Population coding of visual stimuli by cortical neurons tuned to more than one dimension

Neurons in the visual cortex are typically selective to a number of stimulus dimensions. Thus, there is a basic ambiguity in relating the response level of a single neuron to the stimulus values. It is shown that a multi-dimensional stimulus may be coded reliably by an ensemble of neurons, using a weighted average population coding model. Each neurons' contribution to the population signal for each dimension is the product of its response magnitude and its preferred value for that dimension. The sum of the products was normalized by the sum of the ensemble responses. Simulation results show that the representation accuracy increases as the square root of the number of units irrespective of the number of dimensions. Comparison of a specific 2D case of this population code for orientation and spatial frequency to behavioral discrimination levels yields that 10³–10⁴ neurons are needed to reach psychophysical performance. Introduction of each additional dimension requires about 1.7 times the number of neurons in the ensemble to reach the same level of accuracy. This result suggests that neurons may be selective for only 3 to 5 dimensions. It also provides another rationale for the existence of parallel processing streams in vision.     

Learning a grating discrimination task broadens human spatial frequency tuning

 The effect of spatial frequency discrimination learning on spatial frequency detection tuning curves, obtained by a summation to threshold paradigm, has been investigated. Three human observers were exposed to a grating discrimination task for longer than two weeks, and their detection thresholds for compound Gabor gratings were measured before and after this time interval. Discrimination thresholds decreased continuously and substantially during the course of learning, while the spatial frequency detection tuning curves show significant broadening in the posttest. Calculating the discrimination resolution of an ensemble of sensory coding units shows that larger bandwidths lead to better spatial frequency discrimination performance if pattern discrimination rests on multidimensional comparison or one-dimensional scaling of the spatial frequency parameter. Further, it is shown that a multiple-mechanism nonlinear pooling model is capable of explaining the results if plasticity of coding unit bandwidth or adaptive weights of the coding unit responses at the stage of response integration is assumed. The alternative sources of plasticity and the consequences of the findings for psychophysical modeling are discussed. Received: 8 September 1999 / Accepted in revised form: 16 October 2000     

A theory for the use of visual orientation information which exploits the columnar structure of striate cortex

A neural model is constructed based on the structure of a visual orientation hypercolumn in mammalian striate cortex. It is then assumed that the perceived orientation of visual contours is determined by the pattern of neuronal activity across orientation columns. Using statistical estimation theory, limits on the precision of orientation estimation and discrimination are calculated. These limits are functions of single unit response properties such as orientation tuning width, response amplitude and response variability, as well as the degree of organization in the neural network. It is shown that a network of modest size, consisting of broadly orientation selective units, can reliably discriminate orientation with a precision equivalent to human performance. Of the various network parameters, the discrimination threshold depends most critically on the number of cells in the hypercolumn. The form of the dependence on cell number correctly predicts the results of psychophysical studies of orientation discrimination. The model system's performance is also consistent with psychophysical data in two situations in which human performance is not optimal. First, interference with orientation discrimination occurs when multiple stimuli activate cells in the same hypercolumn. Second, systematic errors in the estimation of orientation can occur when a stimulus is composed of intersecting lines. The results demonstrate that it is possible to relate neural activity to visual performance by an examination of the pattern of activity across orientation columns. This provides support for the hypothesis that perceived orientation is determined by the distributed pattern of neural activity. The results also encourage the view of neural activity. The results also are determined by the responses of many neurons rather than the sensitivity of individual cells.     

Modeling inhibition of type II units in the dorsal cochlear nucleus

 Type II units in the dorsal cochlear nucleus (DCN) are characterized by vigorous but nonmonotonic responses to best frequency tones as a function of sound pressure level, and relatively weak responses to noise. A model of DCN neural circuitry was used to explore two hypothetical mechanisms by which neurons may be endowed with type II unit response properties. Both mechanisms assume that type II units receive excitatory input from auditory nerve (AN) fibers and inhibitory input from an unspecified class of cochlear nucleus interneurons that also receive excitatory AN input. The first mechanism, a lateral inhibition (LI) model, supposes that type II units receive inhibitory input from a number of narrowly tuned interneurons whose best frequencies (BFs) flank the BF of the type II unit. Tonal stimuli near BF result in only weak inhibitory input, but broadband stimuli recruit enough lateral inhibitors to greatly weaken the type II unit response. The second mechanism, a wideband inhibition (WBI) model, supposes that type II units receive inhibitory input from interneurons that are broadly tuned so that they respond more vigorously to broadband stimuli than to tones. Physiological and anatomical evidence points to the possible existence of such a class of neurons in the cochlear nucleus. The model extends an earlier computer model of an iso-frequency DCN patch to multiple frequency slices and adds a population of interneurons to provide the inhibition to model type II units (called I2-cells). The results show that both mechanisms accurately simulate responses of type II units to tones and noise. An experimental paradigm for distinguishing the two mechanisms is proposed. Received: 30 December 1996/Accepted in revised form: 13 March 1997     

