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149 nips-2005-Optimal cue selection strategy

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Author: Vidhya Navalpakkam, Laurent Itti

Abstract: Survival in the natural world demands the selection of relevant visual cues to rapidly and reliably guide attention towards prey and predators in cluttered environments. We investigate whether our visual system selects cues that guide search in an optimal manner. We formally obtain the optimal cue selection strategy by maximizing the signal to noise ratio (SN R) between a search target and surrounding distractors. This optimal strategy successfully accounts for several phenomena in visual search behavior, including the effect of target-distractor discriminability, uncertainty in target’s features, distractor heterogeneity, and linear separability. Furthermore, the theory generates a new prediction, which we verify through psychophysical experiments with human subjects. Our results provide direct experimental evidence that humans select visual cues so as to maximize SN R between the targets and surrounding clutter.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Optimal cue selection strategy Vidhya Navalpakkam Department of Computer Science USC, Los Angeles navalpak@usc. [sent-1, score-0.312]

2 edu Abstract Survival in the natural world demands the selection of relevant visual cues to rapidly and reliably guide attention towards prey and predators in cluttered environments. [sent-3, score-0.338]

3 We investigate whether our visual system selects cues that guide search in an optimal manner. [sent-4, score-0.465]

4 We formally obtain the optimal cue selection strategy by maximizing the signal to noise ratio (SN R) between a search target and surrounding distractors. [sent-5, score-0.923]

5 This optimal strategy successfully accounts for several phenomena in visual search behavior, including the effect of target-distractor discriminability, uncertainty in target’s features, distractor heterogeneity, and linear separability. [sent-6, score-0.702]

6 Furthermore, the theory generates a new prediction, which we verify through psychophysical experiments with human subjects. [sent-7, score-0.024]

7 Our results provide direct experimental evidence that humans select visual cues so as to maximize SN R between the targets and surrounding clutter. [sent-8, score-0.255]

8 1 Introduction Detecting a yellow tiger among distracting foliage in different shades of yellow and brown requires efﬁcient top-down strategies that select relevant visual cues to enable rapid and reliable detection of the target among several distractors. [sent-9, score-0.777]

9 For simple scenarios such as searching for a red target, the Guided Search theory [17] predicts that search efﬁciency can be improved by boosting the red feature in a top-down manner. [sent-10, score-0.305]

10 But for more complex and natural scenarios such as detecting a tiger in the jungle or looking for a face in a crowd, ﬁnding the optimum amount of top-down enhancement to be applied to each low-level feature dimension encoded by the early visual system is non-trivial. [sent-11, score-0.247]

11 It must not only consider features present in the target, but also those present in the distractors. [sent-12, score-0.035]

12 In this paper, we formally obtain the optimal cue selection strategy and investigate whether our visual system has evolved to deploy it. [sent-13, score-0.525]

13 In section 2, we formulate cue selection as an optimization problem where the relevant goal is to maximize the signal to noise ratio (SN R) of the saliency map, so that the target becomes most salient and quickly draws attention, thereby minimizing search time. [sent-14, score-0.997]

14 In section 4, we describe the design and analysis of psychophysics experiments to test new, counter-intuitive predictions of the theory. [sent-16, score-0.042]

15 The results of our study suggest that humans deploy optimal cue selection strategies to detect targets in cluttered and distracting environments. [sent-17, score-0.446]

16 2 Formalizing visual search as an optimization problem To quickly ﬁnd a target among distractors, we wish to maximize the salience of the target relative to the distractors. [sent-18, score-1.309]

17 Thus we can deﬁne the signal to noise ratio (SN R) as the ratio of salience of the target to the distractors. [sent-19, score-0.738]

18 Assuming that visual cues or features are encoded by populations of neurons in early visual areas, we deﬁne the optimal cue selection strategy as the best choice of neural response gain that maximizes the signal to noise ratio (SN R). [sent-20, score-1.027]

19 In the rest of this section, we formally obtain the optimal choice of gain in neural responses that will maximize SN R. [sent-21, score-0.149]

20 Hence, we express SN R as the ratio of expected salience of the target over expected salience of the distractors, with the expectation taken over all possible target and distractor locations, their features and spatial conﬁgurations, and over several repeated trials. [sent-23, score-1.616]

