The fitness was defined as the difference between the network output and the desired output, in similarity to the linear model and then averaged over all possible input/ output pairs.

We begin with a simple linear model of a multilayered network and later extend this framework to nonlinear models as well.

In the linear model , the total input-output relationship of the network is given by the product of the matrices A1, A2,.

The linear model builds a continuous-valued, internal percept§ of stimulus value by the animal on each trial.

To emulate the discrimination tasks, we also need to model the animal’s decision policy, which converts the continuous percept§ into a binary choice c. While the linear model is rather universal, the decision model will depend on the specifics of each experimental task.

Even if the real percept formation departs from linearity, fitting a linear model will most likely retain meaningful estimates for the coarse information (temporal scales, number of neurons involved) that we seek to estimate in our work.

Other work has suggested or implicitly used a linear model of effort discounting [31,37], and, more recently, a quadratic function [40].

Critically, we note that previous studies did not directly compare the performance of the hyperbolic or linear model to any alternative models, and did not dissociate choices involving delay and effort costs.

The second model previously suggested to describe effort discounting [37] is a simple linear model , which implies a constant integration of effort independent of reward amount, i.e., an additional fixed cost AC devalues a reward by the same amount, regardless of whether it is added to a small or a large preexisting effort level: