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

Models of inhibitory control

We survey models of response inhibition having different degrees of mathematical, computational and neurobiological specificity and generality. The independent race model accounts for performance of the stop-signal or countermanding task in terms of a race between GO and STOP processes with stochastic finishing times. This model affords insights into neurophysiological mechanisms that are reviewed by other authors in this volume. The formal link between the abstract GO and STOP processes and instantiating neural processes is articulated through interactive race models consisting of stochastic accumulator GO and STOP units. This class of model provides quantitative accounts of countermanding performance and replicates the dynamics of neural activity producing that performance. The interactive race can be instantiated in a network of biophysically plausible spiking excitatory and inhibitory units. Other models seek to account for interactions between units in frontal cortex, basal ganglia and superior colliculus. The strengths, weaknesses and relationships of the different models will be considered. We will conclude with a brief survey of alternative modelling approaches and a summary of problems to be addressed including accounting for differences across effectors, species, individuals, task conditions and clinical deficits.This article is part of the themed issue 'Movement suppression: brain mechanisms for stopping and stillness'.

Of monkeys and men: Impatience in perceptual decision-making

For decades sequential sampling models have successfully accounted for human and monkey decision-making, relying on the standard assumption that decision makers maintain a pre-set decision standard throughout the decision process. Based on the theoretical argument of reward rate maximization, some authors have recently suggested that decision makers become increasingly impatient as time passes and therefore lower their decision standard. Indeed, a number of studies show that computational models with an impatience component provide a good fit to human and monkey decision behavior. However, many of these studies lack quantitative model comparisons and systematic manipulations of rewards. Moreover, the often-cited evidence from single-cell recordings is not unequivocal and complimentary data from human subjects is largely missing. We conclude that, despite some enthusiastic calls for the abandonment of the standard model, the idea of an impatience component has yet to be fully established; we suggest a number of recently developed tools that will help bring the debate to a conclusive settlement.

Model-based cognitive neuroscience

This special issue explores the growing intersection between mathematical psychology and cognitive neuroscience. Mathematical psychology, and cognitive modeling more generally, has a rich history of formalizing and testing hypotheses about cognitive mechanisms within a mathematical and computational language, making exquisite predictions of how people perceive, learn, remember, and decide. Cognitive neuroscience aims to identify neural mechanisms associated with key aspects of cognition using techniques like neurophysiology, electrophysiology, and structural and functional brain imaging. These two come together in a powerful new approach called model-based cognitive neuroscience, which can both inform cognitive modeling and help to interpret neural measures. Cognitive models decompose complex behavior into representations and processes and these latent model states can be used to explain the modulation of brain states under different experimental conditions. Reciprocally, neural measures provide data that help constrain cognitive models and adjudicate between competing cognitive models that make similar predictions about behavior. As examples, brain measures are related to cognitive model parameters fitted to individual participant data, measures of brain dynamics are related to measures of model dynamics, model parameters are constrained by neural measures, model parameters or model states are used in statistical analyses of neural data, or neural and behavioral data are analyzed jointly within a hierarchical modeling framework. We provide an introduction to the field of model-based cognitive neuroscience and to the articles contained within this special issue.

Approaches to Analysis in Model-based Cognitive Neuroscience

Our understanding of cognition has been advanced by two traditionally nonoverlapping and non-interacting groups. Mathematical psychologists rely on behavioral data to evaluate formal models of cognition, whereas cognitive neuroscientists rely on statistical models to understand patterns of neural activity, often without any attempt to make a connection to the mechanism supporting the computation. Both approaches suffer from critical limitations as a direct result of their focus on data at one level of analysis (cf. Marr, 1982), and these limitations have inspired researchers to attempt to combine both neural and behavioral measures in a cross-level integrative fashion. The importance of solving this problem has spawned several entirely new theoretical and statistical frameworks developed by both mathematical psychologists and cognitive neuroscientists. However, with each new approach comes a particular set of limitations and benefits. In this article, we survey and characterize several approaches for linking brain and behavioral data. We organize these approaches on the basis of particular cognitive modeling goals: (1) using the neural data to constrain a behavioral model, (2) using the behavioral model to predict neural data, and (3) fitting both neural and behavioral data simultaneously. Within each goal, we highlight a few particularly successful approaches for accomplishing that goal, and discuss some applications. Finally, we provide a conceptual guide to choosing among various analytic approaches in performing model-based cognitive neuroscience.

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.

Linking Theoretical Decision-making Mechanisms in the Simon Task with Electrophysiological Data: A Model-based Neuroscience Study in Humans

A current challenge for decision-making research is in extending models of simple decisions to more complex and ecological choice situations. Conflict tasks (e.g., Simon, Stroop, Eriksen flanker) have been the focus of much interest, because they provide a decision-making context representative of everyday life experiences. Modeling efforts have led to an elaborated drift diffusion model for conflict tasks (DMC), which implements a superimposition of automatic and controlled decision activations. The DMC has proven to capture the diversity of behavioral conflict effects across various task contexts. This study combined DMC predictions with EEG and EMG measurements to test a set of linking propositions that specify the relationship between theoretical decision-making mechanisms involved in the Simon task and brain activity. Our results are consistent with a representation of the superimposed decision variable in the primary motor cortices. The decision variable was also observed in the EMG activity of response agonist muscles. These findings provide new insight into the neurophysiology of human decision-making. In return, they provide support for the DMC model framework.

