Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism

Abstract:Predicting observed dynamics does not establish recovery of the underlying physical mechanism. Can machine learning retrace the hidden-state reasoning behind the Hodgkin-Huxley (HH) model? We train structured latent models on simulated current and voltage, withholding gate identities and trajectories from training and model selection. We then test response prediction, state recovery, protocol transfer, and agreement with HH dynamics. Prediction error and its cross-seed spread both drop sharply at three latent dimensions under the tested protocols, while gate recovery under new protocols improves through five to six coordinates. State recovery depends on which observations the chart uses. Observed voltage improves current-clamp decoding relative to freely predicted voltage. Under voltage clamp, adding latent state to command voltage raises m-state $R^2$ from 0.976 to above 0.99, yet the transported field disagrees with HH on identical smooth samples. Known invertible HH coordinates achieve high fast-m field agreement under the same audit procedure. An exact HH identity decomposes the discrepancy into time-scale-weighted state error and a residual in the transported field; these terms can cancel or reinforce. These findings concern the tested models and charts. They support evaluating state and dynamics recovery separately, including chart inputs and transported-field agreement across interventions.

22 pages, 7 figures. Code available at this https URL

Machine Learning (cs.LG)

arXiv:2609.34566 [cs.LG]

(or arXiv:2609.34566v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.34566 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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