Inferring Latent Dynamics Underlying Neural Population Activity via Neural Differential Equations

Timothy D. Kim, Thomas Z. Luo, Jonathan W. Pillow, Carlos D. Brody
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:5551-5561, 2021.

Abstract

An important problem in systems neuroscience is to identify the latent dynamics underlying neural population activity. Here we address this problem by introducing a low-dimensional nonlinear model for latent neural population dynamics using neural ordinary differential equations (neural ODEs), with noisy sensory inputs and Poisson spike train outputs. We refer to this as the Poisson Latent Neural Differential Equations (PLNDE) model. We apply the PLNDE framework to a variety of synthetic datasets, and show that it accurately infers the phase portraits and fixed points of nonlinear systems augmented to produce spike train data, including the FitzHugh-Nagumo oscillator, a 3-dimensional nonlinear spiral, and a nonlinear sensory decision-making model with attractor dynamics. Our model significantly outperforms existing methods at inferring single-trial neural firing rates and the corresponding latent trajectories that generated them, especially in the regime where the spike counts and number of trials are low. We then apply our model to multi-region neural population recordings from medial frontal cortex of rats performing an auditory decision-making task. Our model provides a general, interpretable framework for investigating the neural mechanisms of decision-making and other cognitive computations through the lens of dynamical systems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-kim21h, title = {Inferring Latent Dynamics Underlying Neural Population Activity via Neural Differential Equations}, author = {Kim, Timothy D. and Luo, Thomas Z. and Pillow, Jonathan W. and Brody, Carlos D.}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {5551--5561}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/kim21h/kim21h.pdf}, url = {https://proceedings.mlr.press/v139/kim21h.html}, abstract = {An important problem in systems neuroscience is to identify the latent dynamics underlying neural population activity. Here we address this problem by introducing a low-dimensional nonlinear model for latent neural population dynamics using neural ordinary differential equations (neural ODEs), with noisy sensory inputs and Poisson spike train outputs. We refer to this as the Poisson Latent Neural Differential Equations (PLNDE) model. We apply the PLNDE framework to a variety of synthetic datasets, and show that it accurately infers the phase portraits and fixed points of nonlinear systems augmented to produce spike train data, including the FitzHugh-Nagumo oscillator, a 3-dimensional nonlinear spiral, and a nonlinear sensory decision-making model with attractor dynamics. Our model significantly outperforms existing methods at inferring single-trial neural firing rates and the corresponding latent trajectories that generated them, especially in the regime where the spike counts and number of trials are low. We then apply our model to multi-region neural population recordings from medial frontal cortex of rats performing an auditory decision-making task. Our model provides a general, interpretable framework for investigating the neural mechanisms of decision-making and other cognitive computations through the lens of dynamical systems.} }
Endnote
%0 Conference Paper %T Inferring Latent Dynamics Underlying Neural Population Activity via Neural Differential Equations %A Timothy D. Kim %A Thomas Z. Luo %A Jonathan W. Pillow %A Carlos D. Brody %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-kim21h %I PMLR %P 5551--5561 %U https://proceedings.mlr.press/v139/kim21h.html %V 139 %X An important problem in systems neuroscience is to identify the latent dynamics underlying neural population activity. Here we address this problem by introducing a low-dimensional nonlinear model for latent neural population dynamics using neural ordinary differential equations (neural ODEs), with noisy sensory inputs and Poisson spike train outputs. We refer to this as the Poisson Latent Neural Differential Equations (PLNDE) model. We apply the PLNDE framework to a variety of synthetic datasets, and show that it accurately infers the phase portraits and fixed points of nonlinear systems augmented to produce spike train data, including the FitzHugh-Nagumo oscillator, a 3-dimensional nonlinear spiral, and a nonlinear sensory decision-making model with attractor dynamics. Our model significantly outperforms existing methods at inferring single-trial neural firing rates and the corresponding latent trajectories that generated them, especially in the regime where the spike counts and number of trials are low. We then apply our model to multi-region neural population recordings from medial frontal cortex of rats performing an auditory decision-making task. Our model provides a general, interpretable framework for investigating the neural mechanisms of decision-making and other cognitive computations through the lens of dynamical systems.
APA
Kim, T.D., Luo, T.Z., Pillow, J.W. & Brody, C.D.. (2021). Inferring Latent Dynamics Underlying Neural Population Activity via Neural Differential Equations. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:5551-5561 Available from https://proceedings.mlr.press/v139/kim21h.html.

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