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231 nips-2008-Temporal Dynamics of Cognitive Control

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Author: Jeremy Reynolds, Michael C. Mozer

Abstract: Cognitive control refers to the ﬂexible deployment of memory and attention in response to task demands and current goals. Control is often studied experimentally by presenting sequences of stimuli, some demanding a response, and others modulating the stimulus-response mapping. In these tasks, participants must maintain information about the current stimulus-response mapping in working memory. Prominent theories of cognitive control use recurrent neural nets to implement working memory, and optimize memory utilization via reinforcement learning. We present a novel perspective on cognitive control in which working memory representations are intrinsically probabilistic, and control operations that maintain and update working memory are dynamically determined via probabilistic inference. We show that our model provides a parsimonious account of behavioral and neuroimaging data, and suggest that it offers an elegant conceptualization of control in which behavior can be cast as optimal, subject to limitations on learning and the rate of information processing. Moreover, our model provides insight into how task instructions can be directly translated into appropriate behavior and then efﬁciently reﬁned with subsequent task experience. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract Cognitive control refers to the ﬂexible deployment of memory and attention in response to task demands and current goals. [sent-7, score-0.768]

2 In these tasks, participants must maintain information about the current stimulus-response mapping in working memory. [sent-9, score-0.251]

3 Prominent theories of cognitive control use recurrent neural nets to implement working memory, and optimize memory utilization via reinforcement learning. [sent-10, score-0.69]

4 We present a novel perspective on cognitive control in which working memory representations are intrinsically probabilistic, and control operations that maintain and update working memory are dynamically determined via probabilistic inference. [sent-11, score-0.898]

5 We show that our model provides a parsimonious account of behavioral and neuroimaging data, and suggest that it offers an elegant conceptualization of control in which behavior can be cast as optimal, subject to limitations on learning and the rate of information processing. [sent-12, score-0.487]

6 Moreover, our model provides insight into how task instructions can be directly translated into appropriate behavior and then efﬁciently reﬁned with subsequent task experience. [sent-13, score-0.598]

7 Classic examples of experimental tasks requiring this ability include Stroop, Wisconsin card sorting, and task switching (for a review, see [1]). [sent-16, score-0.453]

8 Although these paradigms vary in superﬁcial features, they share the key underlying property that successful performance involves updating and maintaining a task set. [sent-17, score-0.264]

9 For example, in Wisconsin card sorting, participants are asked to classify cards with varying numbers of instances of a colored symbol. [sent-21, score-0.255]

10 The classiﬁcation might be based on color, symbol, or numerosity; instructions require participants to identify the current dimension through trial and error, and perform the appropriate classiﬁcation until the dimension switches after some unspeciﬁed number of trials. [sent-22, score-0.556]

11 Thus, it requires participants to maintain a task set—the classiﬁcation dimension—in working memory (WM). [sent-23, score-0.547]

12 Likewise, in the Stroop task, stimuli are color names presented in various ink colors, and the task set speciﬁes whether the color is to be named or the word is to be read. [sent-24, score-0.832]

13 To understand cognitive control, we need to characterize the brain’s policy for updating, maintaining, and utilizing task set. [sent-25, score-0.436]

14 Moreover, we need to develop theories of how task instructions are translated into a policy, and how this policy is reﬁned with subsequent experience performing a task. [sent-26, score-0.496]

15 For example, in the Wisconsin card sorting task, the control instruction—the classiﬁcation dimension—would be bound to a variable, and responses would be produced by rules of the form, “If the current dimension is D and the stimulus is X, respond Y”. [sent-31, score-0.516]

16 Consider the following phenomena: • When participants are asked to switch tasks, performance on the ﬁrst trial following a switch is inefﬁcient, although performance on subsequent trials is efﬁcient, suggesting that loading a new task set depends on actually performing the new task [3]. [sent-33, score-0.95]

17 • Switch costs are asymmetric, such that switching from an easy task to a difﬁcult task is easier than vice-versa [4]. [sent-35, score-0.494]

18 For example, in the Stroop task, reading the word is quick and accurate, but naming the ink color is not [5]. [sent-37, score-0.337]

19 • The difﬁculty of a particular task depends not only on the characteristics of the task itself, but also on context in which participants might be called upon to perform [6]. [sent-38, score-0.582]

