Center Publications

Where we allocate our visual spatial attention depends upon a continual competition between internally gen- erated goals and external distractions. Recently it was shown that single neurons in the macaque lateral intraparietal area (LIP) can predict the amount of time a distractor can shift the locus of spatial attention away from a goal. We propose that this remarkable dy- namical correspondence between single neurons and attention can be explained by a network model in which generically high-dimensional firing-rate vectors rapidly decay to a single mode. We find direct experi- mental evidence for this model, not only in the original attentional task, but also in a very different task involv- ing perceptual decision making. These results confirm a theoretical prediction that slowly varying activity pat- terns are proportional to spontaneous activity, pose constraints on models of persistent activity, and sug- gest a network mechanism for the emergence of ro- bust behavioral timing from heterogeneous neuronal populations.

Understanding neural responses with natural stimuli has increasingly become an essential part of characterizing neural coding. Neural responses are commonly characterized by a linear-nonlinear (LN) model, in which the output of a linear filter applied to the stimulus is transformed by a static nonlinearity to determine neural response. To estimate the linear filter in the LN model, studies of responses to natural stimuli commonly use methods that are unbiased only for a linear model (in which there is no static nonlinearity): spike-triggered averages with correction for stimulus power spectrum, with or without regularization. While these methods work well for artificial stimuli, such as Gaussian white noise, we show here that they estimate neural filters of LN models from responses to natural stimuli much more poorly. We studied simple cells in cat primary visual cortex. We demonstrate that the filters computed by directly taking the nonlinearity into account have better predictive power and depend less on the stimulus than those computed under the linear model. With noise stimuli, filters computed using the linear and LN models were similar, as predicted theoretically. With natural stimuli, filters of the two models can differ profoundly. Noise and natural stimulus filters differed significantly in spatial properties, but these differences were exaggerated when filters were computed using the linear rather that the LN model. While regularization of filters computed under the linear model improved their predictive power, it also led to systematic distortions of their spatial frequency profiles, especially at low spatial and temporal frequencies.

There are two basic problems in the statistical analysis of neural data. The ``encoding'' problem concerns how information is encoded in neural spike trains: can we predict the spike trains of a neuron (or population of neurons), given an arbitrary stimulus or observed motor response? Conversely, the ``decoding'' problem concerns how much information is in a spike train: in particular, how well can we estimate the stimulus that gave rise to the spike train? This chapter describes statistical model-based techniques that in some cases provide a unified solution to these two coding problems. These models can capture stimulus dependencies as well as spike history and interneuronal interaction effects in population spike trains, and are intimately related to biophysically-based models of integrate-and-fire type. We describe flexible, powerful likelihood-based methods for fitting these encoding models and then for using the models to perform optimal decoding. Each of these (apparently quite difficult) tasks turn out to be highly computationally tractable, due to a key concavity property of the model likelihood. Finally, we return to the encoding problem to describe how to use these models to adaptively optimize the stimuli presented to the cell on a trial-by-trial basis, in order that we may infer the optimal model parameters as efficiently as possible.

Gain modulation, in which the sensitivity of a neural response to one input is modified by a second input, is studied at single-neuron and network levels. At the single neuron level, gain modulation can arise if the two inputs are subject to a direct multiplicative interaction. Alternatively, these inputs can be summed in a linear manner by the neuron and gain modulation can arise, instead, from a nonlinear input-output relationship. We derive a mathematical constraint that can distinguish these two mechanisms even though they can look very similar, provided sufficient data of the appropriate type are available. Previously, it has been shown in coordinate transformation studies that artificial neurons with sigmoid transfer functions can acquire a nonlinear additive form of gain modulation through learning-driven adjustment of synaptic weights. We use the constraint derived for single-neuron studies to compare responses in this network with those of another network model based on a biologically inspired transfer function that can support approximately multiplicative interactions.

Receptor neurons may not encode sensory information in an efficient manner. A new paper supports the idea that the brain achieves optimal encoding downstream of sensory transduction through additional processing.

