Decision-making with multiple alternatives

In the paper

“Four factors affect buildup: decision outcome, motion strength, number of choices present and the passage of time (Figures 4 and 5).”

In the paper

“These differences were largest at lower motion strengths but significant at all motion strengths (Fig. 1e, p<0.01).”

In the paper

“Target appearance caused a large, transient increase in firing rate (Fig. 2a,c, left) followed by the establishment of a baseline firing rate as the monkey awaited the onset of the random dot motion.”

In the paper

“Firing rate was also reduced in the 90° control task, though much less than in the 4-choice task (Fig. 3d, 3.7±2.1 sp/s lower on the 90° control task than on the 2-choice task, p<0.05).”

In the paper

“Further, on both tasks, we observed a time-dependent rise in firing rates that may impose a deadline for deciding.”

In the paper

“In both tasks, accuracy was nearly perfect at high motion strengths and fell toward chance with lower motion strengths (Fig. 1d).”

In the paper

“Accuracy on this task emulated the standard 2-choice task (Fig. 1f), albeit with longer RTs, which fell between those on the standard 2- and 4-choice conditions (Fig. 1g).”

In the paper

“Further, unlike the buildup rates at the beginning of the decision, the firing rates at the end of decisions for Tin did not vary as a function of motion strength (p>0.57 for 2 and 4-choice) and were the same for correct and error trials (p>0.78 for 2- and 4-choice).”

In the paper

“Firing rates tended to be lower on the 4-choice task overall (difference = 9.81±4.08 sp/s, p<0.02).”

In the paper

“We observed a weak dependence of firing rate on motion strength, but the effects were not statistically reliable (p>0.07 in all cases).”

In the paper

“Although the monkeys distributed their choices with nearly equal frequency to all (two or four) choice targets, firing rates increased as a function of time.”

In the paper

“This difference, present in individual neurons (e.g., Fig. 6a), was highly significant across the population (Fig. 6b,c, p<0.0005) and in both monkeys individually (excursion difference: Monkey I: 4.7±0.27 sp/s, p<0.02, Monkey S: 11.9±1.0 sp/s, p<0.005).”

In the paper

“For motion toward Tout, increasing motion strength suppressed buildup rate slightly more in the 2-choice condition, but the difference was not reliable (difference = 0.50±0.31 sp.s−2.%coh−1; p=0.11, see Methods, Eq. 3).”

In the paper

“The magnitude of this difference depends on which interval we use to estimate firing rates at the end of the trial, but the effect is statistically significant for a wide range (Supplementary Fig 2c).”

In the paper

“The model provides an adequate account of both RT and accuracy on both tasks (smooth curves Figure 1,d–g).”

In the paper

“A prominent buildup in firing rate does not depend on motion strength or direction and is not explained by the monkey’s choice, as seen in 0% motion strength trials, which favor all directions equally, on average (Fig. 4a–d, cyan traces).”

In the paper

“Stronger motion was associated with lower buildup rates (note the negative slopes).”

• Also stated in: § Supplementary Material · plain

  “The magnitude of the coherence-dependent change of buildup was greater in the 2-choice task (mean difference = 0.075±0.021 sp·s−2·%coh−1 less negative for 4-choice trials, p<0.001).”

In the paper

“However, the effect of choice number on firing rate excursion that we report here was present for a range of time intervals, centered up to 130 ms before the saccade (Supplementary Fig. 2c).”

• Also stated in: § Supplementary Material · plain

  “Firing rate excursions were significantly larger for 4-choice than for 2-choice responses over a wide range of termination intervals.”

In the paper

“The mean response to T90 targets is similar to the mean response to Tout targets, suggesting that they are not in a suppressive region of the RF or its surround.”

• Also stated in: § Supplementary Material · plain

  “The arrow indicates the mean difference (0.36±0.63 sp/s larger for T90 choices than for Tout choices, p=0.57).”

In the paper

“Similar urgency signals are observed on trials with nonzero motion strengths (data not shown).”

• Also stated in: § Supplementary Materials · plain

  “Similar urgency signals are observed on trials with nonzero motion strengths (data not shown).”

In the paper

“The rates are ¼ for 180° choices and ½ for the combined±90° choices.”

In the paper

“Stronger motion was associated with larger buildup rates (note the positive slopes).”

• Also stated in: § Supplementary Material · plain

  “The magnitude of the coherence-dependent change was similar for 2- and 4-choice conditions (mean difference = 0.02±0.03 sp·s−2·% coh−1, p=0.53, arrow).”

In the paper

“This difference is similar in magnitude to the one seen in the epoch preceding onset of random dot motion (Fig. 3, main text).”

In the paper

“they continue to rise until ~10 ms before saccade initiation, on average.”

In the paper

“the trend was for slightly faster saccades on the 4-choice task (mean percent difference = −1.37±0.5%, p<0.01).”

In the paper

“The arrow indicates the mean difference (0.36±0.63 sp/s larger for T90 choices than for Tout choices, p=0.57).”