21 Mean salience of the Target SN R = Mean salience of the distractor Search array and its stimuli: Let search array A be a two-dimensional display that consists of one target T and several distractors Dj (j = 1. [sent-24, score-1.924]

22 Let the display be divided into an invisible N × N grid, with one item occuring at each cell (x, y) in the grid. [sent-28, score-0.089]

23 Let the color, contrast, orientation and other target parameters θT be chosen from a distribution P (θ|T ). [sent-29, score-0.323]

24 Similarly, for each distractor Dj , let its parameters θDj be sampled independently from a distribution P (θ|D). [sent-30, score-0.223]

25 Thus, search array A has a ﬁxed choice of target and distractor parameters. [sent-31, score-0.815]

26 Next, the spatial conﬁguration C is decided by a random permutation of some assignment of the target and distractors to the N 2 cells in A (such that there is exactly one item in each cell). [sent-32, score-0.76]

27 Thus, for a given search array A, the spatial conﬁguration as well as stimulus parameters are ﬁxed. [sent-33, score-0.336]

28 Finally, given a choice of parameter θ and its spatial location (x, y), we generate an image pattern R(θ) (a set of pixels and their values) and embed it at location (x, y) in search array A. [sent-34, score-0.359]

29 Saliency computation: Let the input search array A be processed by a population of neurons with gaussian tuning curves tuned to different stimulus parameters such as µ1 , µ2 , . [sent-36, score-0.523]

30 The output of this early visual processing stage is used to compute saliency maps si (x, y, A) of search array A, that consist of the visual salience at every location (x, y) for feature-values µi (i = 1. [sent-40, score-1.026]

31 Let si (x, y, A) be combined linearly to form S(x, y, A), the overall salience at location (x, y). [sent-44, score-0.376]

32 Further, assuming a multiplicative gain gi on the ith saliency map, we obtain: S(x, y, A) = gi si (x, y, A) (1) i Salience of the target and distractors: Let ST (A) be a random variable representing the salience of the target T in search array A. [sent-45, score-1.88]

33 To factor out the variability due to internal noise η, we consider Eη [ST (A)], which is the mean salience of the target over repeated identical presentations of A. [sent-46, score-0.666]

34 Further, let EC [ST (A)] be the mean salience of the target averaged over all spatial conﬁgurations of a given set of target and distractor parameters. [sent-47, score-1.216]

35 Similarly, Eθ|T [ST (A)] is the mean salience of the target over all target parameters. [sent-48, score-0.961]

36 The mean salience of the target combined over several repeated presentations of the search array A (to factor out internal noise η), over all spatial conﬁgurations C, and over all choices of target parameters θ|T is given below. [sent-49, score-1.29]

37 Further, since η, C and θ are independent random variables, we can rewrite the joint expectation as follows: E[ST (A)] = Eθ|T [EC [Eη [ST (A)]]] (2) Let SD (A) represent the mean salience of distractors Dj (j = 1. [sent-50, score-0.664]

38 Similar to computing the mean salience of the target, we ﬁnd the mean salience of distractors over all η, C and θ|D. [sent-54, score-0.979]

39 SD (A) = EDj [siDj (A)] (3) E[SD (A)] = Eθ|D [EC [Eη [SD (A)]]] (4) SN R and its optimization: The additive salience and multiplicative gain hypothesis in eqn. [sent-55, score-0.37]

40 SN Ri = EΘ|T [EC [Eη [siT (A)]]]/EΘ|D [EC [Eη [siD (A)]]] (10) The sign of the derivative, d dgi SN R gi =1 tells us whether gi should be increased, de- creased or maintained at the baseline activation 1 in order to maximize SN R. [sent-58, score-0.507]

41 SN Ri SN R < = > d SN R < 0 ⇒ SN R increases as gi decreases ⇒ gi < 1 dgi d 1⇒ SN R = 0 ⇒ SN R does not change with gi ⇒ gi = 1 dgi d 1⇒ SN R > 0 ⇒ SN R increases as gi increases ⇒ gi > 1 dgi 1⇒ (11) (12) (13) Thus, we obtain an intuitive result that gi increases as SN Ri increases. [sent-59, score-1.641]

42 3 Predictions of the optimal cue selection strategy To understand the implications of biasing features according to the optimal cue selection strategy, we simulate a simple model of early visual cortex. [sent-62, score-0.86]

