Appendix 1—table 3. Mathematical definition of models included an inverse temperature parameter.

Model	Cost function	Softmax function
1	${\displaystyle SV=\left(R\right)-\left({\beta }_E\cdot E^2\right)}$	${\displaystyle p\left(accept\right)=\frac{1}{1+e^{-\tau (SV)}}}$
2	${\displaystyle SV=\left({\mathit{\beta }}_{\mathit{R}}\cdot R\right)-\left({\mathit{\beta }}_{\mathit{E}}\cdot E^2\right)}$	${\displaystyle p\left(accept\right)=\frac{1}{1+e^{-\tau (SV)}}}$
3	${\displaystyle SV=\left(R\right)-\left({\mathit{\beta }}_{\mathit{E}}\cdot E^2\right)}$	${\displaystyle p\left(accept\right)=\frac{1}{1+e^{-\tau (\alpha +SV)}}}$
4	${\displaystyle SV=\left({\mathit{\beta }}_{\mathit{R}}\cdot R\right)-\left({\mathit{\beta }}_{\mathit{E}}\cdot E^2\right)}$	${\displaystyle p\left(accept\right)=\frac{1}{1+e^{-\tau (\alpha +SV)}}}$