20 To account for phenomena such as these, theories of control have in recent years focused on how control can be implemented in cortical neural networks. [sent-39, score-0.487]

21 In the prevailing neural-network-based theory, task set is represented in an activity-based memory system, i. [sent-40, score-0.34]

22 For example, in the Stroop task, instructions to report the ink color might bias the neural population representing colors—i. [sent-44, score-0.465]

23 , increase their baseline activity prior to stimulus onset—such that when stimulus information arrives, it will reach threshold more rapidly, and will beat out the neural population that represents word orthography in triggering response systems [7]. [sent-46, score-0.754]

24 In this framework, a control policy must specify the updating and maintenance task set, which involves when to gate new representations into WM and the strength of the recurrent connection that maintains the memory. [sent-47, score-0.663]

25 First, like their symbolic predecessors, the neural network models must often be crippled arbitrarily to explain data; for example, by limiting the strength of recurrent memory connections, the models obtain task set decay and can explain error data. [sent-52, score-0.506]

26 Second, the models require a stage of training which is far more akin to how a monkey learns to perform a task than to how people follow task instructions. [sent-53, score-0.418]

27 The reinforcement-learning based models require a long stage of trial-and-error learning before the appropriate control policy emerges. [sent-54, score-0.251]

28 Whereas monkeys are often trained for months prior to testing, a notable characteristic of humans is that they can perform a task adequately on the ﬁrst trial from task instructions [11]. [sent-55, score-0.732]

29 Additionally, as a more abstract framework than the neural net theories, one aim is to provide insight as to how task instructions can be used directly and immediately to control behavior. [sent-59, score-0.568]

30 That is, instead of proposing that task set is stored in an all-or-none fashion, we wish to allow for task set—as well as all cortical representations—to be treated as random variables. [sent-61, score-0.467]

31 Given inherently probabilistic representations, it is natural to treat the problems of task set updating, maintenance and utilization as probabilistic inference. [sent-63, score-0.292]

32 By analogy, our approach to cognitive control treats task set as a latent variable that must be inferred from observations. [sent-76, score-0.539]

33 A second, distinct inference problem is to determine the correct response on the current trial from the current stimulus and the trial history. [sent-80, score-0.81]

34 Thus, in our approach, control and response selection are cast as inference under uncertainty. [sent-81, score-0.366]

35 Each experiment involves a complex task environment in which experimental participants are required to switch among eight tasks that have different degrees of overlap and inconsistency with one another. [sent-84, score-0.71]

36 Having constrained the model by ﬁtting behavioral data, we then show that the model can explain neuroimaging data. [sent-85, score-0.363]

37 Beyond accounting for data, the model provides an elegant theoretical framework in which control and response selection can be cast as optimal, subject to limitations on the processing architecture. [sent-87, score-0.417]

38 In each experiment, participants are shown blocks of 12 trials, preceded by a cue that indicates which of the eight tasks is to be performed with the stimuli in that block. [sent-89, score-0.516]

39 The notation indicates that task 3 requires a left response to the green square, a right response to a red square, and no response (hereafter, no-go) to a white square. [sent-97, score-0.892]

40 Task 4 is identical to task 3, and the duplication is included because the tasks are described as distinct to participants and each is associated with a unique task cue. [sent-98, score-0.784]

41 The duplication makes the stimulus-response mapping twice as likely, because the eight tasks have uniform priors. [sent-99, score-0.307]

42 Task 1 (lower left corner of the ﬁgure) requires a left response for a green square and no-go for a white square. [sent-100, score-0.259]

43 There are no red stimuli in the task 1 blocks, and the green→left mapping is depicted twice to indicate that the probability of a green square appearing in the block is twice that of a white square. [sent-101, score-0.603]

44 The four tasks in the lower row allow for only one possible response (not counting no-go as a response), whereas the four tasks in the upper row demand that a choice be made between two possible responses. [sent-104, score-0.577]

45 Thus, the two rows differ in terms of the demands placed on response selection. [sent-116, score-0.251]

46 In the leftmost column, task identity does not matter, because each mapping (e. [sent-118, score-0.317]

47 In contrast, tasks utilizing yellow, blue, and cyan stimuli involve varied mappings. [sent-121, score-0.25]

48 The tasks in the middle column are somewhat less dependent on task identity, because the stimulus-response mappings called for have the highest prior. [sent-123, score-0.369]