43 We assume that each feature dimension is encoded by a population of neurons with overlapping gaussian tuning curves that are broadly tuned to different features in that dimension. [sent-63, score-0.324]

44 Let fi (θ) represent the tuning curve of the ith neuron in a population of broadly tuned neurons with overlapping tuning curves. [sent-64, score-0.404]

45 Let the tuning width σ and amplitude a be equal for all neurons, and µi represent the preferred stimulus parameter (or feature) of the ith neuron. [sent-65, score-0.137]

46 fi (θ) = a (θ − µi )2 exp − σ 2σ 2 (16) Let r(Θ(x, y, A)) = {r1 (Θ(x, y, A)). [sent-66, score-0.057]

47 rn (Θ(x, y, A))} be the population response to a stimulus parameter Θ(x, y, A) at a location (x, y) in search array A, where ri refers to the response of the ith neuron and n is the total number of neurons in the population. [sent-69, score-0.737]

48 Let the neural response ri (Θ(x, y, A)) be a Poisson random variable. [sent-70, score-0.166]

49 P (ri (Θ(x, y, A)) = z) = Pfi (Θ(x,y,A)) (z) (17) For simplicity, let’s assume that the local neural response ri (Θ(x, y, A)) is a measure of salience si (x, y, A). [sent-71, score-0.513]

50 2, 4, 10, 16, 17, we can derive the mean salience of the target and distractor, and use it to compute SN Ri . [sent-73, score-0.638]

51 si (x, y, A) E[siT (A)] = ri (Θ(x, y, A)) = Eθ|T [fi (θ)] (18) (19) E[siD (A)] = Eθ|D [fi (θ)] (20) Eθ|T [fi (θ)] Eθ|D [fi (θ)] (21) SN Ri = Finally, the gains gi on each saliency map can be found using eqn. [sent-74, score-0.538]

52 Thus, for a given distribution of stimulus parameters for the target P (θ|T ) and distractors P (θ|D), we simulate the above model of early visual cortex, compute salience of target and distractors, compute SN Ri and obtain gi . [sent-76, score-1.695]

53 In the rest of this section, we plot the distribution of optimal choice of gains gi for an exhaustive list of conditions where knowledge of the target and distractors varies from complete certainty to uncertainty. [sent-77, score-0.979]

54 Unknown target and distractors: In the trivial case where there is no knowledge of the target and distractors, all cues are equally relevant and the optimal choice of gains is the same as baseline activation (unity). [sent-78, score-0.902]

55 This prediction is consistent with visual search experiments that observe slow search when the target and distractors are unknown due to reversal between trials [1, 2]. [sent-80, score-1.172]

56 Search for a known target: During search for a known target, the optimal strategy predicts that SN R can be maximised by boosting neurons according to how strongly they respond to the target feature (as shown in ﬁgure 1, predicted SN R is 12. [sent-81, score-0.834]

57 Thus, a neuron that is optimally tuned to the target feature receives maximal gain. [sent-83, score-0.55]

58 This prediction is consistent with single unit recordings on feature-based attention which show that the gain in neural response depends on the similarity between the neuron’s preferred feature and the target feature [3, 4]. [sent-84, score-0.56]

59 Role of uncertainty in target features: When there’s uncertainty in the target’s features, i. [sent-85, score-0.373]

60 , when the target’s parameter assumes multiple values according to some probability distribution P (θ|T ), the optimal strategy predicts that SN R decreases, leading to a slower search (as shown in ﬁgure 1, SN R decreases from 12. [sent-87, score-0.376]

61 This result is consistent with psychophysics experiments which suggest that better knowledge of the target leads to faster search [5, 6]. [sent-89, score-0.537]

62 Distractor heterogeneity: While searching for an unknown target among known distractors, the optimal strategy predicts that SN R can be maximised by suppressing the neurons tuned to the distractors (see ﬁgure 1). [sent-90, score-1.121]

63 But as we increase distractor heterogeneity or the number of distractor types, it predicts a decrease in SN R (from 36 dB to 17 dB, ﬁgure 1). [sent-91, score-0.584]

64 Discriminability between target and distractors: Several experiments and theories have studied the effect of target-distractor discriminability [10]-[17]. [sent-93, score-0.443]

65 The optimal cue selection strategy also shows that if the target and distractors are very different or highly discriminable, SN R is high and the search is efﬁcient (SN R = 51. [sent-94, score-1.222]

