigates the performance of population codes when the fluctuations in neural activity have mutual correlation with strength being proportional to the neuronal firing rate (multiplicative noise). The neural field is used to calculate the Fisher information, which is decomposed in two parts, one due to the tuning function and spatial correlation, and the other due to the multiplicative structure. Their different characteristics are studied. The paper also investigates three types of maximum likelihood method, namely, decoding by using faithful and unfaithful models and the Center of Mass strategy, and compares their performances in terms of decoding accuracy and computational complexity.

Neural population codes

In many regions of the brain, information is represented by patterns of activity occurring over populations of neurons. Understanding the encoding of information in neural population activity is important both for grasping the fundamental computations underlying brain function, and for interpreting signals that may be useful for the control of prosthetic devices. We concentrate on the representation of information in neurons with Poisson spike statistics, in which information is contained in the average spike firing rate. We analyze the properties of population codes in terms of the tuning functions that describe individual neuron behavior. The discussion centers on three computational questions: first, what information is encoded in a population; second, how does the brain compute using populations; and third, when is a population optimal? To answer these questions, we discuss several methods for decoding population activity in an experimental setting. We also discuss how computation can be performed within the brain in networks of interconnected populations. Finally, we examine questions of optimal design of population codes that may help to explain their particular form and the set of variables that are best represented. We show that for population codes based on neurons that have a Poisson distribution of spike probabilities, the behavior and computational properties of the code can be understood in terms of the tuning properties of individual cells.

Attention modulation of neural tuning through peak and base rate in correlated firing

The present study investigates the influence of attention modulation on neural tuning functions under a Gaussian correlation structure. Recent experiments have shown that attention modulates the tuning curve via its height and base rate. Inspired by this experimental finding, we previously showed the effective size of attention modulation (i.e. the critical length) on the neural population that enhances encoding accuracy. The previous result, however, was obtained under the assumption of uncorrelated firing, i.e. stimulus-conditional independence of neural responses. A question still remains whether the above findings can be applied to correlated firing. It is important to investigate this issue partly because neural firings are usually correlated but even more so because common attentional inputs may cause correlated firings. The present study first provides the general framework of attention modulation in relation to an attended stimulus and an actual stimulus and then shows the existence of a critical length under a Gaussian correlation structure. In order to improve encoding accuracy, measured by the Fisher information, the height and the base rate should be increased when the attended stimulus is in the critical length from the peak of the tuning curve and decreased otherwise. Furthermore, we confirm that a similar nature of the critical length also holds even when the neural decoder uses an uncorrelated unfaithful model. Thus, the existence of the critical length seems to be a ubiquitous phenomenon in attention modulation, and so its implications are discussed.

Attention modulation of neural tuning through peak and base rate

This study investigates the influence of attention modulation on neural tuning functions. It has been shown in experiments that attention modulation alters neural tuning curves. Attention has been considered at least to serve to resolve limiting capacities and to increase the sensitivity to attended stimulus, while the exact functions of attention are still under debate. Inspired by recent experimental results on attention modulation, we investigate the influence of changes in the height and base rate of the tuning curve on the encoding accuracy, using the Fisher information. Under an assumption of stimulus-conditional independence of neural responses, we derive explicit conditions that determine when the height and base rate should be increased or decreased to improve encoding accuracy. Notably, a decrease in the tuning height and base rate can improve the encoding accuracy in some cases. Our theoretical results can predict the effective size of attention modulation on the neural population with respect to encoding accuracy. We discuss how our method can be used quantitatively to evaluate different aspects of attention function.

A spiking neural network architecture for nonlinear function approximation

Multilayer perceptrons have received much attention in recent years due to their universal approximation capabilities. Normally, such models use real valued continuous signals, although they are loosely based on biological neuronal networks that encode signals using spike trains. Spiking neural networks are of interest both from a biological point of view and in terms of a method of robust signaling in particularly noisy or difficult environments. It is important to consider networks based on spike trains. A basic question that needs to be considered however, is what type of architecture can be used to provide universal function approximation capabilities in spiking networks? In this paper, we propose a spiking neural network architecture using both integrate-and-fire units as well as delays, that is capable of approximating a real valued function mapping to within a specified degree of accuracy.

Computational model of the role of sensory disorganization in focal task-specific dystonia

We present a new computational model for the development of task-specific focal dystonia. The purpose of the model is to explain how altered sensory representations can lead to abnormal motor behavior. Dystonia is described as the result of excessive gain through a sensorimotor loop. The gain is determined in part by the sensory cortical area devoted to each motor function, and behaviors that lead to abnormal increases in sensory cortical area are predicted to lead to dystonia. Properties of dystonia including muscular co-contraction, overflow movements, and task specificity are predicted by properties of a linear approximation to the loop transformation. We provide simulations of several different mechanisms that can cause the gain to exceed 1 and the motor activity to become sustained and uncontrolled. The model predicts that normal plasticity mechanisms may contribute to worsening of symptoms over time.