Neural ensemble coding of target identity in echolocating bats

Most insectivorous bats use echolocation to determine the identity of flying insects. Among the many target features that are so extracted, the insect's wingbeat pattern and frequency appear to serve as useful cues for identification. Biosonar pulses impinging on the fluttering wings of an insect are returned as echoes whose amplitudes vary with time, thus providing a characteristic signature of the insect. It has been shown previously that neurons in the inferior colliculus, a midbrain auditory nucleus, of the little brown bat respond to sound stimuli that mimic echoes from fluttering targets. To examine the manner in which target identity is represented in the inferior colliculus, an ensemble coding analysis using a filter-based approach was undertaken. The analysis indicates that a discrete subset of neurons in the inferior colliculus, the onset units, are strongly tuned to wingbeat frequencies of targets that the bat hunts, and that ensemble response reaches a maximum at a distinct phase of the prey capture maneuver: the late approach stage. On the basis of the analysis it is hypothesized that inferior colliculus neurons may play an important role in target detection-identification processing. Although ensemble coding of temporally sequenced information has not been analyzed in the auditory system so far, this study indicates that this method of coding may provide the information necessary to detect and identify targets during prey capture. Received: 4 December 1995 / Accepted in revised form: 19 April 1996     

Vector reconstruction from firing rates

In a number of systems including wind detection in the cricket, visual motion perception and coding of arm movement direction in the monkey and place cell response to position in the rat hippocampus, firing rates in a population of tuned neurons are correlated with a vector quantity. We examine and compare several methods that allow the coded vector to be reconstructed from measured firing rates. In cases where the neuronal tuning curves resemble cosines, linear reconstruction methods work as well as more complex statistical methods requiring more detailed information about the responses of the coding neurons. We present a new linear method, the optimal linear estimator (OLE), that on average provides the best possible linear reconstruction. This method is compared with the more familiar vector method and shown to produce more accurate reconstructions using far fewer recorded neurons.     

Tuned inhibition in perceptual decision-making circuits can explain seemingly suboptimal confidence behavior

Current dominant views hold that perceptual confidence reflects the probability that a decision is correct. Although these views have enjoyed some empirical support, recent behavioral results indicate that confidence and the probability of being correct can be dissociated. An alternative hypothesis suggests that confidence instead reflects the magnitude of evidence in favor of a decision while being relatively insensitive to the evidence opposing the decision. We considered how this alternative hypothesis might be biologically instantiated by developing a simple neural network model incorporating a known property of sensory neurons: tuned inhibition. The key idea of the model is that the level of inhibition that each accumulator unit receives from units with the opposite tuning preference, i.e. its inhibition ‘tuning’, dictates its contribution to perceptual decisions versus confidence judgments, such that units with higher tuned inhibition (computing relative evidence for different perceptual interpretations) determine perceptual discrimination decisions, and units with lower tuned inhibition (computing absolute evidence) determine confidence. We demonstrate that this biologically plausible model can account for several counterintuitive findings reported in the literature where confidence and decision accuracy dissociate. By comparing model fits, we further demonstrate that a full complement of behavioral data across several previously published experimental results—including accuracy, reaction time, mean confidence, and metacognitive sensitivity—is best accounted for when confidence is computed from units without, rather than units with, tuned inhibition. Finally, we discuss predictions of our results and model for future neurobiological studies. These findings suggest that the brain has developed and implements this alternative, heuristic theory of perceptual confidence computation by relying on the diversity of neural resources available.     

