Bridging Neural and Computational Viewpoints on Perceptual Decision-Making
Authors: Redmond G. O’Connell, Michael N. Shadlen, KongFatt Wong-Lin, Simon P. Kelly
Journal: Trends in Neurosciences (2018)

Sequential sampling models have been widely embraced in contemporary decision neuroscience. The models come in many forms that, despite containing fundamentally different algorithmic elements, can make highly similar predictions for behaviour. Consequently, it can be difficult to definitively adjudicate between alternative models based solely on quantitative fits to behaviour. The discovery of brain signals that reflect key neural computations underpinning decision-making is opening new avenues for empirically testing and refining model predictions. Neurophysiological research is highlighting the multilayered neural architecture for implementing even the most elementary sensorimotor decisions. We do not yet know how many processing layers are required nor what distinct computations are performed at each layer. Sequential sampling models have provided a dominant theoretical framework guiding computational and neurophysiological investigations of perceptual decision-making. While these models share the basic principle that decisions are formed by accumulating sensory evidence to a bound, they come in many forms that can make similar predictions of choice behaviour despite invoking fundamentally different mechanisms. The identification of neural signals that reflect some of the core computations underpinning decision formation offers new avenues for empirically testing and refining key model assumptions. Here, we highlight recent efforts to explore these avenues and, in so doing, consider the conceptual and methodological challenges that arise when seeking to infer decision computations from complex neural data. Sequential sampling models have provided a dominant theoretical framework guiding computational and neurophysiological investigations of perceptual decision-making. While these models share the basic principle that decisions are formed by accumulating sensory evidence to a bound, they come in many forms that can make similar predictions of choice behaviour despite invoking fundamentally different mechanisms. The identification of neural signals that reflect some of the core computations underpinning decision formation offers new avenues for empirically testing and refining key model assumptions. Here, we highlight recent efforts to explore these avenues and, in so doing, consider the conceptual and methodological challenges that arise when seeking to infer decision computations from complex neural data. The term 'decision-making' often calls to mind scenarios such as voting in an election or selecting a course of study. Yet, even simply perceiving our sensory environment relies on a continuous stream of elementary judgments, known as 'perceptual decisions'. In some cases, perceptual decisions can be as consequential as those requiring more abstract judgements (e.g., is the traffic light red or green?). In the highly complex and dynamic environment that we inhabit, making accurate and timely decisions is a considerable challenge for the brain, since the information it receives is almost always to some degree unreliable. Understanding how the brain overcomes the challenges associated with perceptual decision-making could also illuminate broader principles of computation that extend to a range of cognitive operations [1Shadlen M.N. Kiani R. Decision making as a window on cognition.Neuron. 2013; 80: 791-806Abstract Full Text Full Text PDF PubMed Scopus (157) Google Scholar]. The theoretical foundations for modern research on perceptual decision-making were laid within mathematical psychology, with the development of 'sequential sampling' or evidence accumulation (see Glossary) models [2Laming D.R.J. Information Theory of Choice-Reaction Times. Academic Press, 1968Google Scholar, 3Link S.W. The Wave Theory of Difference and Similarity. Laurence Erlbaum Associates, 1992Google Scholar, 4Link S.W. Heath R.A. A sequential theory of psychological discrimination.Psychometrika. 1975; 40: 77-105Crossref Scopus (0) Google Scholar, 5Ratcliff R. A theory of memory retrieval.Psychol. Rev. 1978; 83: 59-108Crossref Scopus (0) Google Scholar, 6Vickers D. Decision Processes in Visual Perception. Academic Press, 1979Google Scholar]. These models have a long history of successfully accounting for choice behaviour in a range of contexts and, in addition, the core computations that they specify appear to be mirrored in certain components of neural activity in the rodent [7Hanks T.D. et al.Distinct relationships of parietal and prefrontal cortices to evidence accumulation.Nature. 