13To take the best actions, we often need to maintain and update beliefs about variables that cannot be directly 14 observed. To understand the principles underlying such belief updates, we need tools to uncover subjects' 15 belief dynamics from natural behaviour. We tested whether eye movements could be used to infer subjects' 16 beliefs about latent variables using a naturalistic, visuomotor navigation task. We observed eye movements 17 that appeared to continuously track the goal location even when no visible target was present there. Accurate 18 goal-tracking was associated with improved task performance, and inhibiting eye movements in humans 19 impaired navigation precision. By using passive stimulus playback and manipulating stimulus reliability, we 20 show that subjects' eye movements are likely voluntary, rather than reflexive. These results suggest that 21 gaze dynamics play a key role in action-selection during challenging visuomotor behaviours, and may 22 possibly serve as a window into the subject's dynamically evolving internal beliefs. 23 88 the range of target distances and the duration for which the target was visible (see Methods). All subjects 89 were head-fixed, and we recorded each subject's movement trajectory (Fig 1Dmiddle) as well as eye 90 position (Fig 1Dright) throughout each trial.
91Behavioural performance 92 Figure 1E shows the performance of the monkeys in this task. Both radial distance (Fig 1E -left) and 93 angular eccentricity (Fig 1E -right) of the monkeys' responses (stopping location) were highly correlated 94 with the target location across trials ( = 3 monkeys, Pearson's ± standard deviation, radial distance: 95 0.72 ± 0.1, angle: 0.84 ± 0.1) suggesting that their behaviour was appropriate for the task. To test whether 96 their performance was accurate, we regressed their responses against target locations. The slope of the 97 regression was close to unity both for radial distance (mean ± standard deviation = 0.92 ± 0.06) and angle 98 (0.98 ± 0.1) suggesting that the monkeys were nearly unbiased (Fig 1F -green). We did notice modest 99 undershooting for distant targets, an effect that is likely due to growing position uncertainty described in 100 previous work (Lakshminarasimhan et al., 2018). 101 We showed previously that humans are systematically biased when performing this task without feedback, 102 and that the bias was likely due to prior expectations that make them underestimate their movement 103 velocities (Lakshminarasimhan et al., 2018). Consistent with those findings, human subjects overshot the 104 target in an initial block of trials in which no feedback was provided (Fig S1C; = 5, mean slope ± standard deviation, radial distance: 1.21 ± 0.2, angle: 1.78 ± 0.3), to a degree that was proportional to 106 target distance. With feedback, however, the same subjects quickly adapted their responses to produce 107 nearly unbiased performance (Fig 1F -purple, see Fig S1D for individual trials; mean slope ± standard 108 deviation, radial distance: 0.95 ± 0.1, angle:...
