Relating a Spiking Neural Network Model and the Diffusion Model of Decision-Making.

Many models of decision making assume accumulation of evidence to threshold as a core mechanism to predict response probabilities and response times. A spiking neural network model (Wang, 2002) instantiates these mechanisms at the level of biophysically-plausible pools of neurons with excitatory and inhibitory connections, and has numerous model parameters tuned by physiological measures. The diffusion model (Ratcliff, 1978) is a cognitive model that can be fitted to a range of behaviors and conditions. We investigated how parameters of the cognitive-level diffusion model relate to the parameters of a neural-level spiking model. In each simulated "experiment", we generated "data" from the spiking neural network by factorially combining a manipulation of choice difficulty (via the input to the spiking model) and a manipulation of one of the core parameters of the spiking model. We then fitted the diffusion model to these simulated data to observe how manipulation of each core spiking model parameter mapped on to fitted drift rate, response threshold, and non-decision time. Manipulations of parameters in the spiking model related to input sensitivity, threshold, and stimulus processing time mapped on to their conceptual analogues in the diffusion model, namely drift rate, threshold, and non-decision time. Manipulations of parameters in the spiking model with no direct analogue to the diffusion model, non-stimulus-specific background input, strength of recurrent excitation, and receptor conductances, mapped on to threshold in the diffusion model. We discuss implications of these results for interpretations of fits of the diffusion model to behavioral data.

Psychophysical reverse correlation reflects both sensory and decision-making processes.

Goal-directed behavior depends on both sensory mechanisms that gather information from the outside world and decision-making mechanisms that select appropriate behavior based on that sensory information. Psychophysical reverse correlation is commonly used to quantify how fluctuations of sensory stimuli influence behavior and is generally believed to uncover the spatiotemporal weighting functions of sensory processes. Here we show that reverse correlations also reflect decision-making processes and can deviate significantly from the true sensory filters. Specifically, changes of decision bound and mechanisms of evidence integration systematically alter psychophysical reverse correlations. Similarly, trial-to-trial variability of sensory and motor delays and decision times causes systematic distortions in psychophysical kernels that should not be attributed to sensory mechanisms. We show that ignoring details of the decision-making process results in misinterpretation of reverse correlations, but proper use of these details turns reverse correlation into a powerful method for studying both sensory and decision-making mechanisms.

RELATING ACCUMULATOR MODEL PARAMETERS AND NEURAL DYNAMICS.

Accumulator models explain decision-making as an accumulation of evidence to a response threshold. Specific model parameters are associated with specific model mechanisms, such as the time when accumulation begins, the average rate of evidence accumulation, and the threshold. These mechanisms determine both the within-trial dynamics of evidence accumulation and the predicted behavior. Cognitive modelers usually infer what mechanisms vary during decision-making by seeing what parameters vary when a model is fitted to observed behavior. The recent identification of neural activity with evidence accumulation suggests that it may be possible to directly infer what mechanisms vary from an analysis of how neural dynamics vary. However, evidence accumulation is often noisy, and noise complicates the relationship between accumulator dynamics and the underlying mechanisms leading to those dynamics. To understand what kinds of inferences can be made about decision-making mechanisms based on measures of neural dynamics, we measured simulated accumulator model dynamics while systematically varying model parameters. In some cases, decision- making mechanisms can be directly inferred from dynamics, allowing us to distinguish between models that make identical behavioral predictions. In other cases, however, different parameterized mechanisms produce surprisingly similar dynamics, limiting the inferences that can be made based on measuring dynamics alone. Analyzing neural dynamics can provide a powerful tool to resolve model mimicry at the behavioral level, but we caution against drawing inferences based solely on neural analyses. Instead, simultaneous modeling of behavior and neural dynamics provides the most powerful approach to understand decision-making and likely other aspects of cognition and perception.

Hierarchical decision processes that operate over distinct timescales underlie choice and changes in strategy.

Decision-making in a natural environment depends on a hierarchy of interacting decision processes. A high-level strategy guides ongoing choices, and the outcomes of those choices determine whether or not the strategy should change. When the right decision strategy is uncertain, as in most natural settings, feedback becomes ambiguous because negative outcomes may be due to limited information or bad strategy. Disambiguating the cause of feedback requires active inference and is key to updating the strategy. We hypothesize that the expected accuracy of a choice plays a crucial rule in this inference, and setting the strategy depends on integration of outcome and expectations across choices. We test this hypothesis with a task in which subjects report the net direction of random dot kinematograms with varying difficulty while the correct stimulus-response association undergoes invisible and unpredictable switches every few trials. We show that subjects treat negative feedback as evidence for a switch but weigh it with their expected accuracy. Subjects accumulate switch evidence (in units of log-likelihood ratio) across trials and update their response strategy when accumulated evidence reaches a bound. A computational framework based on these principles quantitatively explains all aspects of the behavior, providing a plausible neural mechanism for the implementation of hierarchical multiscale decision processes. We suggest that a similar neural computation-bounded accumulation of evidence-underlies both the choice and switches in the strategy that govern the choice, and that expected accuracy of a choice represents a key link between the levels of the decision-making hierarchy.

