Diffusion models to distinguish endogenous and exogenous temporal attention

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The Government of the Russian federation

Federal State Autonomous Educational Institution of Higher Professional Education

National Research University - Higher School of Economics

Institute of Cognitive Neurosciences,

Master's program

“Cognitive sciences and technologies: from neuron to cognition”

Final qualifying work - MASTER THESIS

«Diffusion Models to Distinguish Endogenous and Exogenous Temporal Attention»

Introduction

Historically, in science, different approaches and models were proposed for studying attention. One of the earliest models was to consider attention as a filter or bottleneck, through which information is selected for further processing. A more recent and very persistent idea in the field of visual attention is the spotlight metaphor. In this sense, attention is often compared to a spotlight that highlights certain locations in space. The use of this metaphor is convenient to emphasize the limited capacity of attention and spatial dynamics of attention. Nowadays, attention is still broadly defined as a process of selecting some information for further processing and getting rid of other, irrelevant information for a particular task. This way sensory overload is avoided and an organism may process only the most relevant information. So, attention is considered as a dynamic system within which interaction between top-down (task relevant) and bottom-up (stimuli-driven) processes exists. Within that system selection of information is operated at multiple levels, such as perceptual, semantic or response-based. The question about the extent to which attention is operated by external stimuli or internal states served as a starting point to divide attention in different ways, depending on the model explaining functioning and nature of attention. In the next few paragraphs, we will briefly consider how attention might be described and interpreted based on certain models or approaches.

One of the classic approaches of studying spatial attention is a division into overt and covert orienting of attention. Overt orienting involves moving eyes to change attentional focus. However, it also possible to move attention without moving the eyes or head and this case is called covert orienting. The premotor theory of attention (Rizzolatti, Riggio, Dascola, & Umiltб, 1987) proposes that orienting of attention is just the preparation of motor actions. The premotor theory makes specific neuroanatomical predictions about the identity of neural substrates related to attention and neural substrates related to motor preparation of eye movements, namely concluding that covert orienting is just a motor plan that is below motion threshold. While there are certainly many overlaps between spatial attention and eye movements, there is substantial evidence that the two networks are not identical, and this is particularly true for endogenous attention (see Smith & Schenk, 2012 for a review).

Another classic approach of studying attention was proposed by Posner in the 80s, again mostly accentuating the spatial basis of visual attention. Posner also formulated the spatial cueing task and offered to study attention by dividing it functionally into endogenous (intrinsic, voluntary) and exogenous (sudden change in the environment) orienting (Posner, 1980). In other words, he offered to split attention into two opposite processes based on how attention is oriented towards different stimuli. Later Posner and Peterson proposed to divide attention into three components (functions) of attention or 3 attentional networks - Alertness, Orienting and Executive function (Posner & Petersen, 1990; Posner & Cohen, 1994). Attentional network test - a combination of the Posner cueing paradigm and the Eriksen flanker test was used to test whether these three different types of attention operate together or independently and to what extent.

Briefly, these types of attention may be defined as follows: The Alertness function is the ability to prepare and sustain state of alertness to process signals that has high priority. The orienting function is an ability to detect where in space a certain stimulus is localized. The executive control function allows to resolve different types of conflicts between stimuli (Kulikova, 2017). There is also much physiological evidence in support of this division (Fan et al., 2009). Exogenous orienting of attention is usually considered as an automatic process. However, recent studies question this thesis arguing that the attentional set might play an important role in modulating the exogenous orienting (Arnott & Pratt, 2002). Therefore exogenous cues might attract attention not so automatically (Malevich, Ardasheva, Krьger, & MacInnes, 2018). Also, there is supporting evidence for the idea of two functionally and anatomically distinct neural networks (Coull, Frith, Bьchel, & Nobre, 2000). The dorsal frontoparietal network is related to endogenous orienting of attention. It provides the selection of sensory stimuli according to expectation and inner goals. The ventral frontoparietal network is linked to exogenous orienting of attention. It provides detection of salient or unexpected stimuli (Coull, Frith, Bьchel, & Nobre, 2000; see Chica, Bartolomeo, & Lupiбсez, 2013 for a review).