A single trial analysis of EEG in recognition memory: Tracking the neural correlates of memory strength

Recent work in perceptual decision-making has shown that although two distinct neural components differentiate experimental conditions (e.g., did you see a face or a car), only one tracked the evidence guiding the decision process. In the memory literature, there is a distinction between a fronto-central evoked potential measured with EEG beginning at 350ms that seems to track familiarity and a late parietal evoked potential that peaks at 600ms that tracks recollection. Here, we applied single-trial regressor analysis (similar to multivariate pattern analysis, MVPA) and diffusion decision modeling to EEG and behavioral data from two recognition memory experiments to test whether these two components contribute to the recognition decision process. The regressor analysis only involved whether an item was studied or not and did not involve any use of the behavioral data. Only late EEG activity distinguishes studied from not studied items that peaks at about 600ms following each test item onset predicted the diffusion model drift rate derived from the behavioral choice and reaction times (but only for studied items). When drift rate was made a linear function of the trial-level regressor values, the estimate for studied items was different than zero. This showed that the later EEG activity indexed the trial-to-trial variability in drift rate for studied items. Our results provide strong evidence that only a single EEG component reflects evidence being used in the recegnition decision process.

Comparing fixed and collapsing boundary versions of the diffusion model

Optimality studies and studies of decision-making in monkeys have been used to support a model in which the decision boundaries used to evaluate evidence collapse over time. This article investigates whether a diffusion model with collapsing boundaries provides a better account of human data than a model with fixed boundaries. We compared the models using data from four new numerosity discrimination experiments and two previously published motion discrimination experiments. When model selection was based on BIC values, the fixed boundary model was preferred over the collapsing boundary model for all of the experiments. When model selection was carried out using a parametric bootstrap cross-fitting method (PBCM), which takes into account the flexibility of the alternative models and the ability of one model to account for data from another model, data from 5 of 6 experiments favored either fixed boundaries or boundaries with only negligible collapse. We found that the collapsing boundary model produces response times distributions with the same shape as those produced by the fixed boundary model and that its parameters were not well-identified and were difficult to recover from data. Furthermore, the estimated boundaries of the best-fitting collapsing boundary model were relatively flat and very similar to those of the fixed-boundary model. Overall, a diffusion model with decision boundaries that converge over time does not provide an improvement over the standard diffusion model for our tasks with human data.

Will big data yield new mathematics? An evolving synergy with neuroscience

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin-Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

Diffusion Decision Model: Current Issues and History

There is growing interest in diffusion models to represent the cognitive and neural processes of speeded decision making. Sequential-sampling models like the diffusion model have a long history in psychology. They view decision making as a process of noisy accumulation of evidence from a stimulus. The standard model assumes that evidence accumulates at a constant rate during the second or two it takes to make a decision. This process can be linked to the behaviors of populations of neurons and to theories of optimality. Diffusion models have been used successfully in a range of cognitive tasks and as psychometric tools in clinical research to examine individual differences. In this review, we relate the models to both earlier and more recent research in psychology.

Neural control of visual search by frontal eye field: chronometry of neural events and race model processes

We investigated the chronometry of neural processes in frontal eye fields of macaques performing double-step saccade visual search in which a conspicuous target changes location in the array on a random fraction of trials. Durations of computational processes producing a saccade to original and final target locations (GO1 and GO2, respectively) are derived from response times (RT) on different types of trials. In these data, GO2 tended to be faster than GO1, demonstrating that inhibition of the initial saccade did not delay production of the compensated saccade. Here, we measured the dynamics of visual, visuomovement, and movement neuron activity in relation to these processes by examining trials when neurons instantiated either process. First, we verified that saccades were initiated when the discharge rate of movement neurons reached a threshold that was invariant across RT and trial type. Second, the time when visual and visuomovement neurons selected the target and when movement neuron activity began to accumulate were not significantly different across trial type. Third, the interval from the beginning of accumulation to threshold of movement-related activity was significantly shorter when instantiating the GO2 relative to the GO1 process. Differences observed between monkeys are discussed. Fourth, random variation of RT was accounted for to some extent by random variation in both the onset and duration of selective activity of each neuron type but mostly by variation of movement neuron accumulation duration. These findings offer new insights into the sources of control of target selection and saccade production in dynamic environments.

Using Decision Models to Enhance Investigations of Individual Differences in Cognitive Neuroscience

There is great interest in relating individual differences in cognitive processing to activation of neural systems. The general process involves relating measures of task performance like reaction times or accuracy to brain activity to identify individual differences in neural processing. One limitation of this approach is that measures like reaction times can be affected by multiple components of processing. For instance, some individuals might have higher accuracy in a memory task because they respond more cautiously, not because they have better memory. Computational models of decision making, like the drift–diffusion model and the linear ballistic accumulator model, provide a potential solution to this problem. They can be fitted to data from individual participants to disentangle the effects of the different processes driving behavior. In this sense the models can provide cleaner measures of the processes of interest, and enhance our understanding of how neural activity varies across individuals or populations. The advantages of this model-based approach to investigating individual differences in neural activity are discussed with recent examples of how this method can improve our understanding of the brain–behavior relationship.

Irrational time allocation in decision-making

Time is an extremely valuable resource but little is known about the efficiency of time allocation in decision-making. Empirical evidence suggests that in many ecologically relevant situations, decision difficulty and the relative reward from making a correct choice, compared to an incorrect one, are inversely linked, implying that it is optimal to use relatively less time for difficult choice problems. This applies, in particular, to value-based choices, in which the relative reward from choosing the higher valued item shrinks as the values of the other options get closer to the best option and are thus more difficult to discriminate. Here, we experimentally show that people behave sub-optimally in such contexts. They do not respond to incentives that favour the allocation of time to choice problems in which the relative reward for choosing the best option is high; instead they spend too much time on problems in which the reward difference between the options is low. We demonstrate this by showing that it is possible to improve subjects' time allocation with a simple intervention that cuts them off when their decisions take too long. Thus, we provide a novel form of evidence that organisms systematically spend their valuable time in an inefficient way, and simultaneously offer a potential solution to the problem.

Different Ways of Linking Behavioral and Neural Data via Computational Cognitive Models

Cognitive neuroscientists sometimes apply formal models to investigate how the brain implements cognitive processes. These models describe behavioral data in terms of underlying, latent variables linked to hypothesized cognitive processes. A goal of model-based cognitive neuroscience is to link these variables to brain measurements, which can advance progress in both cognitive and neuroscientific research. However, the details and the philosophical approach for this linking problem can vary greatly. We propose a continuum of approaches that differ in the degree of tight, quantitative, and explicit hypothesizing. We describe this continuum using four points along it, which we dub qualitative structural, qualitative predictive, quantitative predictive, and single model linking approaches. We further illustrate by providing examples from three research fields (decision making, reinforcement learning, and symbolic reasoning) for the different linking approaches.