In the paper

“Second, neuronal firing rates in the lateral intraparietal area (LIP) are consistent with evidence accumulation 2,7–9.”

What the sources say

• Not checked yetcites [2] Roitman, J.D. & Shadlen, M.N. Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. J. Neurosci. 22, 9475–9489 (2002). source
• Not checked yetcites [7] Shadlen, M.N. & Newsome, W.T. Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. J. Neurophysiol. 86, 1916–1936 (2001). source
• Not checked yetcites [8] Hanks, T.D., Ditterich, J. & Shadlen, M.N. Microstimulation of macaque area LIP affects decision-making in a motion discrimination task. Nat. Neurosci. 9, 682–689 (2006). source
• Not checked yetcites [9] Huk, A.C. & Shadlen, M.N. Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making. J. Neurosci. 25, 10420–10436 (2005). source

In the paper

“Multi- and single-unit responses with these characteristics are common in the ventral portion of LIP targeted in these experiments (LIPv 11).”

What the sources say

• Not checked yetcites [11] Lewis, J.W. & Van Essen, D.C. Corticocortical connections of visual, sensorimotor and multimodal processing areas in the parietal lobe of the macaque monkey. J. Comp. Neurol. 428, 112–137 (2000). source

In the paper

“First, a formal model of bounded accumulation accounts quantitatively for subjects’ speed and accuracy3,6.”

What the sources say

• Not checked yetcites [3] Palmer, J., Huk, A.C. & Shadlen, M.N. The effect of stimulus strength on the speed and accuracy of a perceptual decision. J. Vis. 5, 376–404 (2005). source
• Not checked yetcites [6] Mazurek, M.E., Roitman, J.D., Ditterich, J. & Shadlen, M.N. A role for neural integrators in perceptual decision making. Cereb. Cortex 13, 1257–1269 (2003). source

In the paper

“Specifically, when stimulus motion favors the target in the response field (RF) of an LIP neuron, firing rates build up progressively as monkeys form their decisions; the rate of buildup is proportional to motion strength.”

What the sources say

• Not checked yetcites [2] Roitman, J.D. & Shadlen, M.N. Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. J. Neurosci. 22, 9475–9489 (2002). source
• Not checked yetcites [7] Shadlen, M.N. & Newsome, W.T. Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. J. Neurophysiol. 86, 1916–1936 (2001). source
• Not checked yetcites [8] Hanks, T.D., Ditterich, J. & Shadlen, M.N. Microstimulation of macaque area LIP affects decision-making in a motion discrimination task. Nat. Neurosci. 9, 682–689 (2006). source
• Not checked yetcites [9] Huk, A.C. & Shadlen, M.N. Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making. J. Neurosci. 25, 10420–10436 (2005). source

In the paper

“We conclude that the smaller angular separation between targets contributes to the reduction in activity seen in the 4-choice task in this epoch, but the reduction is largely explained by the number of choices.”

In the paper

“This model—especially the hybrid of fixed and free terms—is not unique but underscores the consistency of physiological and behavioral measurements within the framework of bounded accumulation.”

In the paper

“Moreover this buildup begins at a fixed time after the onset of motion and signals the end of decision (for Tin) by achieving a critical level.”

In the paper

“The set was identical in all conditions, so the 2-choice task was easy, probably explaining the faster RTs here.”

In the paper

“The positive buildup rates at all motion strengths and for all directions effectively impose a deadline on the decision process—a deadline that is earlier when there are just 2 choices.”

In the paper

“This hypothesis was suggested by theorists5,28,29 but had not been tested.”

What the sources say

• Not checked yetcites [5] Laming, D.R.J. Information Theory of Choice-Reaction Times (Wiley, New York, 1968).
• Not checked yetcites [28] Usher, M. & McClelland, J.L. The time course of perceptual choice: the leaky, competing accumulator model. Psychol. Rev. 108, 550–592 (2001). source
• Not checked yetcites [29] McMillen, T. & Holmes, P. The dynamics of choice among multiple alternatives. J. Math. Psychol. 50, 30–57 (2006). source

In the paper

“All these observations are consistent with longer RTs on the 4-choice task: it takes longer for LIP firing rates to undergo the larger excursion.”

In the paper

“Many models are proposed to explain the coordination of RT and choice accuracy in 2-choice tasks 4,18,25–27. These models share a common feature: a termination bound is applied to some form of evidence representation, the decision variable.”