Coming back to Posner's endogenous and exogenous orienting, we can assume that one of the primary purposes of this approach was to understand how to define components of orienting of attention separately and how they interact. However, the problem is that Fan, Posner, and others define and study these components of attention and their interaction only within single snapshot (single trial), not considering the fact that attention can also be directed or focused to a specific moment in time (Correa, Lupiбсez, Milliken, & Tudela, 2004). However, in real-life people use temporal information to adjust their behavior in continuously changing environments. Temporal expectations about future events might improve behavior on a par with spatial attention. The good example to illustrate what is temporal attention is a famous trick with the expectation of pain. Let us say the girl is afraid of injection. The nurse might offer her to make the injection on count “three”. However, she does it earlier on count “two”. The perception of pain became impaired because stimulus appeared in unexpected time. Here attention is distracted away from the real moment of injection allowing to eliminate the perception of pain (Correa, Cappucci, Nobre, & Lupiбсez, 2010). So, we can roughly say that temporal attention is about one point in time, whereas snapshot (spatial attention) is about one point in space. And both spatial and temporal aspects of attention are essential to understand how this mechanism functions. Before concentrating on studies that test temporal aspects of attention, we will take a closer look at the two modes of attention, their functioning, and their interactions.

Chapter 1. Temporal attention

1.2 Methodological problems of isolating modes of temporal attention

We usually consider attention as the process of allocating information-processing resources, but attention can be understood as operating on different modes and different domains. Klein and Lawrence suggested the division where role of domains might include space, time, sense, and task (Klein & Lawrence, 2012). Also, in this view, each domain has two modes - exogenous and endogenous (Posner, 2011). In previous sections we have considered how endogenous and exogenous modes of attention, as different processes with different mechanisms underlying their functioning, operate within space domain. Further we will consider mostly time domain and exogenous and endogenous modes within this domain.

Attention to time might be attracted both exogenously, which means that it is a quite automatic process and endogenously, meaning volitional nature, including expectations, inner goals, memory traces, and predictions. However, there exist some methodological issues of isolating them completely. Usually, to study temporal attention researchers manipulate such independent variables, as task complexity, probability of target occurrence, distribution of stimulus onset asynchrony (SOA) between trials or between blocks, modality and intensity of stimuli, duration of cues and targets. However, until recently there was no reliable method to combine these variables in such a way to study automatic and voluntary components, as a purely isolated mechanism. The main reason why it was so - is because of the inability to control the impact of endogenous temporal attention during studying exogenous temporal attention. If a cue includes some temporal information about the following target, it interferes the separate studying of exogenous component. Drawing an analogy with spatial attention studies, like Posner's task, it would be like studying covert orienting of attention, but with informative peripheral cues. Such cue might increase the probability of spatial orienting; however, it both contains information value related to endogenous control and exogenous capture of attention by peripheral cue. The opposite side is inability to control the impact of exogenous component during the studying of endogenous component because just the appearance of the cue is itself the change in intensity of visual stimuli. It would be like to study the effect of the information content of spatial cue when we only use peripheral cue that appears at probable target locations (Lawrence & Klein, 2013).

A few techniques were proposed to control and measure the impact of temporal expectations on performance. For example, expectation can be measured by the amount and predictability of a foreperiod - the time interval between cue and target. By varying this interval in many ways under many experimental paradigms, two well replicated foreperiod effects were obtained (Niemi & Naatanen, 1981; Nobre & Coull, 2010). When it is fixed foreperiod effect, namely when the time interval between cue and target stimuli is constant during the whole block, the bigger foreperiod, the slower RTs. And in case of varied foreperiod effect, namely when the interval between cue and target is varied within a block of trials, with an increase of foreperiod, RTs are getting slower. However, even in varied foreperiod condition, some expectations are formed according to the progress of the experiment. For example, if a participant expects the target to appear in a short time period after the cue and target does not appear, then it will certainly appear after a long time period. That means that if in the experiment each SOA occurs with equal probability, then the momentary probability of target's appearance increases along with the time. Such a situation was called “aging foreperiods”. And this ability to learn temporal contingencies between cue and target to improve performance was called “Hazard sensitivity”. To reduce this sort of confound, researchers used “non-aging foreperiods”. In that case, the exponential distribution of foreperiods is used that allows to make constant the probability of each target appearance during the whole experiment (Gabay & Henik, 2010; Niemi & Naatanen, 1981). Also, so-called catch trials were used for the same purpose. But even these manipulations cannot totally eliminate the formation of contingencies, because cue always precedes the target, which means that participant learns that he or she should pay less attention to the period of time when cue appears. That means that in any way there is some extent of endogenous component inclusion. Now we can clearly see that it is quite difficult to divide exogenous and endogenous modes of temporal attention purely (Cohen, 2014; Lawrence & Klein, 2013a; Weinbach & Henik, 2012). Before proceeding to the study where this problem was solved, we concentrate on different cueing effects obtained in different studies that better characterize the phenomena of temporal attention.