The importance of decision onset

The neural mechanisms of decision making are thought to require the integration of evidence over time until a response threshold is reached. Much work suggests that response threshold can be adjusted via top-down control as a function of speed or accuracy requirements. In contrast, the time of integration onset has received less attention and is believed to be determined mostly by afferent or preprocessing delays. However, a number of influential studies over the past decade challenge this assumption and begin to paint a multifaceted view of the phenomenology of decision onset. This review highlights the challenges involved in initiating the integration of evidence at the optimal time and the potential benefits of adjusting integration onset to task demands. The review outlines behavioral and electrophysiolgical studies suggesting that the onset of the integration process may depend on properties of the stimulus, the task, attention, and response strategy. Most importantly, the aggregate findings in the literature suggest that integration onset may be amenable to top-down regulation, and may be adjusted much like response threshold to exert cognitive control and strategically optimize the decision process to fit immediate behavioral requirements.

Using Covert Response Activation to Test Latent Assumptions of Formal Decision-Making Models in Humans

Most decisions that we make build upon multiple streams of sensory evidence and control mechanisms are needed to filter out irrelevant information. Sequential sampling models of perceptual decision making have recently been enriched by attentional mechanisms that weight sensory evidence in a dynamic and goal-directed way. However, the framework retains the longstanding hypothesis that motor activity is engaged only once a decision threshold is reached. To probe latent assumptions of these models, neurophysiological indices are needed. Therefore, we collected behavioral and EMG data in the flanker task, a standard paradigm to investigate decisions about relevance. Although the models captured response time distributions and accuracy data, EMG analyses of response agonist muscles challenged the assumption of independence between decision and motor processes. Those analyses revealed covert incorrect EMG activity ("partial error") in a fraction of trials in which the correct response was finally given, providing intermediate states of evidence accumulation and response activation at the single-trial level. We extended the models by allowing motor activity to occur before a commitment to a choice and demonstrated that the proposed framework captured the rate, latency, and EMG surface of partial errors, along with the speed of the correction process. In return, EMG data provided strong constraints to discriminate between competing models that made similar behavioral predictions. Our study opens new theoretical and methodological avenues for understanding the links among decision making, cognitive control, and motor execution in humans.

SIGNIFICANCE STATEMENT

Sequential sampling models of perceptual decision making assume that sensory information is accumulated until a criterion quantity of evidence is obtained, from where the decision terminates in a choice and motor activity is engaged. The very existence of covert incorrect EMG activity ("partial error") during the evidence accumulation process challenges this longstanding assumption. In the present work, we use partial errors to better constrain sequential sampling models at the single-trial level.

LIP activity in the interstimulus interval of a change detection task biases the behavioral response

When looking around at the world, we can only attend to a limited number of locations. The lateral intraparietal area (LIP) is thought to play a role in guiding both covert attention and eye movements. In this study, we tested the involvement of LIP in both mechanisms with a change detection task. In the task, animals had to indicate whether an element changed during a blank in the trial by making a saccade to it. If no element changed, they had to maintain fixation. We examine how the animal's behavior is biased based on LIP activity prior to the presentation of the stimulus the animal must respond to. When the activity was high, the animal was more likely to make an eye movement toward the stimulus, even if there was no change; when the activity was low, the animal either had a slower reaction time or maintained fixation, even if a change occurred. We conclude that LIP activity is involved in both covert and overt attention, but when decisions about eye movements are to be made, this role takes precedence over guiding covert attention.

A Multi-Area Stochastic Model for a Covert Visual Search Task

Decisions typically comprise several elements. For example, attention must be directed towards specific objects, their identities recognized, and a choice made among alternatives. Pairs of competing accumulators and drift-diffusion processes provide good models of evidence integration in two-alternative perceptual choices, but more complex tasks requiring the coordination of attention and decision making involve multistage processing and multiple brain areas. Here we consider a task in which a target is located among distractors and its identity reported by lever release. The data comprise reaction times, accuracies, and single unit recordings from two monkeys’ lateral interparietal area (LIP) neurons. LIP firing rates distinguish between targets and distractors, exhibit stimulus set size effects, and show response-hemifield congruence effects. These data motivate our model, which uses coupled sets of leaky competing accumulators to represent processes hypothesized to occur in feature-selective areas and limb motor and pre-motor areas, together with the visual selection process occurring in LIP. Model simulations capture the electrophysiological and behavioral data, and fitted parameters suggest that different connection weights between LIP and the other cortical areas may account for the observed behavioral differences between the animals.

Discriminating evidence accumulation from urgency signals in speeded decision making

The dominant theoretical paradigm in explaining decision making throughout both neuroscience and cognitive science is known as “evidence accumulation”--The core idea being that decisions are reached by a gradual accumulation of noisy information. Although this notion has been supported by hundreds of experiments over decades of study, a recent theory proposes that the fundamental assumption of evidence accumulation requires revision. The "urgency gating" model assumes decisions are made without accumulating evidence, using only moment-by-moment information. Under this assumption, the successful history of evidence accumulation models is explained by asserting that the two models are mathematically identical in standard experimental procedures. We demonstrate that this proof of equivalence is incorrect, and that the models are not identical, even when both models are augmented with realistic extra assumptions. We also demonstrate that the two models can be perfectly distinguished in realistic simulated experimental designs, and in two real data sets; the evidence accumulation model provided the best account for one data set, and the urgency gating model for the other. A positive outcome is that the opposing modeling approaches can be fruitfully investigated without wholesale change to the standard experimental paradigms. We conclude that future research must establish whether the urgency gating model enjoys the same empirical support in the standard experimental paradigms that evidence accumulation models have gathered over decades of study.

