Input-to-state stability of chemical reaction networks with application to molecular computation

What the math gives to ML

The paper develops input-to-state stability (ISS) certificates for time-varying mass-action reaction networks, including weakly reversible networks with nonzero deficiency and multiple linkage classes, and some non-weakly-reversible networks after linear-conjugacy or reconstruction transformations. The transferable mechanism is a positive dynamical module whose hidden state remains bounded and returns toward an equilibrium under bounded perturbations of its rate inputs, with a quantitative ISS gain. A neural implementation is a positive neural ODE or state-space block in which gates, step sizes, or external context modulate reaction-like rates, while a free-energy Lyapunov monitor or penalty rejects parameter regions whose empirical disturbance-to-state gain exceeds a target.