The origin of orientation selectivity in primary visual cortex (V1) is a model problem for understanding cerebral cortical circuitry. A key constraint is that orientation tuning width is invariant under changes in stimulus contrast. We have previously shown that this can arise from the combination of feedforward lateral geniculate nucleus (LGN) input and an orientation-untuned component of feedforward inhibition that dominates excitation. However, these models did not include the large background voltage noise observed in vivo. Here, we include this noise and examine a simple model of cat V1 response. Constraining our simulations to fit physiological data, our single model parameter is the strength of feedforward inhibition relative to LGN excitation. With physiological noise, the contrast invariance of orientation tuning depends little on inhibition level, although very weak or very strong inhibition leads to weak broadening or sharpening, respectively, of tuning with contrast. For any inhibition level, an alternative measure of orientation tuning -- the circular variance -- decreases with contrast as observed experimentally. These results arise primarily because the voltage noise causes large inputs to be much more strongly amplified than small ones in evoking spiking responses, relatively suppressing responses to nonpreferred stimuli. However, inhibition comparable to or stronger than excitation appears necessary to suppress spiking responses to nonpreferred orientations to the extent seen in vivo and to allow the emergence of a tuned mean voltage response. These two response properties provide the strongest constraints on model details. Antiphase inhibition from inhibitory simple cells, and not just untuned inhibition from inhibitory complex cells, appears necessary to fully explain these aspects of cortical orientation tuning.

Volitional behavior relies on the brainÕs ability to remap sensory flow to motor programs whenever demanded by a changed behavioral context. To investigate the circuit basis of such flexible behavior, we have developed a biophysically based decision-making network model of spiking neurons for arbitrary sensorimotor mapping. The model quantitatively reproduces behavioral and prefrontal single-cell data from an experiment in which monkeys learn visuomotor associations that are reversed unpredictably from time to time. We show that when synaptic modifications occur on multiple timescales, the model behavior becomes flexible only when needed: slow components of learning usually dominate the decision process. However, if behavioral contexts change frequently enough, fast components of plasticity take over, and the behavior exhibits a quick forget-and-learn pattern. This model prediction is confirmed by monkey data. Therefore, our work reveals a scenario for conditional associative learning that is distinct from instant switching between sets of well-established sensorimotor associations.

We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods.

Both in vivo and in vitro recordings indicate that neuronal mem- brane potentials can make spontaneous transitions between distinct up and down states. At the network level, populations of neurons have been observed to make these transitions synchronously. Although synap- tic activity and intrinsic neuron properties play an important role, the precise nature of the processes responsible for these phenomena is not known. Using a computational model we explore the interplay between intrinsic neuronal properties and synaptic fluctuations. Model neurons of the integrate-and-fire type were extended by adding a nonlinear mem- brane current. Networks of these neurons exhibit large amplitude syn- chronous spontaneous fluctuations that make the neurons jump between up and down states, thereby producing bimodal membrane potential distributions. The effect of sensory stimulation on network responses depends on whether the stimulus is applied during an up state or deeply inside a down state. External noise can be varied to modulate the net- work continuously between two extreme regimes in which it remains permanently in either the up or the down state.

Recent developments in multi-electrode recordings enable the simultaneous measurement of the spiking activity of many neurons. Analysis of such multineuronal data is one of the key challenges in computational neuroscience today. In this work, we develop a multivariate point-process model in which the observed activity of a network of neurons depends on three terms: 1) the experimentally-controlled stimulus; 2) the spiking history of the observed neurons; and 3) a latent noise source that corresponds, for example, to ``common input'' from an unobserved population of neurons that is presynaptic to two or more cells in the observed population. We develop an expectation-maximization algorithm for fitting the model parameters; here the expectation step is based on a continuous-time implementation of the extended Kalman smoother, and the maximization step involves two concave maximization problems which may be solved in parallel. The techniques developed allow us to solve a variety of inference problems in a straightforward, computationally efficient fashion; for example, we may use the model to predict network activity given an arbitrary stimulus, infer a neuron's firing rate given the stimulus and the activity of the other observed neurons, and perform optimal stimulus decoding and prediction. We present several detailed simulation studies which explore the strengths and limitations of our approach.

Memories maintained in patterns of synaptic connectivity are rapidly over-written and destroyed by ongoing plasticity due to the storage of new memories. Short memory lifetimes arise from the bound that must be imposed on synaptic efficacy in any realistic model. We explore whether memory performance can be improved by allowing synapses to traverse a large number of states before reaching their bounds, or by changing the way these bounds are imposed. In the case of hard bounds memory lifetimes grow proportional to the square of the number synaptic states, but only if potentiation and depression are precisely balanced. Improved performance can be obtained without fine tuning by imposing soft bounds, but this improvement is only linear in the number of synaptic states. We explore a number of other possibilities and conclude that improving memory performance requires a more radical modification of the standard model of memory storage.