Speed-accuracy tradeoff by a control signal with balanced excitation and inhibition

A hallmark of flexible behavior is the brain's ability to dynamically adjust speed and accuracy in decision-making. Recent studies suggested that such adjustments modulate not only the decision threshold, but also the rate of evidence accumulation. However, the underlying neuronal-level mechanism of the rate change remains unclear. In this work, using a spiking neural network model of perceptual decision, we demonstrate that speed and accuracy of a decision process can be effectively adjusted by manipulating a top-down control signal with balanced excitation and inhibition [balanced synaptic input (BSI)]. Our model predicts that emphasizing accuracy over speed leads to reduced rate of ramping activity and reduced baseline activity of decision neurons, which have been observed recently at the level of single neurons recorded from behaving monkeys in speed-accuracy tradeoff tasks. Moreover, we found that an increased inhibitory component of BSI skews the decision time distribution and produces a pronounced exponential tail, which is commonly observed in human studies. Our findings suggest that BSI can serve as a top-down control mechanism to rapidly and parametrically trade between speed and accuracy, and such a cognitive control signal presents both when the subjects emphasize accuracy or speed in perceptual decisions.

Different target-discrimination times can be followed by the same saccade-initiation timing in different stimulus conditions during visual searches

The neuronal processes that underlie visual searches can be divided into two stages: target discrimination and saccade preparation/generation. This predicts that the length of time of the prediscrimination stage varies according to the search difficulty across different stimulus conditions, whereas the length of the latter postdiscrimination stage is stimulus invariant. However, recent studies have suggested that the length of the postdiscrimination interval changes with different stimulus conditions. To address whether and how the visual stimulus affects determination of the postdiscrimination interval, we recorded single-neuron activity in the lateral intraparietal area (LIP) when monkeys (Macaca fuscata) performed a color-singleton search involving four stimulus conditions that differed regarding luminance (Bright vs. Dim) and target-distractor color similarity (Easy vs. Difficult). We specifically focused on comparing activities between the Bright-Difficult and Dim-Easy conditions, in which the visual stimuli were considerably different, but the mean reaction times were indistinguishable. This allowed us to examine the neuronal activity when the difference in the degree of search speed between different stimulus conditions was minimal. We found that not only prediscrimination but also postdiscrimination intervals varied across stimulus conditions: the postdiscrimination interval was longer in the Dim-Easy condition than in the Bright-Difficult condition. Further analysis revealed that the postdiscrimination interval might vary with stimulus luminance. A computer simulation using an accumulation-to-threshold model suggested that the luminance-related difference in visual response strength at discrimination time could be the cause of different postdiscrimination intervals.

Probabilistic Decision Making with Spikes: From ISI Distributions to Behaviour via Information Gain

Computational theories of decision making in the brain usually assume that sensory 'evidence' is accumulated supporting a number of hypotheses, and that the first accumulator to reach threshold triggers a decision in favour of its associated hypothesis. However, the evidence is often assumed to occur as a continuous process whose origins are somewhat abstract, with no direct link to the neural signals - action potentials or 'spikes' - that must ultimately form the substrate for decision making in the brain. Here we introduce a new variant of the well-known multi-hypothesis sequential probability ratio test (MSPRT) for decision making whose evidence observations consist of the basic unit of neural signalling - the inter-spike interval (ISI) - and which is based on a new form of the likelihood function. We dub this mechanism s-MSPRT and show its precise form for a range of realistic ISI distributions with positive support. In this way we show that, at the level of spikes, the refractory period may actually facilitate shorter decision times, and that the mechanism is robust against poor choice of the hypothesized data distribution. We show that s-MSPRT performance is related to the Kullback-Leibler divergence (KLD) or information gain between ISI distributions, through which we are able to link neural signalling to psychophysical observation at the behavioural level. Thus, we find the mean information needed for a decision is constant, thereby offering an account of Hick's law (relating decision time to the number of choices). Further, the mean decision time of s-MSPRT shows a power law dependence on the KLD offering an account of Piéron's law (relating reaction time to stimulus intensity). These results show the foundations for a research programme in which spike train analysis can be made the basis for predictions about behavior in multi-alternative choice tasks.

Neural activity in the medial temporal lobe reveals the fidelity of mental time travel

Neural circuitry in the medial temporal lobe (MTL) is critically involved in mental time travel, which involves the vivid retrieval of the details of past experience. Neuroscientific theories propose that the MTL supports memory of the past by retrieving previously encoded episodic information, as well as by reactivating a temporal code specifying the position of a particular event within an episode. However, the neural computations supporting these abilities are underspecified. To test hypotheses regarding the computational mechanisms supported by different MTL subregions during mental time travel, we developed a computational model that linked a blood oxygenation level-dependent signal to cognitive operations, allowing us to predict human performance in a memory search task. Activity in the posterior MTL, including parahippocampal cortex, reflected how strongly one reactivates the temporal context of a retrieved memory, allowing the model to predict whether the next memory will correspond to a nearby moment in the study episode. A signal in the anterior MTL, including perirhinal cortex, indicated the successful retrieval of list items, without providing information regarding temporal organization. A hippocampal signal reflected both processes, consistent with theories that this region binds item and context information together to form episodic memories. These findings provide evidence for modern theories that describe complementary roles of the hippocampus and surrounding parahippocampal and perirhinal cortices during the retrieval of episodic memories, shaping how humans revisit the past.