1.3 Temporal effects observed in different studies

Computational models became a very powerful tool for testing psychological theories in addition to behavioral inferences (Ratcliff & McKoon, 2008; Voss, Rothermund, & Voss, 2004; White & Curl, 2018). One way to model the process of decision making in two-alternative forced choice (2AFC) task is based on the assumption that to choose between two alternatives, the participant has to accumulate the necessary amount of information towards one of them.

After this amount of information exceeds a certain threshold, the decision is made. During each trial, a participant accumulates evidence towards either one alternative or another. This idea of information sampling is peculiar to the whole family of sequential-sampling models.

For example, one of the earliest accumulator models was a random-walk model, that is quite simple and suitable for discrete evidence accumulation, making the sampling process to take place in different steps (Stone, 1960;P. L. Smith & Vickers, 1988; see Forstmann, Ratcliff, & Wagenmakers, 2016; Ratcliff for a review, see Smith, Brown, & McKoon, 2016 for a review).

Predicted latency, in this case, is evaluated as the number of steps that were needed to cross a decision boundary. Threshold or decision boundary is determined by one of the model's parameters, that will be discussed further. For continuous evidence, accumulation diffusion models are usually used. Sequential-sampling models might differ in terms of a number of accumulators, absoluteness or relativeness of decision rules. Or these might be models with constant of varied drift rate, with either stochastic or deterministic evidence (Farrell & Lewandowsky, 2018). So, depending on the task at hand and the nature of data, different classes of models might be used (Figure 3 represent the relationships between models).

Figure 3. Relationships between models (from Chica, 2013)

The Drift-diffusion model is one of the sequential sampling models that was successfully applied to different cognitive tasks and might help to explain the decision-making process. It was initially used for the analysis of the memory retrieval process (Ratcliff, 1978.; Ratcliff & McKoon, 2008). Given the mean reaction times and standard deviation - parameters of reaction time distribution - it is possible to infer the components of cognitive processing of information from a particular dataset. Drift-diffusion models were also applied for investigation of performance across a range of tasks, such as numerosity visual perception (Ratcliff & Rouder, 1998), and task-switching (Schmitz & Voss, 2012; Voss, Voss, & Lerche, 2015). There is also an established match between drift-diffusion models and neurophysiological measures, such as single cell recordings (Roitman & Shadlen, 2002), fMRI (Ratcliff, Philiastides, & Sajda, 2009), EEG (Ratcliff, Philiastides, & Sajda, 2009), and TMS (Philiastides, Auksztulewicz, Heekeren, & Blankenburg, 2011), which states for biological correspondence.

One of the main goals and advantages of drift-diffusion models is the correspondence between the parameters of the model and components of processing. Consequently, we can observe the effects of experimental manipulations on the components. So, the model gives an opportunity to decompose the data the way that it allows studying certain components individually (Ratcliff & McKoon, 2008). Another great advantage of drift-diffusion model is that the process of evidence accumulation might be linked to the behavior of neuron's populations. So, diffusion models are widely used for clinical research as well, that often allows to examine individual differences (Ratcliff & Childers, 2015). In our case, the drift-diffusion model might be used for analyzing data from our dot motion experiment to understand which experimental manipulations affect which decision components.

Drift-diffusion model also catches the accuracy of data, as well as right-skewness of reaction time distribution that is observed in human data for simple decision processes and which is one of the requirements for using this model (Ratcliff & McKoon, 2008). Another great advantage of the drift-diffusion model is its property to differentiate the process of accumulation information which is necessary for making a decision and two other processes, such as encoding of information and execution of particular response. To apply the model correctly, one should remember that the model has its restrictions for use, which are:

1) average responses should not be longer than 1500ms.

2) it must be simple-step decisions (usually only for two alternatives), which suits well many cognitive tasks, including ours (Ratcliff & McKoon, 2008).

Figure 4 - Decision-making process through drift-diffusion model (from Ratcliff & McKoon, 2008). z - starting point, a and O - decision boundaries, v - drift rate.

As seen in Figure 4 above, when random walk exceeds one of two thresholds (decision boundary), the response is given. In this case one response is correct, meanwhile, the other one is considered an error. Decision boundary “a” is the threshold for correct response and decision boundary “0” is the threshold for an incorrect response. Distance between starting point “z” and one of the boundaries stands for the amount of information needed to make a response. During one trial information is accumulated from starting point towards the boundary. Drift rate “v” is the parameter that defines the rate of accumulation of information or quality of information extracted from the stimulus. At the beginning of each trial starting point, “z” might be biased towards one or another boundary. This shift is determined by the information that the participant has about stimuli and its change during the experiment. Finally, the distance between both thresholds is usually considered as a measure of conservatism which means that the closer boundaries to each other, the higher the probability that the random walk curve will reach the opposite boundary. And vice versa (Ratcliff et al., 2016; Ratcliff, Smith, & McKoon, 2015; Voss et al., 2004).

