Smooth Surrogate Models Approve Impossible Firing Patterns: A Hidden Flaw in Writing Brain Codes

Designing stimulation to drive a neuron at a target firing rate often relies on a smooth, differentiable surrogate of the cell’s steady-state rate–current (f–I) curve, but I show that this convenience comes at a cost: the smoothness that makes the surrogate optimizable also erases the hard boundaries of the neuron’s writable rate set. For a Type-II excitable Hodgkin–Huxley model, the only achievable steady rates are silence or a band from approximately 55 to 115 Hz; yet a smooth surrogate fit to the cell’s own responses certifies targets throughout the unwritable low-rate gap and beyond the depolarization-block ceiling, reporting zero optimization error while the real neuron remains silent. The failure is invariant to surrogate fit quality (in-band R2 from 0.67 to 1.00) and is conditioned by the target cell’s onset bifurcation class: Type-II neurons exhibit an unwritable gap (∼55 Hz in Hodgkin–Huxley, ∼67 Hz in Connor–Stevens Type-II), whereas Type-I neurons, including Connor–Stevens Type-I and the Wang–Buzsáki interneuron, fire continuously toward zero. A minimal feasibility screen against the true f–I curve removes the silent mis-certification. These results establish that the excitability class of the target cell determines whether a smooth f–I surrogate can safely be used to write a rate code, and that a deliberately inserted feasibility check restores safety without abandoning the differentiable optimization framework.