Neural Mechanisms of Post-error Adjustments of Decision Policy in Parietal Cortex.

Humans often slow down after mistakes (post-error slowing [PES]), but the neural mechanism and adaptive role of PES remain controversial. We studied changes in the neural mechanisms of decision making after errors in humans and monkeys that performed a motion direction discrimination task. We found that PES is mediated by two factors: a reduction in sensitivity to sensory information and an increase in the decision bound. Both effects are implemented through dynamic changes in the decision-making process. Neuronal responses in the monkey lateral intraparietal area revealed that bound changes are implemented by decreasing an evidence-independent urgency signal. They also revealed a reduction in the rate of evidence accumulation, reflecting reduced sensitivity. These changes in the bound and sensitivity provide a quantitative account of choices and response times. We suggest that PES reflects an adaptive increase of decision bound in anticipation of maladaptive reductions in sensitivity to incoming evidence.

Response times from ensembles of accumulators.

Decision-making is explained by psychologists through stochastic accumulator models and by neurophysiologists through the activity of neurons believed to instantiate these models. We investigated an overlooked scaling problem: How does a response time (RT) that can be explained by a single model accumulator arise from numerous, redundant accumulator neurons, each of which individually appears to explain the variability of RT? We explored this scaling problem by developing a unique ensemble model of RT, called e pluribus unum, which embodies the well-known dictum "out of many, one." We used the e pluribus unum model to analyze the RTs produced by ensembles of redundant, idiosyncratic stochastic accumulators under various termination mechanisms and accumulation rate correlations in computer simulations of ensembles of varying size. We found that predicted RT distributions are largely invariant to ensemble size if the accumulators share at least modestly correlated accumulation rates and RT is not governed by the most extreme accumulators. Under these regimes the termination times of individual accumulators was predictive of ensemble RT. We also found that the threshold measured on individual accumulators, corresponding to the firing rate of neurons measured at RT, can be invariant with RT but is equivalent to the specified model threshold only when the rate correlation is very high.

On the origin of event-related potentials indexing covert attentional selection during visual search: timing of selection by macaque frontal eye field and event-related potentials during pop-out search.

Event-related potentials (ERPs) have provided crucial data concerning the time course of psychological processes, but the neural mechanisms producing ERP components remain poorly understood. This study continues a program of research in which we investigated the neural basis of attention-related ERP components by simultaneously recording intracranially and extracranially from macaque monkeys. Here, we compare the timing of attentional selection by the macaque homologue of the human N2pc component (m-N2pc) with the timing of selection in the frontal eye field (FEF), an attentional-control structure believed to influence posterior visual areas thought to generate the N2pc. We recorded FEF single-unit spiking and local field potentials (LFPs) simultaneously with the m-N2pc in monkeys performing an efficient pop-out search task. We assessed how the timing of attentional selection depends on task demands by direct comparison with a previous study of inefficient search in the same monkeys (e.g., finding a T among Ls). Target selection by FEF spikes, LFPs, and the m-N2pc was earlier during efficient pop-out search rather than during inefficient search. The timing and magnitude of selection in all three signals varied with set size during inefficient but not efficient search. During pop-out search, attentional selection was evident in FEF spiking and LFP before the m-N2pc, following the same sequence observed during inefficient search. These observations are consistent with the hypothesis that feedback from FEF modulates neural activity in posterior regions that appear to generate the m-N2pc even when competition for attention among items in a visual scene is minimal.

Response variability of frontal eye field neurons modulates with sensory input and saccade preparation but not visual search salience.

Discharge rate modulation of frontal eye field (FEF) neurons has been identified with a representation of visual search salience (physical conspicuity and behavioral relevance) and saccade preparation. We tested whether salience or saccade preparation are evident in the trial-to-trial variability of discharge rate. We quantified response variability via the Fano factor in FEF neurons recorded in monkeys performing efficient and inefficient visual search tasks. Response variability declined following stimulus presentation in most neurons, but despite clear discharge rate modulation, variability did not change with target salience. Instead, we found that response variability was modulated by stimulus luminance and the number of items in the visual field independently of attentional demands. Response variability declined to a minimum before saccade initiation, and presaccadic response variability was directionally tuned. In addition, response variability was correlated with the response time of memory-guided saccades. These results indicate that the trial-by-trial response variability of FEF neurons reflects saccade preparation and the strength of sensory input, but not visual search salience or attentional allocation.

