Task

(Fig 1 in paper)

(Fig 1 in paper)

Rats: 14 Long Evans rats. Controlled water schedule → water reward & punishment noise.

Training: Automated training protocol

Stimulus duration: 0.5 - 2 sec.

Sessions: At least 50 trials. Percent correct above 75% and fixation-drop rate below 25%. Average of 120 min on a single-day. Anti-biasing algorithm generates trials with correct answer on opposite side of rat’s favored side.

Claims from paper

Aim of study

probe whether rodents can optimally discount evidence by adapting the timescale over which they accumulate it.

Claimed results

Optimal timescale for evidence discounting depends on both:

environment volatility

noise in sensory processing

Rats accumulate (almost) optimally, if both variables above are considered.

Rats adapt their integration timescale to the volatility of the environment (short → long → short).

Model makes quantitative predictions about timing of changes of mind.

Overall, paper establishes a quantitative behavioral framework to study adaptive evidence accumulation.

Optimal evidence accumulation model

Called ‘nonlinear theory’ in the paper

$\displaystyle \frac{da}{dt} = \delta_{R,t}-\delta_{L,t}-\frac{2h}{\kappa}\sinh(\kappa a)$

a

is the posterior-odds ratio

\delta_{R,t},\ \ \delta_{L,t}

are the right and left auditory click trains (sum of delta functions)

h

is the hazard rate, or volatility of the environment

\kappa

is the click reliability parameter. It indicates how much evidence a single click provides.

Effect of sensory noise on click reliability, discount rate and changes of mind timing (Fig 2 in paper)

Linear model

Called ‘linear discounting agent’ in the paper

$\displaystyle \frac{da}{dt} = \delta_{R,t}-\delta_{L,t}-\lambda \cdot a$

\lambda

is the discounting rate

1 / \lambda

is the integration timescale

Discounting rate $\lambda$ varies with sensory noise $n$ (panel G below)

Behavioral $\lambda$ is estimated by fitting an exponential, $ae^{bt}$ , to the reverse kernel curve

​​Task

​​Claims from paper

​​Aim of study

​​Claimed results

​​Optimal evidence accumulation model