Considering the correspondence of the model's parameters and components of cognitive processes, the drift rate is usually interpreted as a representation of task difficulty (Ratcliff et al., 2016). Consequently, for each experimental condition, this parameter should be different in terms of difficulty.

The structure of the drift-diffusion model includes three components that compose the decision (formula below). RT denotes total reaction time. U is stimuli encoding process. В is the decision process itself, and W is response execution. For convenience sake, U and W are collapsed into one non-decisional component that is denoted by mean duration T.

???? = ?? + ?? + ??, ??=??+??

Another parameter of the model, within-trial variability “s” or noise affect drift rate the way that random walks with the same drift rate might terminate at a different time (producing RT distributions) and at different boundaries (producing errors) (Ratcliff & McKoon, 2008).

There is also across-trial variability for some parameters. The drift rate and starting point mostly influence the rate of response. The boundary separation is usually fixed for all trials in the block. Across-trial variability is also responsible for the fact that correct and error responses are different in terms of speed, depending on the instructions. For example, instruction that stress to respond as fast as possible leads to faster but less accurate correct responses. Here errors are faster than correct responses. On the contrary, if it stressed in the instruction to answer as accurate as possible, there are more accurate but less speeded responses. In this case, errors are slower than correct responses (Ratcliff & McKoon, 2008; Ratcliff & Rouder, 1998).

1.5.1 Drift diffusion models applicable to studies of attention

One of the recent works was done by Corey White and Ryan Curl (White & Curl, 2018). The shrinking spotlight diffusion model (SSP) was used to evaluate how attentional processing affects decision processes in the ANT task, depending on different conditions, such as presence or absence of alerting or orienting cues. Alerting cues usually stands for exogenous orienting, whereas orienting cues represent endogenous attention. The main inference from the behavioral analysis supports old and well-established result that attentional cues, unlike their absence, reduce temporal uncertainty, facilitate preparation for upcoming targets and improve processing via multiple decision components. Specifically, alerting and orienting cues improve the ability to narrow attentional focus, the new parameter of the model. As for the model results, authors found that alerting cue, compared to the absence of cue, led to faster nondecision time, which represent either faster encoding process or faster motor execution preparation. Also alerting cue led to stronger perceptual processing and stronger attentional focusing - new parameters of the model. Orienting cues, compared to alerting cues, led to even faster nondecision time, stronger attentional focus and reduction in response caution (speed-accuracy trade-off). So, the SSP model allowed to delineate and determine what factors caused differences in behavior, namely reductions in temporal uncertainty.

A very stable effect related to both endogenous and exogenous modes of attention is if temporal certainty about upcoming target increases, the RTs decreases. However, there is no consensus about what stages of processing are responsible for that. Three main accounts are explaining this effect in terms of diffusion model's parameters. First one considers the possibility that when the participant needs to orient attention to a particular moment in time when the target should appear, it speeds up the rate of evidence accumulation (v) (Grosjean, Rosenbaum, & Elsinger, 2001). Another account proposes that temporal certainty lowers the decision boundary (a). In this case anticipation of the target's onset leads to a decreased threshold and, consequently, less evidence is needed to make a decision, which makes responses faster (Chica et al., 2013). The third account states for general motor system preparation, regardless of choosing a particular response. That assumption makes nondecision time (W) responsible for temporal certainty improvements. There is a study that provides evidence that temporal expectations influence stimulus encoding processing (Seifried, Ulrich, Bausenhart, Rolke, & Osman, 2010). Therefore, by finding which parameter is mainly responsible for improvements caused by temporal certainty, it is possible to make inferences about mechanisms underlying this process. In this sense, interesting results were obtained by Marieke Jepma and colleagues (Jepma, Wagenmakers, & Nieuwenhuis, 2012). Authors used sequential-sampling models of decision making to evaluate what happens with components of information processing when participants use temporal cues to predict the upcoming onset of the target. In their first experiment with foreperiods, temporal certainty did not change the shape of RT distribution but shifted it to the left, which implies that the nondecision component was affected. The results of the second experiment that used temporal-cueing paradigm were consistent with the first one. Therefore, effects of temporal certainty on reaction time add evidence to the third account, that states for changing in the duration of nondecision phase of information processing, but not the decision process itself.

However, there have been no studies where diffusion models were directly applied to studying Exogenous and Endogenous modes of attention.