2015; 520: 220-223Crossref PubMed Scopus (113) Google Scholar], monkey [8Gold J.I. Shadlen M.N. The neural basis of decision making.Annu. Rev. Neurosci. 2007; 30: 535-574Crossref PubMed Scopus (1574) Google Scholar, 9Shadlen M.N. et al.Comment on 'Single-trial spike trains in parietal cortex reveal discrete steps during decision-making'.Science. 2016; 351: 1406Crossref PubMed Scopus (5) Google Scholar], and human brain [10Kelly S.P. O'Connell R.G. The neural processes underlying perceptual decision making in humans: recent progress and future directions.J. Physiol. 2015; 109: 27-37Google Scholar]. Consequently, recent years have witnessed a growth and confluence in research efforts to identify the computations through which perceptual decisions are formed, as well as to map, measure, and manipulate the neural structures and processes through which they are implemented, all anchored to the framework of sequential sampling. These continuing advances have given rise to an expanding repertoire of approaches combining neural and computational viewpoints [11Turner B.M. et al.Approaches to analysis in model-based cognitive neuroscience.J. Math. Psychol. 2017; 76: 65-79Crossref PubMed Scopus (20) Google Scholar]. In this review, we shine a spotlight on recent trends in using one such approach, where neural signals reflecting key aspects of bounded evidence accumulation are used to inform abstract decision models. We discuss the potential of this approach in providing strong grounds for model adjudication in cases where behavioural modelling alone falls short and, thus, for advancing important theoretical debates about decision computations. We also highlight the conceptual and methodological challenges involved. Sequential sampling models were originally based on normative models for minimising the time taken to achieve a certain level of quality-control accuracy [12Wald A. Sequential Analysis. Wiley, 1947Google Scholar]. Sequential sampling models provide quantitatively accurate accounts of behaviour on a range of tasks, including perceptual detections and discriminations, lexical memory, response inhibition, and even social and value-based decisions (comprehensively reviewed in [13Ratcliff R. et al.Diffusion decision model: current issues and history.Trends Cogn. Sci. 2016; 20: 260-281Abstract Full Text Full Text PDF PubMed Scopus (146) Google Scholar, 14Forstmann B.U. et al.Sequential sampling models in cognitive neuroscience: advantages, applications, and extensions.Annu. Rev. Psychol. 2016; 67: 641-666Crossref PubMed Scopus (79) Google Scholar]). This powerful class of psychological process models can explain both random and systematic variations in performance. Furthermore, these models can decompose choice reaction times and accuracy into meaningful latent parameters, such as the strength of the evidence entering the decision process ('drift rate'; i.e., the expectation of the evidence distribution being sampled) and the cumulative quantity required to trigger commitment ('decision bound'). Ongoing research based on these behavioural models continues to fruitfully examine how decisions are shaped by factors such as speed pressure, value, prior knowledge, and distracting information, as well as how perceptual decisions are affected by brain disorders [14Forstmann B.U. et al.Sequential sampling models in cognitive neuroscience: advantages, applications, and extensions.Annu. Rev. Psychol. 2016; 67: 641-666Crossref PubMed Scopus (79) Google Scholar]. Many model variants exist because there are many alternative implementations of a decision process based on sequential sampling (Box 1). In many cases, competing model variants based on fundamentally different mechanisms can produce the same behavioural signature. This problem of model mimicry significantly hampers adjudication between competing accounts, and has given rise to several longstanding debates. To take an instructive example, there is ongoing disagreement about whether the criterion amount of evidence that we require to reach commitment can dynamically change during the course of a decision.Box 1Sequential Sampling Models: Different Flavours for Different Research ObjectivesOver the years, several decision model variants have been developed based on the core principles of sequential sampling and bounded evidence accumulation. In standard, 1D diffusion models, for example, a sequence of samples from a Gaussian distribution representing noisy sensory evidence with, say, mean μ∆t ('drift rate') and variance Δt, is accumulated until the cumulant reaches an upper or lower bound. The drift rate scales with stimulus strength and the bounds are set to achieve a balance between speed and accuracy demands. The subject's overall response time is modelled as a sum of the time it takes this diffusion process to reach the bound, and a 'nondecision' time accounting for additional delays associated with encoding, routing [100Shadlen M.N. Shohamy D. Decision making and sequential sampling from memory.Neuron. 