A learned neural network that simulates properties of the neuronal population vector

This paper considers steady-state and timedependent characteristics of the response of the hidden-layer neurons in a dynamic model for the neural network trained through supervised learning to perform transformation of input signals into output signals. This transformation is set up so as to correspond to variation in the directions of two-dimensional vectors and is treated as creation by the network of a movement direction in response to a stimulus direction. The input vector is encoded in the state of the input layer at the initial instant of time, and the output vector in the state of the output layer at great values of time. After the network has been trained on examples of the input-output relation, the hidden neurons turn out to be broadly tuned to direction. The corresponding dependence for their activity is approximated with a smooth function, whose maximum allows some preferred direction to be attributed to each neuron. If each hidden neuron is assigned a vector pointing in its preferred direction, then any arbitrarily chosen direction can be characterized by an imaginary neuronal population vector (Georgopoulos et al. 1986) defined as the sum of the vectors of preferred direction for the neurons, with the weights equal to their activities for the chosen direction. It is demonstrated that, although hidden neurons are broadly tuned to direction, the population vector points in a direction congruent with that of the input vector at the initial moment of time and accurately predicts the direction of the output vector at great values of time. In between, the population vector turns continuously from the one direction towards the other. The dynamic and stationary properties of the population vector of the hidden-layer neurons, as obtained within the framework of the model in question, show a close similarity to the experimentally observed (Georgopoulos et al. 1986; Georgopoulos et al. 1989) behaviour of the population vector constructed in the same manner on the ensemble of motor cortex neurons sensitive to a certain type of movement.     

The Opponent Channel Population Code of Sound Location Is an Efficient Representation of Natural Binaural Sounds

In mammalian auditory cortex, sound source position is represented by a population of broadly tuned neurons whose firing is modulated by sounds located at all positions surrounding the animal. Peaks of their tuning curves are concentrated at lateral position, while their slopes are steepest at the interaural midline, allowing for the maximum localization accuracy in that area. These experimental observations contradict initial assumptions that the auditory space is represented as a topographic cortical map. It has been suggested that a “panoramic” code has evolved to match specific demands of the sound localization task. This work provides evidence suggesting that properties of spatial auditory neurons identified experimentally follow from a general design principle- learning a sparse, efficient representation of natural stimuli. Natural binaural sounds were recorded and served as input to a hierarchical sparse-coding model. In the first layer, left and right ear sounds were separately encoded by a population of complex-valued basis functions which separated phase and amplitude. Both parameters are known to carry information relevant for spatial hearing. Monaural input converged in the second layer, which learned a joint representation of amplitude and interaural phase difference. Spatial selectivity of each second-layer unit was measured by exposing the model to natural sound sources recorded at different positions. Obtained tuning curves match well tuning characteristics of neurons in the mammalian auditory cortex. This study connects neuronal coding of the auditory space with natural stimulus statistics and generates new experimental predictions. Moreover, results presented here suggest that cortical regions with seemingly different functions may implement the same computational strategy-efficient coding.     

Correlated neuronal discharges that increase coding efficiency during perceptual discrimination

During a sensory discrimination task, the responses of multiple sensory neurons must be combined to generate a choice. The optimal combination of responses is determined both by their dependence on the sensory stimulus and by their cofluctuations across trials-that is, the noise correlations. Positively correlated noise is considered deleterious, because it limits the coding accuracy of populations of similarly tuned neurons. However, positively correlated fluctuations between differently tuned neurons actually increase coding accuracy, because they allow the common noise to be subtracted without signal loss. This is demonstrated with data recorded from the secondary somatosensory cortex of monkeys performing a vibrotactile discrimination task. The results indicate that positive correlations are not always harmful and may be exploited by cortical networks to enhance the neural representation of features to be discriminated.     