66 Otherwise, if they are similar and not well separated in feature space, SN R is low and the search is hard (SN R = 16. [sent-96, score-0.218]

67 Moreover, during search for a less discriminable target from distractors, the optimal strategy predicts that the neuron optimally tuned to the target may not be boosted maximally. [sent-98, score-1.299]

68 Instead, a neuron that is sub-optimally tuned to the target and farther away from the distractors receives maximal gain. [sent-99, score-0.827]

69 This new and counterintuitive prediction is tested by visual search experiments described in the next section. [sent-100, score-0.283]

70 Linear separability effect: The optimal strategy also predicts the linear separability effect [18, 19] which suggests that when the target and distractors are less discriminable, search is easier if the target and distractors can be separated by a line in feature space (see ﬁgure 1). [sent-101, score-1.878]

71 , search for the smallest or largest item is faster than search for a medium-sized item in the display)[20], chromaticity and luminance [21, 19], and orientation [22, 23]. [sent-104, score-0.456]

72 4 Testing new predictions of the optimal cue selection strategy In this section, we describe the design and analysis of psychophysics experiments to verify the counter-intuitive prediction mentioned in the previous section, i. [sent-105, score-0.444]

73 , during searching for a target that is less discriminable from the distractors, a neuron that is sub-optimally tuned to the target’s feature will be boosted more than a neuron that is optimally tuned to the target’s feature. [sent-107, score-0.827]

74 1 Design of psychophysics experiments Our experiments are designed in two phases: phase 1 to set up the top-down bias and phase 2 to measure the bias. [sent-109, score-0.138]

75 Phase 1 - Setup the top-down bias: Subjects perform the primary task T1 which is a visual search for the target among distractors. [sent-110, score-0.643]

76 This task sets the top-down bias on cues so that the target becomes the most salient item in the display, thus accelerating target detection. [sent-111, score-0.882]

77 Subjects are trained on T1 trials until their performance stabilises with at least 80% accuracy. [sent-112, score-0.045]

78 They are instructed to ﬁnd the target (55◦ tilt) among several distractors (50◦ tilt). [sent-113, score-0.709]

79 The target and distractors are the same for all T1 trials. [sent-114, score-0.672]

80 To avoid false reports (which may occur due to boredom or lack of attention) and to verify that subjects indeed ﬁnd the target, we introduce a novel no cheat scheme as follows: After ﬁnding the target among distractors, subjects press any key. [sent-115, score-0.556]

81 Following the key press, we ﬂash a grid of ﬁneprint random numbers brieﬂy (120ms) and ask subjects to report the number at the target’s location. [sent-116, score-0.048]

82 Thus, the top-down bias is set up by performing T1 trials. [sent-118, score-0.036]

83 For each of the four subjects, the number of reports on the steepest (80◦ ), relevant (60◦ ), target (55◦ ) and distractor (50◦ ) cues are shown in these bar plots. [sent-122, score-0.831]

84 As predicted by the theory, a paired t-test reveals that the number of reports on the relevant cue is signiﬁcantly higher (p < 0. [sent-123, score-0.298]

85 05) than the number of reports on the target, distractor and steepest cues, as indicated by the blue star. [sent-124, score-0.355]

86 Phase 2 - Measure the top-down bias: To measure the top-down bias generated by the above task, we randomly insert T2 trials in between T1 trials. [sent-125, score-0.081]

87 Our theory predicts that during search for the target (55◦) among distractors (50◦ ), the most relevant cue will be around 60◦ and not 55◦ . [sent-126, score-1.164]

88 To test this, we brieﬂy (200ms) ﬂash four cues - steepest (S, 80◦ ), relevant as predicted by our theory (R, 60◦ ), target (T, 55◦ ) and distractor (D, 50◦ ). [sent-127, score-0.755]

89 A cue that is biased more appears more salient, attracts a saccade, and gets reported. [sent-128, score-0.185]

90 In other words, the greater the top-down bias on a cue, the higher the number of its reports. [sent-129, score-0.036]

91 According to our theory, there should be higher number of reports on R than T. [sent-130, score-0.076]

92 As mentioned earlier, each subject received training on T1 trials for a few days until the performance (search speed) stabilised with atleast 80% accuracy. [sent-133, score-0.045]

