Figure 5. Fitting the model to experimental data: the model with inference (AN-TN) captures the statistical structure of the data, and accounts for the variability between subjects.

(a) Model comparison for the recurrent session. Bayesian Information Criterion (see Materials and methods) for the models with and without task-set inference. The model provides a significantly better fit with inference than without. (b) Estimate of the inference strength $J_{INC}$ from the task-set network to the associative network connectivity in the model with task-set inference, for both sessions. (c) Proportion correct around the first correct trial, averaged over episodes and over subjects, for the recurrent session. (d) Subject by subject difference between BIC values obtained for models with and without task-set inference, as a function of the inference strength parameter, for the recurrent session. Subjects are classified as ‘exploiting’ or ‘exploring’ from a post-test debriefing. The grey line displays a least-squares regression. (e) Subject by subject performance following the first correct trial in an episode, as a function of the inference strength parameter, for the recurrent session. The performance was computed by considering the 10 trials following the first correct trial of each episode. The grey line displays a least-squares regression. .

Figure 5—figure supplement 1. Model comparison for the recurrent session.

(a) Bayesian Information Criterion (see Materials and methods) for the models with and without task-set inference, for Experiment 2. The model provides a significantly better fit with inference than without ($p=9.1\cdot {10}^{-5}$, $t=4.1$). (b) Proportion correct after an episode switch, averaged over episodes and over subjects, for Experiment 1. (c,d) Opposite of model log-likelihood averaged per trial for the models with and without task-set inference, for Experiment 1 (d) and Experiment 2 (e). The model provides a significantly better fit with inference than without (respectively $p=4.7\cdot {10}^{-12}$, $t=14.0$ and $p=1.3\cdot {10}^{-21}$, $t=17.0$).

Figure 5—figure supplement 2. Learning task-sets with a lower ratio of potentiation versus depression in the task-set network ($Q_P\mathrm{/}{Q}_M\mathrm{=}\mathrm{5}$) by refitting the model, while either fixing $g_I\mathrm{=}\mathrm{0.5}$ or $g_I\mathrm{=}\mathrm{0.2}$.

Mean parameter values over subjects for $Q_P/Q_M=5$ and $g_I=0.5$ are : $\alpha =0.35$, $1/\beta =0.16$, $ϵ=0.050$, $Q_P=0.24$, and $J_{INC}=0.78$. Mean parameter values over subjects for $Q_P/Q_M=5$ and $g_I=0.2$ are : $\alpha =0.35$, $1/\beta =0.15$, $ϵ=0.060$, $Q_P=0.050$, and $J_{INC}=0.68$. This can be compared with Figure 5—source data 1 of the model with $Q_P/Q_M=10$ and $g_I=0.5$. (a) Comparison of BIC for the fit with $Q_P/Q_M=10$ and $g_I=0.5$ used in the main paper, the fit with $Q_P/Q_M=5$ and $g_I=0.5$, and the fit with $Q_P/Q_M=5$ and $g_I=0.2$. A T-test on related samples gives respectively $p=0.25$, $p=0.014$ and $p=5.8\cdot {10}^{-4}$. (b) Comparison of the inference strength parameter values. (c) Proportion correct around the first correct trial, averaged over episodes and over subjects, for Experiment 1. (d,e) Simulation of the model, respectively for $g_I=0.5$ (left) or $g_I=0.2$ (right). Task-sets presentation is periodic for illustration purposes. The simulation corresponds to the average over 500 runs of the recurrent session. For clarity, we did not introduce tricky trials in these simulations. The plots display the average values of task-set network synaptic strengths between neural populations corresponding to each of the three correct task-sets, and spurious connexions.

Figure 5—figure supplement 3. Model fit for both sessions together.

Related to Figure 5. Mean parameter values over subjects for sessions fitted together are : $\alpha =0.35$, $1/\beta =0.15$, $ϵ=0.056$, $Q_P=0.35$, and $J_{INC}=0.28$ to be compared with Figure 5—source data 1. (a) Comparison of BIC for the recurrent session fitted separately, the recurrent session when both sessions are fitted together, the open-ended session fitted separately, and the open-ended session when both sessions are fitted together. The model provides a significantly better fit when sessions are fitted separately (T-test on related samples, $p=1.6\cdot {10}^{-9}$ and $p=3.5\cdot {10}^{-5}$ respectively for recurrent and open-ended sessions). (b) Comparison of the inference strength parameter values when sessions are fitted separately or together. (c) Proportion correct around the first correct trial, averaged over episodes and over subjects, for Experiment 1.