Dorsal premotor cortex: neural correlates of reach target decisions based on a color-location matching rule and conflicting sensory evidence

We recorded single-neuron activity in dorsal premotor (PMd) and primary motor cortex (M1) of two monkeys in a reach-target selection task. The monkeys chose between two color-coded potential targets by determining which target's color matched the predominant color of a multicolored checkerboard-like Decision Cue (DC). Different DCs contained differing numbers of colored squares matching each target. The DCs provided evidence about the correct target ranging from unambiguous (one color only) to very ambiguous and conflicting (nearly equal number of squares of each color). Differences in choice behavior (reach response times and success rates as a function of DC ambiguity) of the monkeys suggested that each applied a different strategy for using the target-choice evidence in the DCs. Nevertheless, the appearance of the DCs evoked a transient coactivation of PMd neurons preferring both potential targets in both monkeys. Reach response time depended both on how long it took activity to increase in neurons that preferred the chosen target and on how long it took to suppress the activity of neurons that preferred the rejected target, in both correct-choice and error-choice trials. These results indicate that PMd neurons in this task are not activated exclusively by a signal proportional to the net color bias of the DCs. They are instead initially modulated by the conflicting evidence supporting both response choices; final target selection may result from a competition between representations of the alternative choices. The results also indicate a temporal overlap between action selection and action initiation processes in PMd and M1.

Biomimetic race model of the loop between the superior colliculus and the basal ganglia: Subcortical selection of saccade targets

The superior colliculus, a laminar structure involved in the retinotopic mapping of the visual field, plays a cardinal role in several cortical and subcortical pathways of the saccadic system. Although the selection of saccade targets has long been thought to be mainly the product of cortical processes, a growing body of evidence hints at the implication of the superior colliculus in selection processes independent from cortical inputs, capable of producing saccades at latencies incompatible with the cortical pathways. This selection ability could be produced firstly by the lateral connections between the neurons of its maps, and secondly by its interactions with the midbrain basal ganglia, already renowned for their role in decision making. We propose a biomimetic population-coded race model of selection based on a dynamic tecto-basal loop that reproduces the observed ability of the superior colliculus to stochastically select between similar stimuli. Our model's selection accuracy depends on the discriminability of the target and the distractors. Our model also offers an explanation for the phenomenon of Remote Distractor Effect based on the lateral connectivity within the basal ganglia circuitry rather than on lateral inhibitions within the collicular maps. Finally, we propose a role for the intermediate layers of the superior colliculus, as stochastic integrators dynamically gated by the selective disinhibition of the basal ganglia channels that is consistent with the recorded activity profiles of these neurons.

Inhibitory control in mind and brain 2.0: blocked-input models of saccadic countermanding

The interactive race model of saccadic countermanding assumes that response inhibition results from an interaction between a go unit, identified with gaze-shifting neurons, and a stop unit, identified with gaze-holding neurons, in which activation of the stop unit inhibits the growth of activation in the go unit to prevent it from reaching threshold. The interactive race model accounts for behavioral data and predicts physiological data in monkeys performing the stop-signal task. We propose an alternative model that assumes that response inhibition results from blocking the input to the go unit. We show that the blocked-input model accounts for behavioral data as accurately as the original interactive race model and predicts aspects of the physiological data more accurately. We extend the models to address the steady-state fixation period before the go stimulus is presented and find that the blocked-input model fits better than the interactive race model. We consider a model in which fixation activity is boosted when a stop signal occurs and find that it fits as well as the blocked input model but predicts very high steady-state fixation activity after the response is inhibited. We discuss the alternative linking propositions that connect computational models to neural mechanisms, the lessons to be learned from model mimicry, and generalization from countermanding saccades to countermanding other kinds of responses.

Revisiting the evidence for collapsing boundaries and urgency signals in perceptual decision-making

For nearly 50 years, the dominant account of decision-making holds that noisy information is accumulated until a fixed threshold is crossed. This account has been tested extensively against behavioral and neurophysiological data for decisions about consumer goods, perceptual stimuli, eyewitness testimony, memories, and dozens of other paradigms, with no systematic misfit between model and data. Recently, the standard model has been challenged by alternative accounts that assume that less evidence is required to trigger a decision as time passes. Such "collapsing boundaries" or "urgency signals" have gained popularity in some theoretical accounts of neurophysiology. Nevertheless, evidence in favor of these models is mixed, with support coming from only a narrow range of decision paradigms compared with a long history of support from dozens of paradigms for the standard theory. We conducted the first large-scale analysis of data from humans and nonhuman primates across three distinct paradigms using powerful model-selection methods to compare evidence for fixed versus collapsing bounds. Overall, we identified evidence in favor of the standard model with fixed decision boundaries. We further found that evidence for static or dynamic response boundaries may depend on specific paradigms or procedures, such as the extent of task practice. We conclude that the difficulty of selecting between collapsing and fixed bounds models has received insufficient attention in previous research, calling into question some previous results.

The what, where, and why of priority maps and their interactions with visual working memory

Priority maps are winner-take-all neural mechanisms thought to guide the allocation of covert and overt attention. Here, we go beyond this standard definition and argue that priority maps play a much broader role in controlling goal-directed behavior. We start by defining what priority maps are and where they might be found in the brain; we then ask why they exist-the function that they serve. We propose that this function is to communicate a goal state to the different effector systems, thereby guiding behavior. Within this framework, we speculate on how priority maps interact with visual working memory and introduce our common source hypothesis, the suggestion that this goal state is maintained in visual working memory and used to construct all of the priority maps controlling the various motor systems. Finally, we look ahead and suggest questions about priority maps that should be asked next.

Reach target selection in humans using ambiguous decision cues containing variable amounts of conflicting sensory evidence supporting each target choice

Human subjects chose between two color-coded reach targets using multicolored checkerboard-like decision cues (DCs) that presented variable amounts of conflicting sensory evidence supporting both target choices. Different DCs contained different numbers of small squares of the two target colors. The most ambiguous DCs contained nearly equal numbers of squares of both target colors. The subjects reached as soon as they selected a target after the appearance of the DC (“choose-and-go” task). The choice behavior of the subjects showed many similarities to prior studies using other stimulus properties (e.g., visual motion coherence, brightness), including progressively longer response times and higher target-choice error rates for more ambiguous DCs. However, certain trends in their choice behavior could not be fully captured by simple drift-diffusion models. Allowing the subjects to view the DCs for a period of time before presenting the targets (“match-to-sample” task) resulted in much shorter response times overall, but also revealed a reluctance of subjects to commit to a decision about the predominant color of the more ambiguous DCs during the initial extended observation period. Model processing and simulation analyses suggest that the subjects might adjust the dynamics of their decision-making process on a trial-to-trial basis in response to the variable level of ambiguous and conflicting evidence in different DCs between trials.