93 Finally, each subject performed 10 blocks of 50 trials each, with T2 trials randomly inserted in between T1 trials. [sent-135, score-0.09]

94 2 Results For each of the four subjects, we extracted the number reports on the steepest (NS ), relevant (NR ), target (NT ) and distractor (ND ) cues, for each block. [sent-137, score-0.715]

95 As predicted by the theory, we found a signiﬁcantly higher number of reports on the relevant cue than the target cue. [sent-140, score-0.621]

96 5 Discussion In this paper, we have investigated whether our visual system has evolved to use optimal top-down strategies to select relevant cues that quickly and reliably detect the target among distracting environments. [sent-141, score-0.775]

97 We formally obtained the optimal cue selection strategy where cues are chosen such that the signal-to-noise ratio (SN R) of the saliency map is maximized, thus maximizing the target’s salience relative to the distractors. [sent-142, score-1.012]

98 The resulting optimal strategy is to boost a cue or feature if it provides higher signal-to-noise ratio than average. [sent-143, score-0.448]

99 Our study complements the recent work on optimal eye movement strategies [24]. [sent-145, score-0.098]

100 Thus, both optimal cue selection and saccade generation are necessary for optimal visual search. [sent-147, score-0.524]

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In this paper, we propose a particular model of the environment suitable for visual search tasks. Rather than explicitly modeling the optimization of attentional control by setting gains, we assume that the optimization process will serve to minimize Equation 1. Because any gain adjustment will facilitate performance in some environmental states and hinder performance in others, an optimized control system should obtain faster reaction times for more probable environmental states. This assumption allows us to explain experimental results in a minimal, parsimonious framework. 3 MODELING THE ENVIRONMENT Focusing on the domain of visual search, we characterize the environment in terms of a probability distribution over configurations of target and distractor features. We distinguish three classes of features: defining, reported, and irrelevant. To explain these terms, consider the task of searching a display of size varying, colored, notched diamonds (Figure 2), with the task of detecting the singleton in color and judging the notch location. Color is the defining feature, notch location is the reported feature, and size is an irrelevant feature. To simplify the exposition, we treat all features as having discrete values, an assumption which is true of the experimental tasks we model. We begin by considering displays containing a single target and a single distractor, and shortly generalize to multidistractor displays. We use the framework of Bayesian networks to characterize the environment. Each feature of the target and distractor is a discrete random variable, e.g., Tcolor for target color and Dnotch for the location of the notch on the distractor. The Bayes net encodes the probability distribution over environmental states; in our working example, this distribution is P(Tcolor, Tsize, Tnotch, Dcolor, Dsize, Dnotch). The structure of the Bayes net specifies the relationships among the features. The simplest model one could consider would be to treat the features as independent, illustrated in Figure 3a for singleton-color search task. The opposite extreme would be the full joint distribution, which could be represented by a look up table indexed by the six features, or by the cascading Bayes net architecture in Figure 3b. The architecture we propose, which we’ll refer to as the dominance model (Figure 3c), has an intermediate dependency structure, and expresses the joint distribution as: P(Tcolor)P(Dcolor |Tcolor)P(Tsize |Tcolor)P(Tnotch |Tcolor)P(Dsize |Dcolor)P(Dnotch |Tcolor). The structured model is constructed based on three rules. 1. The defining feature of the target is at the root of the tree. 2. The defining feature of the distractor is conditionally dependent on the defining feature of the target. We refer to this rule as dominance of the target over the distractor. 3. The reported and irrelevant features of target (distractor) are conditionally dependent on the defining feature of the target (distractor). We refer to this rule as dominance of the defining feature over nondefining features. As we will demonstrate, the dominance model produces a parsimonious account of a wide range of experimental data. 3.1 Updating the environment model The model’s parameters are the conditional distributions embodied in the links. In the example of Figure 3c with binary random variables, the model has 11 parameters. However, these parameters are determined by the environment: To be adaptive in nonstationary environments, the model must be updated following each experienced state. We propose a simple exponentially weighted averaging approach. For two variables V and W with observed values v and w on trial t, a conditional distribution, P t ( V = u W = w ) = δ uv , is (a) Tcolor Dcolor Tsize Tnotch (b) Tcolor Dcolor Dsize Tsize Dnotch Tnotch (c) Tcolor Dcolor Dsize Tsize Dsize Dnotch Tnotch Dnotch FIGURE 3. Three models of a visual-search environment with colored, notched, size-varying diamonds. (a) feature-independence model; (b) full-joint model; (c) dominance model. defined, where δ is the Kronecker delta. The distribution representing the environment E following trial t, denoted P t , is then updated as follows: E E P t ( V = u W = w ) = αP t – 1 ( V = u W = w ) + ( 1 – α )P t ( V = u W = w ) (2) for all u, where α is a memory constant. Note that no update is performed for values of W other than w. An analogous update is performed for unconditional distributions. E How the model is initialized—i.e., specifying P 0 —is irrelevant, because all experimental tasks that we model, participants begin the experiment with many dozens of practice trials. E Data is not collected during practice trials. Consequently, any transient effects of P 0 do E not impact the results. In our simulations, we begin with a uniform distribution for P 0 , and include practice trials as in the human studies. Thus far, we’ve assumed a single target and a single distractor. The experiments that we model involve multiple distractors. The simple extension we require to handle multiple distractors is to define a frequentist probability for each distractor feature V, P t ( V = v W = w ) = C vw ⁄ C w , where C vw is the count of co-occurrences of feature values v and w among the distractors, and C w is the count of w. Our model is extremely simple. Given a description of the visual search task and environment, the model has only a single degree of freedom, α . In all simulations, we fix α = 0.75 ; however, the choice of α does not qualitatively impact any result. 4 SIMULATIONS In this section, we show that the model can explain a range of data from four different experiments examining attentional priming. All experiments measure response times of participants. On each trial, the model can be used to obtain a probability of the display configuration (the environmental state) on that trial, given the history of trials to that point. Our critical assumption—as motivated earlier—is that response times monotonically decrease with increasing probability, indicating that visual information processing is better configured for more likely environmental states. The particular relationship we assume is that response times are linear in log probability. This assumption yields long response time tails, as are observed in all human studies. 4.1 Maljkovic and Nakayama (1994, Experiment 5) In this experiment, participants were asked to search for a singleton in color in a display of three red or green diamonds. Each diamond was notched on either the left or right side, and the task was to report the side of the notch on the color singleton. The well-practiced participants made very few errors. Reaction time (RT) was examined as a function of whether the target on a given trial is the same or different color as the target on trial n steps back or ahead. Figure 4 shows the results, with the human RTs in the left panel and the simulation log probabilities in the right panel. The horizontal axis represents n. Both graphs show the same outcome: repetition of target color facilitates performance. This influence lasts only for a half dozen trials, with an exponentially decreasing influence further into the past. In the model, this decreasing influence is due to the exponential decay of recent history (Equation 2). Figure 4 also shows that—as expected—the future has no influence on the current trial. 4.2 Maljkovic and Nakayama (1994, Experiment 8) In the previous experiment, it is impossible to determine whether facilitation is due to repetition of the target’s color or the distractor’s color, because the display contains only two colors, and therefore repetition of target color implies repetition of distractor color. To unconfound these two potential factors, an experiment like the previous one was con- ducted using four distinct colors, allowing one to examine the effect of repeating the target color while varying the distractor color, and vice versa. The sequence of trials was composed of subsequences of up-to-six consecutive trials with either the target or distractor color held constant while the other color was varied trial to trial. Following each subsequence, both target and distractors were changed. Figure 5 shows that for both humans and the simulation, performance improves toward an asymptote as the number of target and distractor repetitions increases; in the model, the asymptote is due to the probability of the repeated color in the environment model approaching 1.0. The performance improvement is greater for target than distractor repetition; in the model, this difference is due to the dominance of the defining feature of the target over the defining feature of the distractor. 