2016; 90: 927-939Abstract Full Text Full Text PDF PubMed Google Scholar] and/or motor execution processes. In a popular, versatile version of this model, three of the parameters (the starting point, drift rate and nondecision time) are not fixed but rather can vary randomly from trial to trial, which provides significant flexibility to capture relatively fast or slow errors and specific RT distribution shapes [64Ratcliff R. McKoon G. The diffusion decision model: theory and data for two-choice decision tasks.Neural Comput. 2008; 20: 873-922Crossref PubMed Scopus (914) Google Scholar].Both simpler and more complex versions of this model have been developed, and the choice among these depends on research goals. In general, cognitive modelling is primarily concerned with forging abstract mathematical accounts of behaviour, the parameters of which serve as mechanistically interpretable metrics of task performance. Unlike neural or biophysical modelling, cognitive models do not generally strive to represent details of neurophysiological implementation [101Busemeyer J.R. Diederich A. Cognitive Modeling. Sage, 2010Google Scholar]. Several reduced models have been developed to achieve this with computational ease, for example by excluding trial-to-trial variability parameters, where the relative speed of error responses is not critical [102Wagenmakers E.J. et al.An EZ-diffusion model for response time and accuracy.Psychon. Bull. Rev. 2007; 14: 3-22Crossref PubMed Scopus (297) Google Scholar], or by excluding the within-trial noise parameter ('ballistic,' racing accumulators [103Reddi B.A. et al.Accuracy, information, and response time in a saccadic decision task.J. Neurophysiol. 2003; 90: 3538-3546Crossref PubMed Scopus (0) Google Scholar, 104Brown S.D. Heathcote A. The simplest complete model of choice response time: linear ballistic accumulation.Cogn. Psychol. 2008; 57: 153-178Crossref PubMed Scopus (436) Google Scholar]).Toward the more complex end, the leaky competing accumulator model of Usher and McClelland [105Usher M. McClelland J.L. On the time course of perceptual choice: the leaky competing accumulator model.Psychol. Rev. 2001; 108: 550-592Crossref PubMed Google Scholar] parameterises both the degree of competition between alternative accumulators and the leak of information within them, which provides one way to explain limited improvements in accuracy with longer viewing durations. Cortical microcircuit models have been developed that reproduce complex dynamical aspects of neural build-up patterns as well as decision behaviour [40Wang X.J. Probabilistic decision making by slow reverberation in cortical circuits.Neuron. 2002; 36: 955-968Abstract Full Text Full Text PDF PubMed Scopus (590) Google Scholar, 106Wong K.F. Wang X.J. A recurrent network mechanism of time integration in perceptual decisions.J. Neurosci. 2006; 26: 1314-1328Crossref PubMed Scopus (398) Google Scholar], and incorporate well-known motor control circuits, such as the basal ganglia [107Wiecki T.V. Frank M.J. A computational model of inhibitory control in frontal cortex and basal ganglia.Psychol. Rev. 2013; 120: 329-355Crossref PubMed Scopus (146) Google Scholar]. An ongoing challenge is to establish a straightforward mapping between elements of these sometimes complex circuit models and the parameters of the more abstract models. Although cognitive and neural modelling have ostensibly distinct goals, there is valuable but underexploited territory at the interface between them, where models could capture key elements of neural implementation at distinct levels of the sensorimotor hierarchy as well as detailed behavioural trends. Over the years, several decision model variants have been developed based on the core principles of sequential sampling and bounded evidence accumulation. In standard, 1D diffusion models, for example, a sequence of samples from a Gaussian distribution representing noisy sensory evidence with, say, mean μ∆t ('drift rate') and variance Δt, is accumulated until the cumulant reaches an upper or lower bound. The drift rate scales with stimulus strength and the bounds are set to achieve a balance between speed and accuracy demands. The subject's overall response time is modelled as a sum of the time it takes this diffusion process to reach the bound, and a 'nondecision' time accounting for additional delays associated with encoding, routing [100Shadlen M.N. Shohamy D. Decision making and sequential sampling from memory.Neuron. 