49 Thus, the three columns represent a continuum along which the importance of task identity varies, from being completely irrelevant (left column) to being critical for correct performance (right column). [sent-124, score-0.273]

50 Rather than mapping a color to a response, the color determines which property of the stimulus is to be used to select a response. [sent-127, score-0.644]

51 For example, task 3 of Figure 1B demands that a green letter stimulus (denoted as X here) be classiﬁed as a vowel or consonant (property P1), whereas a red letter stimulus be classiﬁed as upper or lower case (property P2). [sent-128, score-0.887]

52 Thus, Experiment 2 places additional demands of stimulus classiﬁcation and selection of the appropriate stimulus dimension. [sent-129, score-0.482]

53 Participants in each experiment received extensive practice on the eight tasks before being tested. [sent-130, score-0.271]

54 1 A Probabilistic Generative Model of Control Tasks Following the style of many probabilistic models in cognitive science, we have designed a generative model of the domain, and then invert the model to perform recognition via Bayesian inference. [sent-133, score-0.255]

55 , the model produces sequences of stimulusresponse pairs such that the actual trial sequence would be generated with high probability. [sent-136, score-0.286]

56 Instead of learning this model from data, though, we assume that task instructions are ’programmed’ into the model. [sent-137, score-0.389]

57 Our generative model of control tasks is sketched in Figure 2A as a dynamical Bayes net. [sent-138, score-0.389]

58 Vertical slices of the model represent the trial sequence, with the subscript denoting the trial index. [sent-139, score-0.421]

59 The B node represents the task associated with the current block of trials. [sent-141, score-0.403]

60 ) The block on trial k has 8 possible values in the experiments we 4 Bk-1 Bk Ck-1 Rk-1 Sk-1 Bk+1 Ck Rk Sk T Ck+1 Rk+1 Sk+1 T T Figure 2: Dynamical Bayes net depiction of our generative model of control tasks, showing the trial-to-trial structure of the model. [sent-143, score-0.609]

61 model, and its value depends on the block on trial k 1. [sent-144, score-0.328]

62 The block determines the category of the stimulus, C, which in turn determines the stimulus identity, S. [sent-145, score-0.419]

63 The categories relevant to the present experiments are: color label, block cue (the cue that identiﬁes the task in the next block), upper/lower case for letters, and consonant/vowel for letters. [sent-146, score-0.629]

64 Finally, the R node denotes the response, which depends both on the current stimulus category and the current block. [sent-150, score-0.327]

65 First, we decompose the category and stimulus representations into shape and color dimensions, expanding C into C color and C shape , and S into S color and S shape . [sent-152, score-1.171]

66 (When we refer to C or S without the superscript, it will denote both the shape and color components. [sent-153, score-0.284]

67 ) Second, we wish to model the temporal dynamics of a single trial, in order to explain response latencies. [sent-154, score-0.292]

68 With normalization of probabilities, this formulation is identical to a naive Bayes model with conditionally independent stimulus observations at each time step. [sent-156, score-0.261]

69 The context is provided by the block B, which is essentially a memory that can be sustained over trials. [sent-159, score-0.274]

70 This distribution is a mixture of a uniform distribution (no memory of block) and an identity mapping (perfect memory). [sent-164, score-0.239]

71 z z P (Ck Bk ) = P (Ck Bk ) + (1 ) NC z , where z color shape and NC z is the number of distinct category values along dimension z, and P ( ) is the probability distribution deﬁned by the experiment and task (see Figure 2B,C). [sent-165, score-0.69]

72 z z P (Sk = s Ck = c T = t) (1 + z M z (s c))t , where z color shape and M z (s c) is a membership function that has value 1 if s is an instance of category c along dimension z, or 0 otherwise. [sent-168, score-0.389]

73 MR SIgnal premotor cortex posterior lateral PFC anterior lateral PFC Single Dual Cshape node B node MODEL Entropy R node Exp. [sent-170, score-0.351]