4.3 Huang, Holcombe, and Pashler (2004, Experiment 1) Huang et al. (2004) and Hillstrom (2000) conducted studies to determine whether repetitions of one feature facilitate performance independently of repetitions of another feature. In the Huang et al. study, participants searched for a singleton in size in a display consisting of lines that were short and long, slanted left or right, and colored white or black. The reported feature was target slant. Slant, size, and color were uncorrelated. Huang et al. discovered that repeating an irrelevant feature (color or orientation) facilitated performance, but only when the defining feature (size) was repeated. As shown in Figure 6, the model replicates human performance, due to the dominance of the defining feature over the reported and irrelevant features. 4.4 Wolfe, Butcher, Lee, and Hyde (2003, Experiment 1) In an empirical tour-de-force, Wolfe et al. (2003) explored singleton search over a range of environments. The task is to detect the presence or absence of a singleton in displays conHuman data Different Color 600 Different Color 590 580 570 15 13 11 9 7 Past 5 3.2 3 Same Color 2.8 Same Color 560 550 Simulation 3.4 log(P(trial)) Reaction Time (msec) 610 3 1 +1 +3 +5 Future 2.6 +7 15 13 Relative Trial Number 11 9 7 Past 5 3 1 +1 +3 +5 Future +7 Relative Trial Number FIGURE 4. Experiment 5 of Maljkovic and Nakayama (1994): performance on a given trial conditional on the color of the target on a previous or subsequent trial. Human data is from subject KN. 650 6 Distractors Same 630 5.5 log(P(trial)) FIGURE 5. Experiment 8 of Maljkovic and Nakayama (1994). (left panel) human data, average of subjects KN and SS; (right panel) simulation Reaction Time (msec) 640 620 Target Same 610 5 Distractors Same 4.5 4 600 Target Same 3.5 590 3 580 1 2 3 4 5 1 6 4 5 6 4 1000 Size Alternate Size Alternate log(P(trial)) Reaction Time (msec) 3 4.2 1050 FIGURE 6. Experiment 1 of Huang, Holcombe, & Pashler (2004). (left panel) human data; (right panel) simulation 2 Order in Sequence Order in Sequence 950 3.8 3.6 3.4 900 3.2 Size Repeat 850 Size Repeat 3 Color Repeat Color Alternate Color Repeat Color Alternate sisting of colored (red or green), oriented (horizontal or vertical) lines. Target-absent trials were used primarily to ensure participants were searching the display. The experiment examined seven experimental conditions, which varied in the amount of uncertainty as to the target identity. The essential conditions, from least to most uncertainty, are: blocked (e.g., target always red vertical among green horizontals), mixed feature (e.g., target always a color singleton), mixed dimension (e.g., target either red or vertical), and fully mixed (target could be red, green, vertical, or horizontal). With this design, one can ascertain how uncertainty in the environment and in the target definition influence task difficulty. Because the defining feature in this experiment could be either color or orientation, we modeled the environment with two Bayes nets—one color dominant and one orientation dominant—and performed model averaging. A comparison of Figures 7a and 7b show a correspondence between human RTs and model predictions. Less uncertainty in the environment leads to more efficient performance. One interesting result from the model is its prediction that the mixed-feature condition is easier than the fully-mixed condition; that is, search is more efficient when the dimension (i.e., color vs. orientation) of the singleton is known, even though the model has no abstract representation of feature dimensions, only feature values. 4.5 Optimal adaptation constant In all simulations so far, we fixed the memory constant. From the human data, it is clear that memory for recent experience is relatively short lived, on the order of a half dozen trials (e.g., left panel of Figure 4). In this section we provide a rational argument for the short duration of memory in attentional control. Figure 7c shows mean negative log probability in each condition of the Wolfe et al. (2003) experiment, as a function of α . To assess these probabilities, for each experimental condition, the model was initialized so that all of the conditional distributions were uniform, and then a block of trials was run. Log probability for all trials in the block was averaged. The negative log probability (y axis of the Figure) is a measure of the model’s misprediction of the next trial in the sequence. For complex environments, such as the fully-mixed condition, a small memory constant is detrimental: With rapid memory decay, the effective history of trials is a high-variance sample of the distribution of environmental states. For simple environments, a large memory constant is detrimental: With slow memory decay, the model does not transition quickly from the initial environmental model to one that reflects the statistics of a new environment. Thus, the memory constant is constrained by being large enough that the environment model can hold on to sufficient history to represent complex environments, and by being small enough that the model adapts quickly to novel environments. If the conditions in Wolfe et al. give some indication of the range of naturalistic