Circadian rhythms are daily oscillations in behaviors that persist in constant light/dark conditions with periods close to 24 hours. A striking feature of these rhythms is that their periods remain fairly constant over a wide range of physiological temperatures, a feature called temperature compensa- tion. Although circadian rhythms have been associated with periodic oscillations in mRNA and protein levels, the question of how to construct a network of chemical reactions that is temperature compensated remains unanswered. We discuss a general framework for building such a network.

The word-frequency effect (WFE) in recognition memory refers to the finding that more rare words are better recognized than more common words. We demonstrate that a familiarity-discrimination model operating on data from a semantic word-association space yields a robust WFE in data on both hit rates and false-alarm rates. Our modeling results suggest that word frequency is encoded in the semantic structure of language, and that this encoding contributes to the WFE observed in item-recognition experiments.

The dynamics of neural networks is influenced strongly by the spectrum of eigenvalues of the matrix describing their synaptic connectivity. In large networks, elements of the synaptic connectivity matrix can be chosen randomly from appropriate distributions, making results from random matrix theory highly relevant. Unfortunately, classic results on the eigenvalue spectra of random matrices do not apply to synaptic connectivity matrices because of the constraint that individual neurons are either excitatory or inhibitory. Therefore, we compute eigenvalue spectra of large random matrices with excitatory and inhibitory columns drawn from distributions with different means and equal or different variances.

We compute the exact spike-triggered average (STA) of the voltage for the nonleaky IF cell in continuous time, driven by Gaussian white noise. The computation is based on techniques from the theory of renewal processes and continuous-time hidden Markov processes (e.g., the backward and forward Fokker-Planck partial differential equations associated with first-passage time densities). From the STA voltage it is straightforward to derive the STA input current. The theory also gives an explicit asymptotic approximation for the STA of the leaky IF cell, valid in the low-noise regime $\sigma \to 0$. We consider both the STA and the conditional average voltage given an observed spike ``doublet'' event, i.e. two spikes separated by some fixed period of silence. In each case, we find that the STA as a function of time-preceding-spike, $\tau$, has a square-root singularity as $\tau$ approaches zero from below, and scales linearly with the scale of injected noise current. We close by briefly examining the discrete-time case, where similar phenomena are observed.

Biophysically accurate multi-compartmental models of individual neurones have signi cantly advanced our understanding of the input-output function of single cells. These models depend on a large number of parameters which are dif cult to estimate. In practise, they are often hand tuned to match measured physiological behaviors, thus raising questions of identifiability and interpretability. We propose a statistical approach to the automatic estimation of various biologically relevant parameters, including 1) the distribution of channel densities; 2) the spatiotemporal pattern of synaptic input; and 3) axial resistances across extended dendrites. Recent experimental advances, notably in voltage-sensitive imaging, motivate us to assume access to: a) the spatiotemporal voltage signal in the dendrite, and b) an approximate description of the channel kinetics of interest. We show here that, given a) and b), the parameters 1)-3) can be inferred simultaneously by nonnegative linear regression; that this optimization problem possesses a unique solution and is guaranteed to converge despite the large number of parameters and their complex nonlinear interaction; and that standard optimization algorithms ef ciently reach this optimum with modest computational and data requirements. We demonstrate that the method leads to accurate estimations on a wide variety of challenging model data sets that include up to on the order of 10,000 parameters (roughly two orders of magnitude more than previously feasible), and describe how the method gives insights into the functional interaction of groups of channels.

Reward-based learning in neural systems is challenging because a large number of parameters that affect network function must be optimized solely on the basis of a reward signal that indicates improved performance. Searching the parameter space for an optimal solution is particularly difficult if the network is large. We show that Hebbian forms of synaptic plasticity applied to synapses between a supervisor circuit and the network it is controlling can effectively reduce the dimension of the space of parameters being searched to support efficient reinforcement-based learning in large networks. The critical element is that the connections between the supervisor units and the network must be reciprocal. Once the appropriate connections have been set up by Hebbian plasticity, a reinforcement-based learning procedure leads to rapid learning in a function approximation task. Hebbian plasticity within the network being supervised ultimately allows the network to perform the task without input from the supervisor.