A mechanism for decision rule discrimination by supplementary eye field neurons

A decision to select an action from alternatives is often guided by rules that flexibly map sensory inputs to motor outputs when certain conditions are satisfied. However, the neural mechanisms underlying rule-based decision making remain poorly understood. Two complementary types of neurons in the supplementary eye field (SEF) of macaques have been identified that modulate activity differentially to interpret rules in an ocular go-nogo task, which stipulates that the animal either visually pursue a moving object if it intersects a visible zone ('go'), or maintain fixation if it does not ('nogo'). These neurons discriminate between go and nogo rule-states by increasing activity to signal their preferred (agonist) rule-state and decreasing activity to signal their non-preferred (antagonist) rule-state. In the current study, we found that SEF neurons decrease activity in anticipation of the antagonist rule-state, and do so more rapidly when the rule-state is easier to predict. This rapid decrease in activity could underlie a process of elimination in which trajectories that do not invoke the preferred rule-state receive no further computational resources. Furthermore, discrimination between difficult and easy trials in the antagonist rule-state occurs prior to when discrimination within the agonist rule-state occurs. A winner-take-all like model that incorporates a pair of mutually inhibited integrators to accumulate evidence in favor of either the decision to pursue or the decision to continue fixation accounts for the observed neural phenomena.

Encoding and decoding in parietal cortex during sensorimotor decision-making

The lateral intraparietal area (LIP) of macaques has been asserted to play a fundamental role in sensorimotor decision-making. Here we dissect the neural code in LIP at the level of individual trial spike trains using a statistical approach based on generalized linear models. We show that LIP responses reflect a combination of temporally-overlapping task and decision-related signals. Our model accounts for the detailed statistics of LIP spike trains, and accurately predicts spike trains from task events on single trials. Moreover, we derive an optimal decoder for heterogeneous, multiplexed LIP responses that could be implemented in biologically plausible circuits. In contrast to interpretations of LIP as providing an instantaneous code for decision variables, we show that optimal decoding requires integrating LIP spikes over two timescales. These analyses provide a detailed understanding of the neural code in LIP, and a framework for studying the coding of multiplexed signals in higher brain areas.

LATER models of neural decision behavior in choice tasks

Reaction time has been increasingly used over the last few decades to provide information on neural decision processes: it is a direct reflection of decision time. Saccades provide an excellent paradigm for this because many of them can be made in a very short time and the underlying neural pathways are relatively well-known. LATER (linear approach to threshold with ergodic rate) is a model originally devised to explain reaction time distributions in simple decision tasks. Recently, however it is being extended to increasingly more advanced tasks, including those with decision errors and those requiring voluntary control such as the antisaccade task and those where sequential decisions are required. The strength of this modeling approach lies in its detailed, quantitative predictions of behavior, yet LATER models still retain their conceptual simplicity that made LATER initially successful in explaining reaction times in simple decision tasks.

On the neural implementation of the speed-accuracy trade-off

Decisions are faster and less accurate when conditions favor speed, and are slower and more accurate when they favor accuracy. This phenomenon is referred to as the speed-accuracy trade-off (SAT). Behavioral studies of the SAT have a long history, and the data from these studies are well characterized within the framework of bounded integration. According to this framework, decision makers accumulate noisy evidence until the running total for one of the alternatives reaches a bound. Lower and higher bounds favor speed and accuracy respectively, each at the expense of the other. Studies addressing the neural implementation of these computations are a recent development in neuroscience. In this review, we describe the experimental and theoretical evidence provided by these studies. We structure the review according to the framework of bounded integration, describing evidence for (1) the modulation of the encoding of evidence under conditions favoring speed or accuracy, (2) the modulation of the integration of encoded evidence, and (3) the modulation of the amount of integrated evidence sufficient to make a choice. We discuss commonalities and differences between the proposed neural mechanisms, some of their assumptions and simplifications, and open questions for future work. We close by offering a unifying hypothesis on the present state of play in this nascent research field.

Response inhibition during perceptual decision making in humans and macaques

Response inhibition in stop signal tasks has been explained as the outcome of a race between GO and STOP processes (e.g., Logan, 1981). Response choice in two-alternative perceptual categorization tasks has been explained as the outcome of an accumulation of evidence for the alternative responses. To begin unifying these two powerful investigation frameworks, we obtained data from humans and macaque monkeys performing a stop signal task with responses guided by perceptual categorization and variable degrees of difficulty, ranging from low to high accuracy. Comparable results across species reinforced the validity of this animal model. Response times and errors increased with categorization difficulty. The probability of failing to inhibit responses on stop signal trials increased with stop signal delay, and the response times for failed stop signal trials were shorter than those for trials with no stop signal. Thus, the Logan race model could be applied to estimate the duration of the stopping process. We found that the duration of the STOP process did not vary across a wide range of discrimination accuracies. This is consistent with the functional, and possibly mechanistic, independence of choice and inhibition mechanisms.

Brain and behavior in decision-making

Speed-accuracy tradeoff (SAT) is an adaptive process balancing urgency and caution when making decisions. Computational cognitive theories, known as “evidence accumulation models”, have explained SATs via a manipulation of the amount of evidence necessary to trigger response selection. New light has been shed on these processes by single-cell recordings from monkeys who were adjusting their SAT settings. Those data have been interpreted as inconsistent with existing evidence accumulation theories, prompting the addition of new mechanisms to the models. We show that this interpretation was wrong, by demonstrating that the neural spiking data, and the behavioural data are consistent with existing evidence accumulation theories, without positing additional mechanisms. Our approach succeeds by using the neural data to provide constraints on the cognitive model. Open questions remain about the locus of the link between certain elements of the cognitive models and the neurophysiology, and about the relationship between activity in cortical neurons identified with decision-making vs. activity in downstream areas more closely linked with motor effectors.