2016; 90: 927-939Abstract Full Text Full Text PDF PubMed Google Scholar] and/or motor execution processes. In a popular, versatile version of this model, three of the parameters (the starting point, drift rate and nondecision time) are not fixed but rather can vary randomly from trial to trial, which provides significant flexibility to capture relatively fast or slow errors and specific RT distribution shapes [64Ratcliff R. McKoon G. The diffusion decision model: theory and data for two-choice decision tasks.Neural Comput. 2008; 20: 873-922Crossref PubMed Scopus (914) Google Scholar]. Both simpler and more complex versions of this model have been developed, and the choice among these depends on research goals. In general, cognitive modelling is primarily concerned with forging abstract mathematical accounts of behaviour, the parameters of which serve as mechanistically interpretable metrics of task performance. Unlike neural or biophysical modelling, cognitive models do not generally strive to represent details of neurophysiological implementation [101Busemeyer J.R. Diederich A. Cognitive Modeling. Sage, 2010Google Scholar]. Several reduced models have been developed to achieve this with computational ease, for example by excluding trial-to-trial variability parameters, where the relative speed of error responses is not critical [102Wagenmakers E.J. et al.An EZ-diffusion model for response time and accuracy.Psychon. Bull. Rev. 2007; 14: 3-22Crossref PubMed Scopus (297) Google Scholar], or by excluding the within-trial noise parameter ('ballistic,' racing accumulators [103Reddi B.A. et al.Accuracy, information, and response time in a saccadic decision task.J. Neurophysiol. 2003; 90: 3538-3546Crossref PubMed Scopus (0) Google Scholar, 104Brown S.D. Heathcote A. The simplest complete model of choice response time: linear ballistic accumulation.Cogn. Psychol. 2008; 57: 153-178Crossref PubMed Scopus (436) Google Scholar]). Toward the more complex end, the leaky competing accumulator model of Usher and McClelland [105Usher M. McClelland J.L. On the time course of perceptual choice: the leaky competing accumulator model.Psychol. Rev. 2001; 108: 550-592Crossref PubMed Google Scholar] parameterises both the degree of competition between alternative accumulators and the leak of information within them, which provides one way to explain limited improvements in accuracy with longer viewing durations. Cortical microcircuit models have been developed that reproduce complex dynamical aspects of neural build-up patterns as well as decision behaviour [40Wang X.J. Probabilistic decision making by slow reverberation in cortical circuits.Neuron. 2002; 36: 955-968Abstract Full Text Full Text PDF PubMed Scopus (590) Google Scholar, 106Wong K.F. Wang X.J. A recurrent network mechanism of time integration in perceptual decisions.J. Neurosci. 2006; 26: 1314-1328Crossref PubMed Scopus (398) Google Scholar], and incorporate well-known motor control circuits, such as the basal ganglia [107Wiecki T.V. Frank M.J. A computational model of inhibitory control in frontal cortex and basal ganglia.Psychol. Rev. 2013; 120: 329-355Crossref PubMed Scopus (146) Google Scholar]. An ongoing challenge is to establish a straightforward mapping between elements of these sometimes complex circuit models and the parameters of the more abstract models. Although cognitive and neural modelling have ostensibly distinct goals, there is valuable but underexploited territory at the interface between them, where models could capture key elements of neural implementation at distinct levels of the sensorimotor hierarchy as well as detailed behavioural trends. In the most widely subscribed models [13Ratcliff R. et al.Diffusion decision model: current issues and history.Trends Cogn. Sci. 2016; 20: 260-281Abstract Full Text Full Text PDF PubMed Scopus (146) Google Scholar] (Box 1), although the bounds can be adjusted across different contexts to emphasise speed versus accuracy, in any given trial the bounds are assumed to be constant over time. Yet, 'collapsing' bounds (i.e., ones that decrease over time within a trial) provide an optimal policy according to normative theory under the common situation where evidence strength varies unpredictably across trials and is sometimes weak [15Malhotra G. et al.Time-varying decision boundaries: insights from optimality analysis.Psychon. Bull. Rev. 2017; 25: 971-996Crossref Scopus (1) Google Scholar, 16Drugowitsch J. et al.The cost of accumulating evidence in perceptual decision making.J. Neurosci. 