Identifying Neural Dynamics Using Nonlinear Interventional State Space Models
Abstract
State-space models (SSMs) recover low-dimensional latent dynamics from high-dimensional observations, but latents are generally not identifiable from observational data alone. Interventional state-space models (iSSMs) use perturbations to break observational symmetries and identify parameters up to permutation, scaling, and shift. However, prior work restricts identifiability to linear latent dynamics and piecewise-linear emissions, excluding many behaviors characteristic of neural circuits. We extend iSSMs to a substantially broader model class: we prove that (i) affine identifiability holds under general injective emission functions and Gaussian latent transitions, and (ii) with interventions, identifiability up to permutation, scaling, and shift is preserved under general nonlinear latent dynamics. We validate our theory on simulated FitzHugh-Nagumo dynamics, and then demonstrate two applications: adjudicating between competing models of decision-making; and predicting responses to unseen micro-stimulation in macaque and human neural recordings, with proof-of-concept generalization to a held-out stimulation site in the latter. Finally, simulations yield practical guidance for designing stimulation protocols that improve identifiability.
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BibTeX
@misc{tolle2026identifying,
title = {{Identifying Neural Dynamics Using Nonlinear Interventional State Space Models}},
author = {Hanna M. Tolle and Carles Balsells-Rodas and Yixin Wang and Pedro A. M. Mediano and Amin Nejatbakhsh},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08113},
eprint = {2611.08113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08113},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Identifying Neural Dynamics Using Nonlinear Interventional State Space Models
AU - Hanna M. Tolle
AU - Carles Balsells-Rodas
AU - Yixin Wang
AU - Pedro A. M. Mediano
AU - Amin Nejatbakhsh
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08113
UR - https://arxiv.org/abs/2611.08113
AB - State-space models (SSMs) recover low-dimensional latent dynamics from high-dimensional observations, but latents are generally not identifiable from observational data alone. Interventional state-space models (iSSMs) use perturbations to break observational symmetries and identify parameters up to permutation, scaling, and shift. However, prior work restricts identifiability to linear latent dynamics and piecewise-linear emissions, excluding many behaviors characteristic of neural circuits. We extend iSSMs to a substantially broader model class: we prove that (i) affine identifiability holds under general injective emission functions and Gaussian latent transitions, and (ii) with interventions, identifiability up to permutation, scaling, and shift is preserved under general nonlinear latent dynamics. We validate our theory on simulated FitzHugh-Nagumo dynamics, and then demonstrate two applications: adjudicating between competing models of decision-making; and predicting responses to unseen micro-stimulation in macaque and human neural recordings, with proof-of-concept generalization to a held-out stimulation site in the latter. Finally, simulations yield practical guidance for designing stimulation protocols that improve identifiability.
ER -