It has been shown that motion aftereffect (MAE) not only is present at the adapted location but also partially transfers to nearby non- adapted locations. However, it is not clear whether MAE transfers across the fixation point. Since cells in area MSTd have receptive fields that cover both sides of the fixation point and since many MSTd cells, but not cells in earlier visual areas, prefer complex motion patterns such as expansion, we tested cross-fixation transfer of MAE induced by expanding random-dots stimuli. We also used rightward translational motion for comparison. Subjects adapted to motion patterns on a fixed side of the fixation point. Dynamic MAE was then measured with a nulling procedure at both the adapted site and the mirror site across the fixation point. SubjectsÕ eye fixation during stimulus presentation was monitored with an infrared eye tracker. At the adapted site, both the expansion and the translation patterns generated strong MAEs, as expected. However, only the expansion pattern, but not translation pattern, generated significant MAE at the mirror site. This remained true even after we adjusted stimulus parameters to equate the strengths of the expansion MAE and translation MAE at the adapted site. We conclude that there is cross-fixation transfer of MAE for expansion motion but not for translational motion.

Neurons recorded from electrode arrays show a remarkable scaling property in their bursts of spontaneous activity, referred to as “avalanches” (Beggs and Plentz, 2003 & 2004). Such scaling suggests a critical property in the coupling of these circuits. We show that similar scaling laws can arise in a simple model for the growth of neuronal processes. In the model (Van Ooyen and Van Pelt, 1994 & 1996), the spatial range of the processes extending from each neuron is represented by a circle that grows or shrinks as a function of the average intracellular calcium concentration. Neurons interact when the circles corresponding to their processes intersect, with a strength proportional to the area of overlap.

Given the extensive attenuation that can occur along dendritic cables, location within the dendritic tree might appear to be a dominant factor in determining the impact of a synapse on the postsynaptic response. By this reasoning, distal syn- apses should have a smaller effect than proximal ones. However, experimental evidence from several types of neurons, such as CA1 pyramidal cells, indicates that a compensatory strengthening of syn- apses counteracts the effect of location on synaptic efficacy. A form of spike-timing-dependent plasticity (STDP), called anti-STDP, com- bined with non-Hebbian activity-dependent plasticity can account for the equalization of synaptic efficacies. This result, obtained originally in models with unbranched passive cables, also arises in multi- compartment models with branched and active dendrites that feature backpropagating action potentials, including models with CA1 py- ramidal morphologies. Additionally, when dendrites support the local generation of action potentials, anti-STDP prevents runaway dendritic spiking and locally balances the numbers of dendritic and backpropa- gating action potentials. Thus in multiple ways, anti-STDP eliminates the location dependence of synapses and allows Hebbian plasticity to operate in a more “democratic” manner.

Several models exist for explaining primary visual cortex (V1) orientation tuning. The modified feedforward model (MFM) and the recurrent model (RM) are major examples. We have implemented these two models, at the same level of detail, alongside a few newer variations, and thoroughly compared their receptive-field structures. We found that antiphase inhibition in the MFM enhances both spatial phase information and orientation tuning, producing well-tuned simple cells. This remains true for a newer version of the MFM that incorporates untuned complex-cell inhibition. In contrast, when the recurrent connections in the RM are strong enough to produce typical V1 orientation tuning, they also eliminate spatial phase information, making the cells com- plex. Introducing phase specificity into the connections of the RM (as done in an original version of the RM) can make the cells phase sensitive, but the cells show an incorrect 90¡ peak shift of orientation tuning under opposite contrast signs. An inhibition-dominant version of the RM can generate well-tuned cells across the simpleÐ complex spectrum, but it predicts that the net effect of cortical interactions is to suppress feedforward excitation across all orientations in simple cells. Finally, adding antiphase inhibition used in the MFM into the RM produces a most general model. We call this new model the modified recurrent model (MRM) and show that this model can also produce well-tuned cells throughout the simpleÐ complex spectrum. Unlike the inhibition-dominant RM, the MRM is consistent with data from cat V1, suggesting that the net effect of cortical interactions is to boost simple cell responses at the preferred orientation. These results sug- gest that the MFM is well suited for explaining orientation tuning in simple cells, whereas the standard RM is for complex cells. The assignment of the RM to complex cells also avoids conflicts between the RM and the experiments of cortical inactivation (done on simple cells) and the spatial-frequency dependency of orientation tuning (found in simple cells). Because orientation-tuned V1 cells show a continuum of simple- to complex-cell behavior, the MRM provides the best description of V1 data.