What the sources say

• Not checked yetcites [4] Link, S.W. & Heath, R.A. A sequential theory of psychological discrimination. Psychometrika 40, 77–105 (1975). source
• Not checked yetcites [18] Reddi, B.A., Asrress, K.N. & Carpenter, R.H. Accuracy, information, and response time in a saccadic decision task. J. Neurophysiol. 90, 3538–35346 (2003). source
• Not checked yetcites [25] Ratcliff, R. & Rouder, J.N. Modeling response times for two-choice decisions. Psychol. Sci. 9, 347–356 (1998). source
• Not checked yetcites [26] Luce, R.D. Response Times: Their Role in Inferring Elementary Mental Organization (Oxford University Press, New York, 1986).
• Not checked yetcites [27] Lo, C.C. & Wang, X.J. Cortico-basal ganglia circuit mechanism for a decision threshold in reaction time tasks. Nat. Neurosci. 9, 956–963 (2006). source

In the paper

“Because chance represents 50% correct, there is less impetus to complete the trial at weak motion strengths, which probably explains the weaker urgency signal, u(t), seen previously in 2-choice experiments2,36.”

What the sources say

• Not checked yetcites [2] Roitman, J.D. & Shadlen, M.N. Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. J. Neurosci. 22, 9475–9489 (2002). source
• Not checked yetcites [36] Ditterich, J. Stochastic models of decisions about motion direction: behavior and physiology. Neural Netw. 19, 981–1012 (2006). source

In the paper

“The DV undergoes a larger excursion in the 4-choice task because the accumulation of evidence begins at a lower starting point”

In the paper

“Buildup rates in LIP reflect, at least in part, this subtraction: a change in motion strength in the direction favoring Tin leads to a proportional rise in buildup rate in LIP, and an opposite change in motion strength leads to a comparable decline.”

In the paper

“When the number of alternatives is increased, all else being equal, the level of uncertainty is initially increased.”

In the paper

“We obtained similar results whether buildup rates were from individual neurons (as described above) or were computed from the average population response (data not shown).”

In the paper

“The null hypothesis, that the number of choices did not affect the excursion, was again rejected at the population level (p<0.01) and in all but one of the individual cells where the effect of firing rate excursion was significant.”

In the paper

“The urgency signal shortens the RTs and leads to an apparent rise in the DV even for processes that accumulate negative evidence.”

In the paper

“A time-dependent rise of firing rate in LIP and elsewhere has been interpreted as a representation of elapsed time in the form of a hazard rate or anticipation function 12,33–35.”

What the sources say

• Not checked yetcites [12] Leon, M.I. & Shadlen, M.N. Representation of time by neurons in the posterior parietal cortex of the macaque. Neuron 38, 317–327 (2003). source
• Not checked yetcites [33] Janssen, P. & Shadlen, M.N. A representation of the hazard rate of elapsed time in macaque area LIP. Nat. Neurosci. 8, 234–241 (2005). source
• Not checked yetcites [34] Brody, C.D., Hernandez, A., Zainos, A. & Romo, R. Timing and neural encoding of somatosensory parametric working memory in macaque prefrontal cortex. Cereb. Cortex 13, 1196–1207 (2003). source
• Not checked yetcites [35] Maimon, G. & Assad, J.A. A cognitive signal for the proactive timing of action in macaque LIP. Nat. Neurosci. 9, 948–955 (2006). source

In the paper

“Thus, it is not surprising that the brain would accrue more evidence before terminating the decision.”

In the paper

“These two methods sometimes yielded slightly different estimates, but the direction and significance of all results reported here was the same for both methods.”

In the paper

“In the latter, the contribution of the two non-opposing directions (T90) was small (figure 4f, red dot-dash trace), but we doubt this will generalize to more directions and choices.”

In the paper

“Long decision times would improve performance above chance (25% correct), but not for the 0% motion strength trials and not by much for the next weakest motion strength.”

In the paper

“Our experiment is not definitive here, in part because the angle between alternatives is large compared to the range of angles that primates can discriminate 22–24.”

What the sources say

• Not checked yetcites [22] Jazayeri, M. & Movshon, J.A. A new perceptual illusion reveals mechanisms of sensory decoding. Nature 446, 912–915 (2007). source
• Not checked yetcites [23] Purushothaman, G. & Bradley, D.C. Neural population code for fine perceptual decisions in area MT. Nat. Neurosci. 8, 99–106 (2005). source
• Not checked yetcites [24] Churchland, A.K. et al. Directional anisotropies reveal a functional segregation of visual motion processing for perception and action. Neuron 37, 1001–1011 (2003). source

In the paper

“The cost is decision time, but this is tempered by implementation of a deadline imposed by the urgency signal.”

In the paper

“The urgency signal is the difference between the observed firing rates and this expectation from unbiased diffusion.”

In the paper

“Analyses using different time intervals affected the reported values of buildup rate only slightly; the largest effect was on buildup rates corresponding to the highest motion strength, owing mainly to the attrition of trials with short RTs.”

In the paper

“Although magnitude of the difference in excursion depends on the choice of termination window, the central claim that excursion is larger on the 4-choice task appears robust.”

In the paper

“the central claim that excursion is larger on the 4-choice task appears robust.”

In the paper

“The urgency signal shortens the RTs and leads to an apparent rise in the DV even for processes that accumulate negative evidence.”

In the paper

“The DV undergoes a larger excursion in the 4-choice task because the accumulation of evidence begins at a lower starting point”