Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism

2026-09-28

AI Summary

This study addresses the challenge of provably recovering physical mechanisms from machine learning predictions of dynamical systems by investigating whether structured latent models can reproduce hidden state inference in the Hodgkin-Huxley (HH) model. Methodologically, it proposes a novel evaluation framework that decouples state recovery from dynamics recovery, integrating cross-seed variance analysis with HH identity error decomposition to train models on simulated current-voltage data under unknown gating identities. Results demonstrate that three-dimensional latent variables substantially reduce prediction errors, while five- to six-dimensional representations enhance gating recovery under novel protocols. Furthermore, the analysis reveals that high R² values can still accompany discrepancies between learned transport fields and true dynamics, clarifying how observational manifolds influence decoding and identifying specific sources of reconstruction error.

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.

Problem

• Hodgkin-Huxley model
• mechanism recovery
• state recovery
• latent dynamics
• machine learning

Innovation

• Hodgkin-Huxley model
• structured latent models
• state recovery
• mechanism discovery
• transported field