Activity-dependent modification of synaptic strengths due to spike-timing-dependent plasticity (STDP) is sensitive to correlations between pre- and postsynaptic firing over timescales of tens of milliseconds. Temporal associations typically encountered in behavioral tasks involve times on the order of seconds. To relate the learning of such temporal associations to STDP, we must account for this large discrepancy in timescales. We show that the gap between synaptic and behavioral timescales can be bridged if the stimuli being associated generate sustained responses that vary appropriately in time. Synapses between neurons that fire this way can be modified by STDP in a manner that depends on the temporal ordering of events separated by several seconds even though the underlying plasticity has a much smaller temporal window.

Many biological systems exhibit complex temporal behavior that cannot be adequately characterized by a single time constant. This dynamics, observed from single channels up to the level of human psychophysics, is often better described by power-law rather than exponential dependences on time. We develop and study the properties of neural models with scale-invariant, power-law adaptation and contrast them with the more commonly studied exponential case. Responses of an adapting firing-rate model to constant, pulsed and oscillating inputs in both the power-law and exponential cases are considered. We construct a spiking model with power-law adaptation based on a nested cascade of processes and show that it can be ÒprogrammedÓ to produce a wide range of time delays. Finally, within a network model, we use power-law adaptation to reproduce long-term features of the tilt aftereffect.

Movement duration is an integral com- ponent of motor control, but nearly all extant optimization models of motor planning prefix duration instead of explaining it. Here we propose a new optimization principle that predicts movement dura- tion. The model assumes that the brain attempts to minimize move- ment duration under the constraint of meeting an accuracy criterion. The criterion is task and context dependent but is fixed for a given task and context. The model determines a unique duration as a trade-off between speed (time optimality) and accuracy (acceptable endpoint scatter). We analyzed the model for a linear motor plant, and obtained a closed-form equation for determining movement duration. By solv- ing the equation numerically with specific plant parameters for the eye and arm, we found that the model can reproduce saccade duration as a function of amplitude (the main sequence), and arm-movement duration as a function of the ratio of target distance to size (FittsÕs law). In addition, it explains the dependency of peak saccadic speed on amplitude and the dependency of saccadic duration on initial eye position. Furthermore, for arm movements, the model predicts a scaling relationship between peak velocity and distance and a reduc- tion in movement duration with a moderate increase in viscosity. Finally, for a linear plant, our model predicts a neural control signal identical to that of the minimum-variance model set to the same movement duration. This control signal is a smooth function of time (except at the endpoint), in contrast to the discontinuous bangÐ bang control found in the time-optimal control literature. We suggest that one aspect of movement planning, as revealed by movement duration, may be to assign an endpoint accuracy criterion for a given task and context.

Sensory neuroscience seeks to understand how the brain encodes natural environments. However, neural coding has largely been studied using simplified stimuli. In order to assess whether the brain's coding strategy depends on the stimulus ensemble, we apply a new information-theoretic method that allows unbiased calculation of neural filters (receptive fields) from responses to natural scenes or other complex signals with strong multipoint correlations. In the cat primary visual cortex we compare responses to natural inputs with those to noise inputs matched for luminance and contrast. We find that neural filters adaptively change with the input ensemble so as to increase the information carried by the neural response about the filtered stimulus. Adaptation affects the spatial frequency composition of the filter, enhancing sensitivity to under-represented frequencies in agreement with optimal encoding arguments. Adaptation occurs over 40 s to many minutes, longer than most previously reported forms of adaptation.

Controlled responses differ from reflexes because they can be turned off and on. This is a critical part of what distinguishes animals from automatons. How does the nervous system gate the flow of information so that a sensory stimulus that elicits a strong response on some occasions, evokes no response on others? A related question concerns how the flow of sensory information is altered when we pay close attention to something as opposed to when we ignore it. Most research in neuroscience focuses on circuits that directly respond to stimuli or generate motor output. But what of the circuits and mechanisms that control these direct responses, that modulate them and turn them off and on?
Self-regulated switching is vital to the operation of complex machines such as computers. The essential building block of a computer is a voltage-gated switch, the transistor, that is turned off and on by the same sorts of currents that it controls. By analogy, the question of my title refers to neural pathways that not only carry the action potentials that arise from neural activity, but are switched off and on by neural activity as well. By what biophysical mechanisms could this occur?
In the spirit of this volume, the point of this contribution is to raise a question, not to answer it. I will discuss three possible mechanisms— neuromodulation, inhibition, and gain modulation—and assess the merits and short-comings of each of them. I have my prejudices, which will become obvious, but I do not want to rule out any of these as candidates, nor do I want to leave the impression that the list is complete or that the problem is in any sense solved.

