# Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism

arXiv: https://arxiv.org/abs/2609.34566 · HTML: https://mlsanity.com/paper/2609.34566/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 46 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge](https://mlsanity.com/paper/1711.07970/) (2017)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [Learning Dynamical Systems from Partial Observations](https://mlsanity.com/paper/1902.11136/) (2019)
- [Discovering Sparse Interpretable Dynamics from Partial Observations](https://mlsanity.com/paper/2107.10879/) (2021)
- [Learning Latent Dynamics for Partially-Observed Chaotic Systems](https://mlsanity.com/paper/1907.02452/) (2019)
- [Beyond Predictions in Neural ODEs: Identification and Interventions](https://mlsanity.com/paper/2106.12430/) (2021)
- [Learning the Hodgkin-Huxley Model with Operator Learning Techniques](https://mlsanity.com/paper/2406.02173/) (2024)
- [Learning Physics Informed Neural ODEs With Partial Measurements](https://mlsanity.com/paper/2412.08681/) (2024)
- [Uncovering differential equations from data with hidden variables](https://mlsanity.com/paper/2002.02250/) (2020)
- [Learning Governing Equations of Unobserved States in Dynamical Systems](https://mlsanity.com/paper/2404.18572/) (2024)
- [Towards an Hybrid Hodgkin-Huxley Action Potential Generation Model](https://mlsanity.com/paper/2304.01346/) (2023)
- [Geometric regularization of autoencoders via observed stochastic dynamics](https://mlsanity.com/paper/2604.16282/) (2026)
- [Parameter identifiability and identifiable combinations in generalized Hodgkin-Huxley models](https://mlsanity.com/paper/1511.05227/) (2015)
- [Discovery of the Hidden State in Ionic Models Using a Domain-Specific Recurrent Neural Network](https://mlsanity.com/paper/2011.07388/) (2020)
- [Correcting model error bias in estimations of neuronal dynamics from time series observations](https://mlsanity.com/paper/2508.19948/) (2025)
- [Learning Hybrid Biophysical Neuron Models with Neural ODEs](https://mlsanity.com/paper/2606.16693/) (2026)

## Abstract (arXiv)

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 R2 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.