In everyday life we constantly balance urgency against caution when making decisions – known as the speed-accuracy tradeoff. Traditionally, computational cognitive theories called “evidence accumulation models” have explained the speed accuracy tradeoff as changes in the amount of evidence necessary to trigger the selection of a response. Recent work recording firing rates from the neurons of monkeys while they made decisions revealed an apparent discrepancy between the firing rates and the way evidence accumulation models explain the speed-accuracy tradeoff. This discrepancy was interpreted as showing that traditional parameter settings were wrong, and that the fundamental dynamic structure of the evidence accumulation model required an addition. This result is important because it calls into question nearly half a century of cognitive science. We show instead that only the parameter settings need be adjusted, not the basic model structure, in order to account for the behavioural data and the recorded neural data. Underlying our results was an integrated approach to the neural and behavioral data, allowing both streams to inform the theoretical development.

The speed-accuracy tradeoff: history, physiology, methodology, and behavior

There are few behavioral effects as ubiquitous as the speed-accuracy tradeoff (SAT). From insects to rodents to primates, the tendency for decision speed to covary with decision accuracy seems an inescapable property of choice behavior. Recently, the SAT has received renewed interest, as neuroscience approaches begin to uncover its neural underpinnings and computational models are compelled to incorporate it as a necessary benchmark. The present work provides a comprehensive overview of SAT. First, I trace its history as a tractable behavioral phenomenon and the role it has played in shaping mathematical descriptions of the decision process. Second, I present a "users guide" of SAT methodology, including a critical review of common experimental manipulations and analysis techniques and a treatment of the typical behavioral patterns that emerge when SAT is manipulated directly. Finally, I review applications of this methodology in several domains.

Performance monitoring in monkey frontal eye field

The frontal eye fields (FEF) are thought to mediate response selection during oculomotor decision tasks. In addition, many FEF neurons have robust postsaccadic responses, but their role in postchoice evaluative processes (online performance monitoring) is only beginning to become apparent. Here we report error-related neural activity in FEF while monkeys performed a biased speed-categorization task that enticed the animals to make impulsive errors. Twenty-three percent of cells in macaque FEF coded an internally generated error-related signal, and many of the same cells also coded task difficulty. The observed responses are primarily consistent with three related concepts that have been associated with performance monitoring: (1) response conflict; (2) uncertainty; and (3) reward prediction. Overall, our findings suggest a novel role for the FEF as part of the neural network that evaluates the preceding choice to optimize behavior in the future.

Humans optimize decision-making by delaying decision onset

Why do humans make errors on seemingly trivial perceptual decisions? It has been shown that such errors occur in part because the decision process (evidence accumulation) is initiated before selective attention has isolated the relevant sensory information from salient distractors. Nevertheless, it is typically assumed that subjects increase accuracy by prolonging the decision process rather than delaying decision onset. To date it has not been tested whether humans can strategically delay decision onset to increase response accuracy. To address this question we measured the time course of selective attention in a motion interference task using a novel variant of the response signal paradigm. Based on these measurements we estimated time-dependent drift rate and showed that subjects should in principle be able trade speed for accuracy very effectively by delaying decision onset. Using the time-dependent estimate of drift rate we show that subjects indeed delay decision onset in addition to raising response threshold when asked to stress accuracy over speed in a free reaction version of the same motion-interference task. These findings show that decision onset is a critical aspect of the decision process that can be adjusted to effectively improve decision accuracy.

Spatial patterns of fixation-switch behavior in strabismic monkeys

PURPOSE

Patients with strabismus perceptually suppress information from one eye to avoid double vision. Mechanisms of visual suppression likely lead to fixation-switch behavior wherein the subject acquires targets with a specific eye depending on target location in space. The purpose of this study was to investigate spatial patterns of fixation-switch behavior in strabismic monkeys.

METHODS

Eye movements were acquired in three exotropic and one esotropic monkey in a binocular viewing saccade task. Spatial patterns of fixation were analyzed by calculating incidence of using either eye to fixate targets presented at various gaze locations.

RESULTS

Broadly, spatial fixation patterns and fixation-switch behavior followed expectations if a portion of the temporal retina was suppressed in exotropia and a portion of the nasal retina was suppressed in esotropia. Fixation-switch occurred for horizontal target locations that were approximately greater than halfway between the lines of sight of the foveating and strabismic eyes. Surprisingly, the border between right eye and left eye fixation zones was not sharply defined and there was a significant extent (>10°) over which the monkeys could acquire a target with either eye.

CONCLUSIONS

We propose that spatial fixation patterns in strabismus can be accounted for in a decision framework wherein the oculomotor system has access to retinal error information from each eye and the brain chooses between them to prepare a saccade. For target locations approximately midway between the two foveae, strength of retinal error representations from each eye is almost equal, leading to trial-to-trial variability in choice of fixating eye.

Modeling the effect of selection history on pop-out visual search

While attentional effects in visual selection tasks have traditionally been assigned “top-down” or “bottom-up” origins, more recently it has been proposed that there are three major factors affecting visual selection: (1) physical salience, (2) current goals and (3) selection history. Here, we look further into selection history by investigating Priming of Pop-out (POP) and the Distractor Preview Effect (DPE), two inter-trial effects that demonstrate the influence of recent history on visual search performance. Using the Ratcliff diffusion model, we model observed saccadic selections from an oddball search experiment that included a mix of both POP and DPE conditions. We find that the Ratcliff diffusion model can effectively model the manner in which selection history affects current attentional control in visual inter-trial effects. The model evidence shows that bias regarding the current trial's most likely target color is the most critical parameter underlying the effect of selection history. Our results are consistent with the view that the 3-item color-oddball task used for POP and DPE experiments is best understood as an attentional decision making task.