Transmission of signals within the brain is essential for cognitive function, but it is not clear how neural circuits support reliable and accurate signal propagation over a sufficiently large dynamic range. Two modes of propagation have been studied: synfire chains, in which synchronous activity travels through feedforward layers of a neuronal network, and the propagation of fluctuations in firing rate across these layers. In both cases, a sufficient amount of noise, which was added to previous models from an external source, had to be included to support stable propagation. Sparse, randomly connected networks of spiking model neurons can generate chaotic patterns of activity. We investigate whether this activity, which is a more realistic noise source, is sufficient to allow for signal transmission. We find that, for rate-coded signals but not for synfire chains, such networks support robust and accurate signal reproduction through up to six layers if appropriate adjustments are made in synaptic strengths. We investigate the factors affecting transmission and show that multiple signals can propagate simultaneously along different pathways. Using this feature, we show how different types of logic gates can arise within the architecture of the random network through the strengthening of specific synapses.

Observers can better discriminate orientation or direction near the cardinal axes than near an oblique axis. We investigated whether this well-known oblique effect is determined by the physical or the perceived axis of the stimuli. Using the simultaneous tilt illusion, we generated perceptually different orientations for the same inner (target) grating by contrasting it with differently oriented outer gratings. Subjects compared the target orientation with a set of reference orientations. If orientation discrimina- bility was determined by the physical orientations, the psychometric curves for the same target grating would be identical. Instead, all subjects produced steeper curves when perceiving target gratings near vertically as opposed to more obliquely. This result of orientation discrimination was confirmed by using adaptation-generated tilt aftereffect to manipulate the perceived ori- entation of a given physical orientation. Moreover, we obtained the same result in direction discrimination by using motion repul- sion to alter the perceived direction of a given physical direction. We conclude that when the perceived orientation or direction differs from the physical orientation or direction, the oblique effect depends on perceived, rather than physical, orientation or direction. Finally, as a by-product of the study, we found that, around the vertical direction, motion repulsion is much stronger when the inducing direction is more clockwise to the test direction than when it is more counterclockwise.

Motion repulsion involves interaction between two directions of motion. Since attention is known to bias interactions among different stimuli, we investigated the effect of attentional tasks on motion repulsion. We used two overlapping sets of random dots moving in different directions. When subjects had to detect a small speed-change or luminance change for dots along one direction, the repulsive influence from the other direction was significantly reduced compared with the control case without attentional tasks. However, when the speed-change could occur to either direction such that subjects had to attend both directions to detect the change, motion repulsion was not different from the control. A further experiment showed that decreasing the difficulty of the atten- tional task resulted in the disappearance of the attentional effect in the case of attention to one direction. Finally, over a wide range of contrasts for the unattended direction, attention reduced repulsion measured with the attended direction. These results are con- sistent with the physiological finding that strong attention to one direction of motion reduces inhibitory effects from the other direction.

Stereo plaid stimuli were created to investigate whether depth perception is determined by an intersection of constraints (IOC) or vector average (VA) operation on the Fourier components, or by the second-order (non-Fourier) feature in a pattern. We first cre- ated stereo plaid stimuli where IOC predicted vertical disparity, VA predicted positive diagonal disparity and the second-order fea- ture predicted negative diagonal disparity. In a depth discrimination task, observers indicated whether they perceived the pattern as near or far relative to a zero-disparity aperture. Observers perception was consistent with the disparity predicted by VA, indicat- ing its dominance over IOC and the second-order feature in this condition. Additional stimuli in which VA predicted vertical dis- parity were created to investigate whether VA would dominate perception when it was a less reliable cue. In this case, observers performance was consistent with disparity predicted by IOC or the second-order feature, not VA. Finally, in order to determine whether the second-order feature contributes to depth perception, stimuli were created where IOC and VA predicted positive hor- izontal disparity while the second-order feature predicted negative horizontal disparity. When the component gratings were oriented near horizontal (±83 from vertical), depth perception corresponded to that predicted by the second-order feature. However, as the components moved away from horizontal (±75 and ±65 from vertical), depth perception was increasingly likely to be predicted by an IOC or VA operation. These experiments suggest that the visual system does not rely exclusively on a single method for com- puting pattern disparity. Instead, it favours the most reliable method for a given condition.