environments an agent encounters, we have a rational account of why attentional priming is so short lived. Whether priming lasts 2 trials or 20, the surprising empirical result is that it does not last 200 or 2000 trials. Our rational argument provides a rough insight into this finding. (a) fully mixed mixed feature mixed dimension blocked 460 (c) Simulation fully mixed mixed feature mixed dimension blocked 4 5 420 log(P(trial)) 440 2 Blocked Red or Vertical Blocked Red and Vertical Mixed Feature Mixed Dimension Fully Mixed 4 3 log(P(trial)) reaction time (msec) (b) Human Data 480 3 2 1 400 1 380 0 360 0 red or vert red and vert target type red or vert red and vert target type 0 0.5 0.8 0.9 0.95 0.98 Memory Constant FIGURE 7. (a) Human data for Wolfe et al. (2003), Experiment 1; (b) simulation; (c) misprediction of model (i.e., lower y value = better) as a function of α for five experimental condition 5 DISCUSSION The psychological literature contains two opposing accounts of attentional priming and its relation to attentional control. Huang et al. (2004) and Hillstrom (2000) propose an episodic account in which a distinct memory trace—representing the complete configuration of features in the display—is laid down for each trial, and priming depends on configural similarity of the current trial to previous trials. Alternatively, Maljkovic and Nakayama (1994) and Wolfe et al. (2003) propose a feature-strengthening account in which detection of a feature on one trial increases its ability to attract attention on subsequent trials, and priming is proportional to the number of overlapping features from one trial to the next. The episodic account corresponds roughly to the full joint model (Figure 3b), and the feature-strengthening account corresponds roughly to the independence model (Figure 3a). Neither account is adequate to explain the range of data we presented. However, an intermediate account, the dominance model (Figure 3c), is not only sufficient, but it offers a parsimonious, rational explanation. Beyond the model’s basic assumptions, it has only one free parameter, and can explain results from diverse experimental paradigms. The model makes a further theoretical contribution. Wolfe et al. distinguish the environments in their experiment in terms of the amount of top-down control available, implying that different mechanisms might be operating in different environments. However, in our account, top-down control is not some substance distributed in different amounts depending on the nature of the environment. Our account treats all environments uniformly, relying on attentional control to adapt to the environment at hand. We conclude with two limitations of the present work. First, our account presumes a particular network architecture, instead of a more elegant Bayesian approach that specifies priors over architectures, and performs automatic model selection via the sequence of trials. We did explore such a Bayesian approach, but it was unable to explain the data. Second, at least one finding in the literature is problematic for the model. Hillstrom (2000) occasionally finds that RTs slow when an irrelevant target feature is repeated but the defining target feature is not. However, because this effect is observed only in some experiments, it is likely that any model would require elaboration to explain the variability. ACKNOWLEDGEMENTS We thank Jeremy Wolfe for providing the raw data from his experiment for reanalysis. This research was funded by NSF BCS Award 0339103. REFERENCES Huang, L, Holcombe, A. O., & Pashler, H. (2004). Repetition priming in visual search: Episodic retrieval, not feature priming. Memory & Cognition, 32, 12–20. Hillstrom, A. P. (2000). Repetition effects in visual search. Perception & Psychophysics, 62, 800-817. Itti, L., Koch, C., & Niebur, E. (1998). A model of saliency-based visual attention for rapid scene analysis. IEEE Trans. Pattern Analysis & Machine Intelligence, 20, 1254–1259. Kearns, M., & Singh, S. (1999). Finite-sample convergence rates for Q-learning and indirect algorithms. In Advances in Neural Information Processing Systems 11 (pp. 996–1002). Cambridge, MA: MIT Press. Koch, C. and Ullman, S. (1985). Shifts in selective visual attention: towards the underlying neural circuitry. Human Neurobiology, 4, 219–227. Maljkovic, V., & Nakayama, K. (1994). Priming of pop-out: I. Role of features. Mem. & Cognition, 22, 657-672. Mozer, M. C. (1991). The perception of multiple objects: A connectionist approach. Cambridge, MA: MIT Press. Rogers, R. D., & Monsell, S. (1995). The cost of a predictable switch between simple cognitive tasks. Journal of Experimental Psychology: General, 124, 207–231. Wolfe, J.M. (1994). Guided Search 2.0: A Revised Model of Visual Search. Psych. Bull. & Rev., 1, 202–238. Wolfe, J. S., Butcher, S. J., Lee, C., & Hyde, M. (2003). Changing your mind: on the contributions of top-down and bottom-up guidance in visual search for feature singletons. Journal of Exptl. Psychology: Human Perception & Performance, 29, 483-502.

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