Traveling Waves and the Processing of Weakly Tuned Inputs in a Cortical Network Module

Recent studies have shown that local cortical feedback can havean important effect on the response of neurons in primary visualcortex to the orientation of visual stimuli. In this work, westudy the role of the cortical feedback in shaping thespatiotemporal patterns of activity in cortex. Two questionsare addressed: one, what are the limitations on the ability ofcortical neurons to lock their activity to rotatingoriented stimuli within a single receptive field? Two, can thelocal architecture of visual cortex lead to the generation ofspontaneous traveling pulses of activity? We study theseissues analytically by a population-dynamic model of ahypercolumn in visual cortex. The order parameter thatdescribes the macroscopic behavior of the network is thetime-dependent population vector of the network. We firststudy the network dynamics under the influence of a weakly tunedinput that slowly rotates within the receptive field. We showthat if the cortical interactions have strong spatialmodulation, the network generates a sharply tuned activityprofile that propagates across the hypercolumn in a path thatis completely locked to the stimulus rotation. The resultantrotating population vector maintains a constant angular lagrelative to the stimulus, the magnitude of which grows with thestimulus rotation frequency. Beyond a critical frequency thepopulation vector does not lock to the stimulus but executes aquasi-periodic motion with an average frequency that is smallerthan that of the stimulus. In the second part we consider thestable intrinsic state of the cortex under the influence of isotropic stimulation. We show that if the local inhibitoryfeedback is sufficiently strong, the network does not settleinto a stationary state but develops spontaneous travelingpulses of activity. Unlike recent models of wave propagation incortical networks, the connectivity pattern in our model isspatially symmetric, hence the direction of propagation ofthese waves is arbitrary. The interaction of these waves withan external-oriented stimulus is studied. It is shown that thesystem can lock to a weakly tuned rotating stimulus if thestimulus frequency is close to the frequency of the intrinsic wave.     

High-Fidelity Coding with Correlated Neurons

Positive correlations in the activity of neurons are widely observed in the brain. Previous studies have shown these correlations to be detrimental to the fidelity of population codes, or at best marginally favorable compared to independent codes. Here, we show that positive correlations can enhance coding performance by astronomical factors. Specifically, the probability of discrimination error can be suppressed by many orders of magnitude. Likewise, the number of stimuli encoded—the capacity—can be enhanced more than tenfold. These effects do not necessitate unrealistic correlation values, and can occur for populations with a few tens of neurons. We further show that both effects benefit from heterogeneity commonly seen in population activity. Error suppression and capacity enhancement rest upon a pattern of correlation. Tuning of one or several effective parameters can yield a limit of perfect coding: the corresponding pattern of positive correlation leads to a ‘lock-in’ of response probabilities that eliminates variability in the subspace relevant for stimulus discrimination. We discuss the nature of this pattern and we suggest experimental tests to identify it.     

Location coding by opponent neural populations in the auditory cortex

Although the auditory cortex plays a necessary role in sound localization, physiological investigations in the cortex reveal inhomogeneous sampling of auditory space that is difficult to reconcile with localization behavior under the assumption of local spatial coding. Most neurons respond maximally to sounds located far to the left or right side, with few neurons tuned to the frontal midline. Paradoxically, psychophysical studies show optimal spatial acuity across the frontal midline. In this paper, we revisit the problem of inhomogeneous spatial sampling in three fields of cat auditory cortex. In each field, we confirm that neural responses tend to be greatest for lateral positions, but show the greatest modulation for near-midline source locations. Moreover, identification of source locations based on cortical responses shows sharp discrimination of left from right but relatively inaccurate discrimination of locations within each half of space. Motivated by these findings, we explore an opponent-process theory in which sound-source locations are represented by differences in the activity of two broadly tuned channels formed by contra- and ipsilaterally preferring neurons. Finally, we demonstrate a simple model, based on spike-count differences across cortical populations, that provides bias-free, level-invariant localization—and thus also a solution to the “binding problem” of associating spatial information with other nonspatial attributes of sounds.     

A dynamical neural network model for motor cortical activity during movement: population coding of movement trajectories

As a dynamical model for motor cortical activity during hand movement we consider an artificial neural network that consists of extensively interconnected neuron-like units and performs the neuronal population vector operations. Local geometrical parameters of a desired curve are introduced into the network as an external input. The output of the model is a time-dependent direction and length of the neuronal population vector which is calculated as a sum of the activity of directionally tuned neurons in the ensemble. The main feature of the model is that dynamical behavior of the neuronal population vector is the result of connections between directionally tuned neurons rather than being imposed externally. The dynamics is governed by a system of coupled nonlinear differential equations. Connections between neurons are assigned in the simplest and most common way so as to fulfill basic requirements stemming from experimental findings concerning the directional tuning of individual neurons and the stabilization of the neuronal population vector, as well as from previous theoretical studies. The dynamical behavior of the model reveals a close similarity with the experimentally observed dynamics of the neuronal population vector. Specifically, in the framework of the model it is possible to describe a geometrical curve in terms of the time series of the population vector. A correlation between the dynamical behavior of the direction and the length of the population vector entails a dependence of the neural velocity on the curvature of the tracing trajectory that corresponds well to the experimentally measured covariation between tangential velocity and curvature in drawing tasks.On leave of absencefrom the Institute of Molecular Genetics, Russian Academy of Sciences, Moscow, Russia.     