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.

Not just the norm: exemplar-based models also predict face aftereffects

The face recognition literature has considered two competing accounts of how faces are represented within the visual system: Exemplar-based models assume that faces are represented via their similarity to exemplars of previously experienced faces, while norm-based models assume that faces are represented with respect to their deviation from an average face, or norm. Face identity aftereffects have been taken as compelling evidence in favor of a norm-based account over an exemplar-based account. After a relatively brief period of adaptation to an adaptor face, the perceived identity of a test face is shifted toward a face with attributes opposite to those of the adaptor, suggesting an explicit psychological representation of the norm. Surprisingly, despite near universal recognition that face identity aftereffects imply norm-based coding, there have been no published attempts to simulate the predictions of norm- and exemplar-based models in face adaptation paradigms. Here, we implemented and tested variations of norm and exemplar models. Contrary to common claims, our simulations revealed that both an exemplar-based model and a version of a two-pool norm-based model, but not a traditional norm-based model, predict face identity aftereffects following face adaptation.

An exemplar of model-based cognitive neuroscience

Are categories learned by forming abstract prototypes or by remembering specific exemplars? Mack, Preston, and Love observed that patterns of functional MRI (fMRI) brain activity were more consistent with patterns of representations predicted by exemplar models than by prototype models. Their work represents the theoretical power of emerging approaches to model-based cognitive neuroscience.

Perceptual modulation of motor--but not visual--responses in the frontal eye field during an urgent-decision task

Neuronal activity in the frontal eye field (FEF) ranges from purely motor (related to saccade production) to purely visual (related to stimulus presence). According to numerous studies, visual responses correlate strongly with early perceptual analysis of the visual scene, including the deployment of spatial attention, whereas motor responses do not. Thus, functionally, the consensus is that visually responsive FEF neurons select a target among visible objects, whereas motor-related neurons plan specific eye movements based on such earlier target selection. However, these conclusions are based on behavioral tasks that themselves promote a serial arrangement of perceptual analysis followed by motor planning. So, is the presumed functional hierarchy in FEF an intrinsic property of its circuitry or does it reflect just one possible mode of operation? We investigate this in monkeys performing a rapid-choice task in which, crucially, motor planning always starts ahead of task-critical perceptual analysis, and the two relevant spatial locations are equally informative and equally likely to be target or distracter. We find that the choice is instantiated in FEF as a competition between oculomotor plans, in agreement with model predictions. Notably, although perception strongly influences the motor neurons, it has little if any measurable impact on the visual cells; more generally, the more dominant the visual response, the weaker the perceptual modulation. The results indicate that, contrary to expectations, during rapid saccadic choices perceptual information may directly modulate ongoing saccadic plans, and this process is not contingent on prior selection of the saccadic goal by visually driven FEF responses.

Production, control, and visual guidance of saccadic eye movements

Primate vision is served by rapid shifts of gaze called saccades. This review will survey current knowledge and particular problems concerning the neural control and guidance of gaze shifts.

Neural chronometry and coherency across speed-accuracy demands reveal lack of homomorphism between computational and neural mechanisms of evidence accumulation

The stochastic accumulation framework provides a mechanistic, quantitative account of perceptual decision-making and how task performance changes with experimental manipulations. Importantly, it provides an elegant account of the speed-accuracy trade-off (SAT), which has long been the litmus test for decision models, and also mimics the activity of single neurons in several key respects. Recently, we developed a paradigm whereby macaque monkeys trade speed for accuracy on cue during visual search task. Single-unit activity in frontal eye field (FEF) was not homomorphic with the architecture of models, demonstrating that stochastic accumulators are an incomplete description of neural activity under SAT. This paper summarizes and extends this work, further demonstrating that the SAT leads to extensive, widespread changes in brain activity never before predicted. We will begin by reviewing our recently published work that establishes how spiking activity in FEF accomplishes SAT. Next, we provide two important extensions of this work. First, we report a new chronometric analysis suggesting that increases in perceptual gain with speed stress are evident in FEF synaptic input, implicating afferent sensory-processing sources. Second, we report a new analysis demonstrating selective influence of SAT on frequency coupling between FEF neurons and local field potentials. None of these observations correspond to the mechanics of current accumulator models.

Competitive Integration of Visual and Goal-related Signals on Neuronal Accumulation Rate: A Correlate of Oculomotor Capture in the Superior Colliculus

The mechanisms that underlie the integration of visual and goal-related signals for the production of saccades remain poorly understood. Here, we examined how spatial proximity of competing stimuli shapes goal-directed responses in the superior colliculus (SC), a midbrain structure closely associated with the control of visual attention and eye movements. Monkeys were trained to perform an oculomotor-capture task [Theeuwes, J., Kramer, A. F., Hahn, S., Irwin, D. E., & Zelinsky, G. J. Influence of attentional capture on oculomotor control. Journal of Experimental Psychology. Human Perception and Performance, 25, 1595–1608, 1999], in which a target singleton was revealed via an isoluminant color change in all but one item. On a portion of the trials, an additional salient item abruptly appeared near or far from the target. We quantified how spatial proximity between the abrupt-onset and the target shaped the goal-directed response. We found that the appearance of an abrupt-onset near the target induced a transient decrease in goal-directed discharge of SC visuomotor neurons. Although this was indicative of spatial competition, it was immediately followed by a rebound in presaccadic activation, which facilitated the saccadic response (i.e., it induced shorter saccadic RT). A similar suppression also occurred at most nontarget locations even in the absence of the abrupt-onset. This is indicative of a mechanism that enabled monkeys to quickly discount stimuli that shared the common nontarget feature. These results reveal a pattern of excitation/inhibition across the SC visuomotor map that acted to facilitate optimal behavior—the short duration suppression minimized the probability of capture by salient distractors, whereas a subsequent boost in accumulation rate ensured a fast goal-directed response. Such nonlinear dynamics should be incorporated into future biologically plausible models of saccade behavior.