2012; 32: 3612-3628Crossref PubMed Scopus (170) Google Scholar], or where responses must be made within a strict deadline [15Malhotra G. et al.Time-varying decision boundaries: insights from optimality analysis.Psychon. Bull. Rev. 2017; 25: 971-996Crossref Scopus (1) Google Scholar, 17Frazier P. Yu A.J. Sequential hypothesis testing under stochastic deadlines.Adv. Neural. Inf. Process Syst. 2008; 20: 465-472Google Scholar]. One of the main reasons why collapsing bounds have not been incorporated in the dominant models is because key behavioural consequences of doing so, such as decreased accuracy for trials with longer reaction times, can be also produced within a drift diffusion model with constant bounds, via an alternative mechanism involving trial-to-trial variability in drift rate [13Ratcliff R. et al.Diffusion decision model: current issues and history.Trends Cogn. Sci. 2016; 20: 260-281Abstract Full Text Full Text PDF PubMed Scopus (146) Google Scholar] (Figure 1). Establishing the relative prominence of these alternative mechanisms in choice behaviour has consequences beyond matters of preference in model-fitting approaches. These alternative accounts reflect fundamentally different algorithmic elements and, therefore, adjudicating between them has important implications for our understanding of normal and abnormal decision-making. For example, there has been an increasing application of sequential sampling models in studies seeking to better understand decision-making deficits observed in psychiatric populations [18Hauser T.U. et al.Increased decision thresholds trigger extended information gathering across the compulsivity spectrum.Transl. Psychiatry. 2017; 7: 1296Crossref PubMed Scopus (0) Google Scholar, 19Ziegler S. et al.Modelling ADHD: a review of ADHD theories through their predictions for computational models of decision-making and reinforcement learning.Neurosci. Biobehav. 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If relatively slow response times were observed for error responses in a given clinical population (e.g., [21Huang Y.T. et al.Different effects of dopaminergic medication on perceptual decision-making in Parkinson's disease as a function of task difficulty and speed-accuracy instructions.Neuropsychologia. 2015; 75: 577-587Crossref PubMed Scopus (9) Google Scholar]), an explanation based on a faster bound collapse (e.g., due to a more impulsive decision policy or aversion to missed deadlines) would have different implications than one based on greater drift rate variability (e.g., due to fluctuations in attentional engagement, see below for further discussion), with respect to both explanatory accounts of the disorder and efforts to treat it. Similarly, an increasing trend in human neuroimaging research is to use decision model parameter estimates from behavioural data fits in statistical analyses to localise decision-relevant brain regions [11Turner B.M. et al.Approaches to analysis in model-based cognitive neuroscience.J. Math. Psychol. 2017; 76: 65-79Crossref PubMed Scopus (20) Google Scholar, 22van Maanen L. et al.Neural correlates of trial-to-trial fluctuations in response caution.J. Neurosci. 2011; 31: 17488-17495Crossref PubMed Scopus (91) Google Scholar]. Here, again, the particular choice of model could have major consequences both for the particular areas identified and the interpretation of the role they might actually have in decision formation [23O'Reilly J.X. Mars R.B. Computational neuroimaging: localising Greek letters? Comment on Forstmann et al.Trends Cogn. Sci. 2011; 15: 450Abstract Full Text Full Text PDF PubMed Google Scholar]. In behavioural model comparisons between two mechanisms that produce the same qualitative behavioural pattern, the outcome can greatly depend on the number and nature of the parameters used to implement those mechanisms. To take an example relevant to the above debate, Hawkins et al. [24Hawkins G.E. et al.Revisiting the evidence for collapsing boundaries and urgency signals in perceptual decision-making.J. Neurosci. 