Smooth Surrogate Models Approve Impossible Firing Patterns

Code, figures, and data for the preprint "Smooth Surrogate Models Approve Impossible Firing Patterns: A Hidden Flaw in Writing Brain Codes" (Peilin (Larry) Zhong, 2026).

Preprint (Zenodo, latest version): https://doi.org/10.5281/zenodo.21645655

A smooth, differentiable surrogate of a Hodgkin-Huxley neuron's firing-rate (f-I) curve silently certifies target firing rates the real neuron cannot produce: the Type-II onset gap below ~55 Hz and depolarization block above ~115 Hz. The failure is invisible to the surrogate's own loss and is invariant to fit quality (even a perfect interpolator fails). A feasibility screen against the true f-I removes it.

Excitability class (added in v1.1.0). The failure is a signature of the target cell's onset bifurcation class. It is present in Type-II models (Hodgkin-Huxley; Connor-Stevens in its Type-II configuration, gap to ~67 Hz) and absent in Type-I models (Connor-Stevens Type-I; the Wang-Buzsaki hippocampal interneuron), which fire continuously toward zero. The effect is robust to +/-20% variation in sodium and potassium conductance. Figures 5 and 6 show the f-I curves by class and the resulting write outcomes.

Python 3 with numpy, scipy, matplotlib (plus jax + jaxley only to re-measure the HH f-I).

cd code
python fit_matches.py            # re-derives + asserts the frozen constants from ../results/hh_fi.npy
python make_figures.py           # regenerates ../figures/ (the four paper figures)
python run_surrogate_blindness.py   # the core result (surrogate certifies impossible codes)
python run_robustness.py            # smoothness is the disease, not fit quality
python run_fix.py                   # the feasibility-screen fix
python run_quantify.py              # how often / how badly it bites

results/hh_fi.npy is the Hodgkin-Huxley f-I curve measured in JAXLEY (code/measure_hh_fi.py).

Pure numpy/scipy/matplotlib (no jaxley needed):

cd code
python gen_canonical_fi.py HH        # measure + archive each model's f-I -> ../results/fi_HH.npy
python gen_canonical_fi.py WB        #   (repeat for WB, CSI, CSII)
python gen_canonical_fi.py CSI
python gen_canonical_fi.py CSII
python make_excitability_figure.py   # figure 5 (f-I by class, gap vs no gap) from the fi_*.npy
python writeblind_by_class.py        # figure 6 (requested vs delivered rate, Type-II vs Type-I)
python robustness_sweep.py CSII      # conductance sweep -> ../results/robustness_gNaK.csv
python robustness_sweep.py CSI

measure_cs_fi.py (Connor-Stevens Type-I/II) and measure_real_cells.py (classic HH, Wang-Buzsaki) hold the model kinetics, transcribed from their cited primary sources.

The two-variable Morris-Lecar model, switched between SNIC (Type-I) and Andronov-Hopf (Type-II) onset by a single parameter change, shows that the low-rate gap is a property of the onset bifurcation rather than of channel complexity (Hopf floor ~10 Hz; SNIC continuous to ~1.2 Hz):

cd code
python measure_ml_fi.py II          # Hopf regime  -> ../results/fi_MLII.npy
python measure_ml_fi.py I           # SNIC regime  -> ../results/fi_MLI.npy
python make_ml_supp_figure.py       # figure S1 -> ../figures/figS1_morris_lecar.{png,pdf}

code/       analysis + figure code (plants, testbed, run_*, make_figures, fit_matches, measure_hh_fi;
            measure_cs_fi, measure_real_cells, gen_canonical_fi, make_excitability_figure,
            writeblind_by_class, robustness_sweep)
figures/    the six paper figures (.png + .pdf)
results/    hh_fi.npy, fi_{HH,WB,CSI,CSII}.npy (measured f-I), robustness_gNaK.csv, run logs

Code: MIT (see LICENSE). The manuscript is CC-BY-4.0.