Sensory processing and the network mechanisms for reading neuronal population codes

In many neuronal systems, information appears to be represented in the activity of populations of neurons. Such neuronal population codes must also be read out, or interpreted, by downstream networks. Recent studies in both vertebrate and invertebrate systems have begun to elucidate some of the general mechanisms underlying these processes. Directed behaviors, that involve a directional response to a directional sensory input, have been a particularly useful context for these studies because, among other things, their input-output relationship is easily defined and experimentally controlled. We have recently shown that the neuronal network underlying a directed behavior in the medicinal leech utilizes a specific population coding scheme based on a neuronal population vector. A population vector of mechanosensory neuron activity correlates well with behavioral output and the connectivity of the downstream network is well suited for accurately reading out this population code. Accepted: 17 April 1999     

Responses of auditory brainstem neurons in the grassfrog to clicks

Single unit recordings were made in the dorsal medullary nucleus and in the torus semicircularis of the immobilized grassfrog. The natural calls have a periodic pulsatile structure. To investigate the coding of pulse repetition rate periodic click trains with varying pulse repetition rate and an ensemble of clicks distributed randomly in time were used as stimuli. In the dorsal medullary nucleus strong time-locking to clicks was found. Most units showed an activation followed by suppression response. Some units showed a preference for pulse repetition rates matching their low-frequency sensitivity. In the torus semicircularis part of the units showed responses similar to dorsal medullary nucleus units. Other response types were activation irrespective of pulse repetition rate, and suppression followed by activation. The responses to the two stimulus ensembles were more compatible in the dorsal medullary nucleus than in the torus semicircularis.     

Modelling spatiotemporal properties of directionally sensitive multi-input single-output systems

The dynamics of directionally tuned linear multi-input single-output systems varies generally as a function of the spatial orientation of the inputs. A linear system receiving directionally specific inputs is represented by a linear combination of the respective input transfer functions. The input-output behaviour of such systems can be described by a vector transfer function which specifies the polarization directions of the system in real space. These directions, which can be either one (unidirectional vector transfer function) or two (bidirectional vector transfer function) but never three, are obtained by computing the eigenvectors and eigenvalues of the system matrix that is defined by the gain and phase values of the system's response to harmonic stimulation directed along three orthogonal directions in space. The spatial tuning behaviour is determined by the quadratic form associated with the system matrix. Neuronal systems with bidirectional vector transfer functions process input information in a plane-specific way and exhibit novel characteristics, very much different from those of systems with unidirectional vector transfer functions.     

Directional operations in the motor cortex modeled by a neural network of spiking neurons

A neural network with realistically modeled, spiking neurons is proposed to model ensemble operations of directionally tuned neurons in the motor cortex. The model reproduces well directional operations previously identified experimentally, including the prediction of the direction of an upcoming movement in reaching tasks and the rotation of the neuronal population vector in a directional transformation task.     

Neural coding of gustatory information.

The nervous system encodes information relating chemical stimuli to taste perception, beginning with transduction mechanisms at the receptor and ending in the representation of stimulus attributes by the activity of neurons in the brain. Recent studies have rekindled the long-standing debate about whether taste information is coded by the pattern of activity across afferent neurons or by specifically tuned 'labeled lines'. Taste neurons are broadly tuned to stimuli representing different qualities and are also responsive to stimulus intensity and often to touch and temperature. Their responsiveness is also modulated by a number of physiological factors. In addition to representing stimulus quality and intensity, activity in taste neurons must code information about the hedonic value of gustatory stimuli. These considerations suggest that individual gustatory neurons contribute to the coding of more than one stimulus parameter, making the response of any one cell meaningful only in the context of the activity of its neighbors.