Table 1. Summary of model variables and paramters.

POMDP Variables	Descriptions
	The hidden variable of POMDP, . In the random dots task, is a constant over time
	The coherence (motion strength) of the random dots task. . is fixed during a task.
	The underlying direction of the random dots task. . is fixed during a task.
	The average spike rate of MT neurons preferring rightward or leftward direction, respectively, as a function of both coherence and described in equations 1.
	The number of spikes emitted by MT neurons preferring rightward or leftward direction, respectively during one POMDP step. follows a Poisson distribution with mean
	Total number of spikes emitted by MT neurons during one POMDP step.
	The noisy observation at time step t, which is a conditional random variable following a Binomial distribution . Note that are conditional dependent of each other given the hidden variable
	The belief (posterior distribution) . With a beta-distributed initial belief , is also beta distributed due to the binomial distributed emission probability . Without loss of generality, throughout the paper.
	Action chosen by the animal at time . .
Model Parameters
	A negative reward associated with the cost of an observation.
	A positive reward associated with a correct eye movement.
	A negative reward associated with an incorrect eye movement.
	The duration of a single observation, the real elapsed time per POMDP step. Only used to translate the number of POMDP time steps to real elapsed time when comparing with experimental data.
	Non-decision residual time. Both and are obtained from a linear regression to compare model predictions (in unit of POMDP steps) with animals' response time (in unit of seconds), independent of the POMDP model.