74 2 Importance of Task Identity Figure 3: (top row) human neuroimaging data from three brain regions [6], (bottom row) entropy read out from three nodes of the model. [sent-174, score-0.357]

75 We would like to read out from the model a response on some trial k, given the stimulus on trial k, Sk , and a history of past stimulus-response pairs, Hk = {S1 . [sent-179, score-0.86]

76 The model initiates a response when one value of Rk passes a threshold θ, i. [sent-191, score-0.24]

77 This yields the response time (RT) t∗ = min t | max P (Rk = r|Sk , T = t, Hk ) > θ r (1) and the response r∗ = argmaxr P (Rk = r|Sk , T = t∗ , Hk ). [sent-194, score-0.378]

78 4 Simulation Results We simulated the model on a trial sequence like that in the human study. [sent-195, score-0.291]

79 , 6 the model never attained the response criterion of Equation 1), or in which the model produced no RT variation across conditions. [sent-217, score-0.291]

80 Koechlin, Ody, and Kouneiher [6] collected not only behavioral data, but also neuroimaging data that identiﬁed brain regions involved in control, and how these brain regions modulated their activation across experimental manipulations. [sent-229, score-0.327]

81 The top row of Figure 3 shows effects of these experimental manipulations on the fMRI BOLD response of three different brain regions. [sent-231, score-0.303]

82 The remarkable result obtained in our simulations is that we identiﬁed three components of the model that produced signatures analogous to those of the fMRI BOLD response in three cortical areas. [sent-232, score-0.289]

83 We hypothesized that neural (fMRI) activity in the brain might be related to the entropy of nodes in the model, on account of the fact that when entropy is high, many possibilities must be simultaneously represented, which may lead to greater BOLD signal. [sent-233, score-0.301]

84 The model entropy results are shown in the bottom row of Figure 3, and comparison with the top row reveals an exact correspondence. [sent-244, score-0.252]

85 Starting with the left column of Figure 3, uncertainty in the model’s response corresponds to activity in premotor cortex. [sent-248, score-0.334]

86 This activity is greater when the block calls for two distinct responses than when it calls for one. [sent-249, score-0.244]

87 In the middle column of Figure 3, the uncertainty of shape categorization corresponds to activity in posterior lateral prefrontal cortex. [sent-250, score-0.35]

88 In the right column of Figure 3, the uncertainty of the task identity (block) in the model corresponds to activity in anterior lateral PFC, a brain region near areas known to be involved in WM maintenance. [sent-252, score-0.543]

89 There is a natural explanation for this inversion, though: entropy is high in the block node when the block representation matters the least, i. [sent-254, score-0.428]

90 , when the stimulus-response mapping does not depend on knowing the task identity. [sent-256, score-0.253]

91 Thus, higher entropy of the block node actually connotes less information to be maintained due to the functional equivalence among classes. [sent-257, score-0.285]

92 5 Discussion We proposed a theoretical framework for understanding cognitive control which provides a parsimonious account of behavioral and neuroimaging data from two large experiments. [sent-258, score-0.539]

93 [6] explain their ﬁndings in terms of a descriptive model that involves a complex hierarchy of control processes within prefrontal cortex. [sent-263, score-0.381]

94 5 0 0 10 20 30 40 50 60 Trial Number 70 80 90 100 1 2 3 4 5 6 7 8 Figure 4: Task (block) representation over a sequence of trials that involves all eight task types. [sent-266, score-0.362]

95 Another novelty of our approach is the notion of that control results from dynamical inference processes, instead of being conceived of as resulting from long-term policy learning. [sent-272, score-0.385]

96 The stimulus stream sometimes supports the WM representation and sometimes disrupts it. [sent-276, score-0.251]

97 Fortunately for the model’s performance, this is exactly the circumstance in which remembering the task identity is least critical. [sent-280, score-0.273]

98 We are currently pursuing opportunities to examine the model’s predictions regarding performance on the ﬁrst trial in a block versus subsequent trials. [sent-283, score-0.328]

99 The model shows an effect observed in the task switching literature: initial trial performance is poor, but control rapidly tunes to the task and subsequent trials are more efﬁcient and roughly comparable. [sent-284, score-0.958]

100 Neuroscience: The architecture of cognitive control in the human prefrontal cortex. [sent-317, score-0.531]

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