Supplementary eye field during visual search: salience, cognitive control, and performance monitoring.

How supplementary eye field (SEF) contributes to visual search is unknown. Inputs from cortical and subcortical structures known to represent visual salience suggest that SEF may serve as an additional node in this network. This hypothesis was tested by recording action potentials and local field potentials (LFPs) in two monkeys performing an efficient pop-out visual search task. Target selection modulation, tuning width, and response magnitude of spikes and LFP in SEF were compared with those in frontal eye field. Surprisingly, only ∼2% of SEF neurons and ∼8% of SEF LFP sites selected the location of the search target. The absence of salience in SEF may be due to an absence of appropriate visual afferents, which suggests that these inputs are a necessary anatomical feature of areas representing salience. We also tested whether SEF contributes to overcoming the automatic tendency to respond to a primed color when the target identity switches during priming of pop-out. Very few SEF neurons or LFP sites modulated in association with performance deficits following target switches. However, a subset of SEF neurons and LFPs exhibited strong modulation following erroneous saccades to a distractor. Altogether, these results suggest that SEF plays a limited role in controlling ongoing visual search behavior, but may play a larger role in monitoring search performance.

Homologous mechanisms of visuospatial working memory maintenance in macaque and human: properties and sources.

Although areas of frontal cortex are thought to be critical for maintaining information in visuospatial working memory, the event-related potential (ERP) index of maintenance is found over posterior cortex in humans. In the present study, we reconcile these seemingly contradictory findings. Here, we show that macaque monkeys and humans exhibit the same posterior ERP signature of working memory maintenance that predicts the precision of the memory-based behavioral responses. In addition, we show that the specific pattern of rhythmic oscillations in the alpha band, recently demonstrated to underlie the human visual working memory ERP component, is also present in monkeys. Next, we concurrently recorded intracranial local field potentials from two prefrontal and another frontal cortical area to determine their contribution to the surface potential indexing maintenance. The local fields in the two prefrontal areas, but not the cortex immediately posterior, exhibited amplitude modulations, timing, and relationships to behavior indicating that they contribute to the generation of the surface ERP component measured from the distal posterior electrodes. Rhythmic neural activity in the theta and gamma bands during maintenance provided converging support for the engagement of the same brain regions. These findings demonstrate that nonhuman primates have homologous electrophysiological signatures of visuospatial working memory to those of humans and that a distributed neural network, including frontal areas, underlies the posterior ERP index of visuospatial working memory maintenance.

From salience to saccades: multiple-alternative gated stochastic accumulator model of visual search.

We describe a stochastic accumulator model demonstrating that visual search performance can be understood as a gated feedforward cascade from a salience map to multiple competing accumulators. The model quantitatively accounts for behavior and predicts neural dynamics of macaque monkeys performing visual search for a target stimulus among different numbers of distractors. The salience accumulated in the model is equated with the spike trains recorded from visually responsive neurons in the frontal eye field. Accumulated variability in the firing rates of these neurons explains choice probabilities and the distributions of correct and error response times with search arrays of different set sizes if the accumulators are mutually inhibitory. The dynamics of the stochastic accumulators quantitatively predict the activity of presaccadic movement neurons that initiate eye movements if gating inhibition prevents accumulation before the representation of stimulus salience emerges. Adjustments in the level of gating inhibition can control trade-offs in speed and accuracy that optimize visual search performance.

Neural mechanisms of saccade target selection: gated accumulator model of the visual-motor cascade.

We review a new computational model developed to understand how evidence about stimulus salience in visual search is translated into a saccade command. The model uses the activity of visually responsive neurons in the frontal eye field as evidence for stimulus salience that is accumulated in a network of stochastic accumulators to produce accurate and timely saccades. We discovered that only when the input to the accumulation process was gated could the model account for the variability in search performance and predict the dynamics of movement neuron discharge rates. This union of cognitive modeling and neurophysiology indicates how the visual-motor transformation can occur, and provides a concrete mapping between neuron function and specific cognitive processes.

Neurally constrained modeling of perceptual decision making.

Stochastic accumulator models account for response time in perceptual decision-making tasks by assuming that perceptual evidence accumulates to a threshold. The present investigation mapped the firing rate of frontal eye field (FEF) visual neurons onto perceptual evidence and the firing rate of FEF movement neurons onto evidence accumulation to test alternative models of how evidence is combined in the accumulation process. The models were evaluated on their ability to predict both response time distributions and movement neuron activity observed in monkeys performing a visual search task. Models that assume gating of perceptual evidence to the accumulating units provide the best account of both behavioral and neural data. These results identify discrete stages of processing with anatomically distinct neural populations and rule out several alternative architectures. The results also illustrate the use of neurophysiological data as a model selection tool and establish a novel framework to bridge computational and neural levels of explanation.