In conclusion, new methods give researchers the ability to run simulations on behavioral data. Computational modeling and, in particular, diffusion models are one of these methods. Diffusion models were successfully applied to behavioral experiment, including attentional studies. By building and comparing different models, we may come to the following inference. If several models have a similar set of parameters that provide them with the best fit for human data, this is believed to be proof that the cognitive processes might share a common biological basis. The similarity of processes is determined by comparing the reaction time distributions (W. J. MacInnes, 2017).

Chapter 2. Research proposal

We have two main goals in this study. First one is to replicate Lawrence and Klein experiment by adding some changes, namely changing the modality of the cue from audial to visual to evaluate the impact of endogenous and exogenous components of temporal attention on the performance separately and within their interaction. We tend to think that it is important to do such replication where all stimuli are visual.

The reason is quite simple. Most of the experiments in this area use visual stimuli both for cues and targets. Also, to generalize and compare results we have to be sure that the factor of the modality of a cue does not significantly affect the results.

Because of this manipulation with changing the modality, we had to change the task from Posner cueing task to random dot motion coherent task. However, in fact, this is still a two-alternative speeded choice task (2ASC) or type of discrimination task. The experiment has within 2 (Contingent/NonContingent conditions) x 2 (NoCue/Cue conditions) design.

The second goal is to apply the drift-diffusion model to our data. This additional procedure will allow us to go deeper into the functioning of exogenous and endogenous modes of attention.

The main idea behind this step is the following. If diffusion model, trained on one condition, might be well fitted to another condition by changing only one parameter of the model, for example, drift rate or nondecision component (depends on the theoretical question), then we might say that this model simulates very similar mechanisms.

Because in this case, the overall structure of the model's parameters would be almost the same for both conditions. Also, when there is no significant difference between the two conditions, changing no parameters would probably give the best match.

On the other hand, when the whole structure of modeling one condition differs from other condition, these are likely different processes, reflected in different model's parameters values and ratios.

As we mentioned before, there are no studies that would directly apply diffusion models to delineating exogenous and endogenous mechanisms. Therefore, hypotheses about model predictions are based both on behavioral assumptions about different nature of attentional modes and on the results of diffusion models applied to different attentional aspects.

Overall Hypothesis: The change of modality of alertness cueing from audial to visual will give the same results as in the Lawrence and Klein experiment.

Hypothesis 1: If the endogenous mode is operated separately, it improves both speed and accuracy (with a maximum magnitude when the signal goes before target by approximately 400ms).

Hypothesis 2: If exogenous mode is operated separately, it improves the speed of response, but accuracy stays the same (with a maximum magnitude when the signal goes before target by approximately 100ms).

Hypothesis 3: If both of them are involved in the process, there is a trade-off of speed and accuracy.

2.2 Experimental design

First independent variable: Contingent condition. This one included five levels (range of different SOAs: -100, 100, 250, 500 and 750ms) that were varied between blocks (to counterbalance all conditions).

NonContingent condition. This one supposes not to have any contingency between signal and target. That means that both cues and targets were presented to the participants in a totally random way independently to each other. After the experiment, different SOA were extracted from it and parsed to compare with the Contingent condition.

Second independent variable: Visual signal (dots from random dot coherent motion task) were used as a cue that was placed in the centre of the screen about the 2-degree size. These dots had two parameters that were varied.

The first parameter is the direction of motion of dots. It might be totally random motion or have some random coherent direction. This parameter was constant during all trials (all the time participants look at randomly moving dots, then at some moment some number of dots start moving coherently for 200ms and then comes back to random movement. The reason why it is constant is because of the purpose to minimize the exogenous impact, but not to get rid of it totally. It is enough to have a salient and conscious change in perception of the signal that participant might subjectively differ, even not understanding what exactly has changed (when participant detect that change in the direction of motion, this change does not change the input into the visual system a lot).

The second parameter is luminance of the signal (baseline/higher) - some baseline luminance of dots and slightly higher luminance of dots, respectively.

NoCue condition. Here motion is constant (constant change), and the luminance of moving dots is the same during the trial. Cue condition. Here motion is constant (constant change) and the luminance of moving dots is higher.

2.2.2 The order of presentation of different combination of variables

(Contingent, Contingent, NonContingent, NonContingent) + (NoCue, Cue, NoCue, Cue)

2nd Quarter: (Contingent, Contingent, NonContingent, NonContingent) + (Cue, NoCue, Cue, NoCue)

3rd Quarter: (NonContingent, NonContingent, Contingent, Contingent) + (NoCue, Cue, NoCue, Cue)