2015; 35: 2476-2484Crossref PubMed Scopus (70) Google Scholar] recently conducted formal model comparisons with several human and monkey data sets to adjudicate between collapsing bounds and drift rate variability. The comparisons were conducted using Bayes Information Criterion (BIC), which balances goodness of fit with model parsimony. The authors found that most data sets were better explained by a constant bound model with drift rate variability. Of note, however, in this comparison, collapsing bound models also included drift rate variability in addition to several parameters describing the collapse (nonlinear functions of time). As a result, the collapsing bound models were at a disadvantage, since BIC metrics penalise for complexity. In an attempt to address this, a second main comparison was made with a collapsing bound model contrived to have the same number of parameters as the constant bound model. Again, the data favoured constant bounds, but again questions remain, since the parameters that were omitted from the collapsing bound model were ones that account for qualitatively distinct and often significant aspects of behavioural data (e.g., fast errors and distribution shape). The simplest way to implement a collapsing bound (i.e., a linear function of time) was not considered. By contrast, a more recent study that did use such a linear implementation showed an improved BIC for a model that included collapsing bounds alongside drift rate variability [25Murphy P.R. et al.Global gain modulation generates time-dependent urgency during perceptual choice in humans.Nat. Commun. 2016; 7: 13526Crossref PubMed Scopus (12) Google Scholar]. Discrepancies such as the one discussed above highlight the difficulties that can arise when adjudicating between alternative models based on behavioural data alone. One approach to break such impasses is to additionally consider the ability of a model to capture key observable aspects of the biological implementation of the decision process [26Bollimunta A. Ditterich J. Local computation of decision-relevant net sensory evidence in parietal cortex.Cereb. 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Banburismus and the brain: decoding the relationship between sensory stimuli, decisions, and reward.Neuron. 2002; 36: 299-308Abstract Full Text Full Text PDF PubMed Scopus (353) Google Scholar], linearly grows in variance as more evidence is sampled over time [35Churchland A.K. et al.Variance as a signature of neural computations during decision making.Neuron. 2011; 69: 818-831Abstract Full Text Full Text PDF PubMed Scopus (160) Google Scholar], and reaches a stereotyped firing level immediately before the perceptual report [36Roitman J.D. Shadlen M.N. Response of neurons in the lateral interparietal area during a combined visual discrimination reaction time task.J. Neurosci. 2002; 22: 9475-9489Crossref PubMed Google Scholar]. More recently, human electrophysiology research has established that signatures of bounded evidence accumulation can also be traced in global, non-invasively recorded signals [25Murphy P.R. et al.Global gain modulation generates time-dependent urgency during perceptual choice in humans.Nat. Commun. 2016; 7: 13526Crossref PubMed Scopus (12) Google Scholar, 37O'Connell R.G. et al.A supramodal accumulation-to-bound signal that determines perceptual decisions in humans.Nat. Neurosci. 2012; 15: 1729-1735Crossref PubMed Scopus (225) Google Scholar, 38Philiastides M.G. et al.Human scalp potentials reflect a mixture of decision-related signals during perceptual choices.J. Neurosci. 2014; 34: 16877-16889Crossref PubMed Scopus (18) Google Scholar, 39de Lange F.P. et al.Prestimulus oscillatory activity over motor cortex reflects perceptual expectations.J. Neurosci. 2013; 33: 1400-1410Crossref PubMed Scopus (0) Google Scholar] (Box 2). In parallel, empirically grounded, biophysically based models have been developed that describe plausible neural circuit configurations capable of implementing computations such as temporal integration (e.g., [40Wang X.J. Probabilistic decision making by slow reverberation in cortical circuits.Neuron. 2002; 36: 955-968Abstract Full Text Full Text PDF PubMed Scopus (590) Google Scholar, 41Koulakov A.A. et al.Model for a robust neural integrator.Nat. Neurosci. 2002; 5: 775-782Crossref PubMed Scopus (0) Google Scholar]). The ability to observe neural signals reflecting decision formation is not only relevant to the construction of such neural network models, but can also provide critical guidance in constructing, constraining, and adjudicating between abstract, cognitive process models. Returning to our example above, collapsing bounds and drift rate variability each make, in fact, specific predictions for neural signals relevant to decision formation, and many data already exist to examine such predictions.Box 2Probing Decision-Related Neural Activity in Non-Invasive