interpretable nonlinear dynamic modeling
Interpretable Nonlinear Dynamic Modeling of Neural Trajectories
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model assumes low-dimensional continuous dynamics in a finite volume. It incorporates a prior assumption about globally contractional dynamics to avoid overly enthusiastic extrapolation outside of the support of observed trajectories. We show that our model can recover qualitative features of the phase portrait such as attractors, slow points, and bifurcations, while also producing reliable long-term future predictions in a variety of dynamical models and in real neural data.
Interpretable Nonlinear Dynamic Modeling of Neural Trajectories
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model assumes low-dimensional continuous dynamics in a finite volume. It incorporates a prior assumption about globally contractional dynamics to avoid overly enthusiastic extrapolation outside of the support of observed trajectories. We show that our model can recover qualitative features of the phase portrait such as attractors, slow points, and bifurcations, while also producing reliable long-term future predictions in a variety of dynamical models and in real neural data.
Reviews: Interpretable Nonlinear Dynamic Modeling of Neural Trajectories
Overall I found the paper to be solid and rather enjoyable, and I would qualify it as a strong candidate for a poster. The authors' method of plotting velocity fields by decomposing the velocity into direction and speed, which they've apparently introduced, is especially effective. It made their arguments and conclusions much easier to follow, and will hopefully be picked up by others. In my opinion stating that this approach leads to "interpretable models" might be somewhat overselling the results – the interpretability of the results is still hampered by the fact that models are composed by 10-100 more or less arbitrary basis functions. That being said, their capacity to reproduce salient features of the phase diagram certainly makes them more interpretable than, say, recurrent neural networks.
Interpretable Nonlinear Dynamic Modeling of Neural Trajectories
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model assumes low-dimensional continuous dynamics in a finite volume. It incorporates a prior assumption about globally contractional dynamics to avoid overly enthusiastic extrapolation outside of the support of observed trajectories. We show that our model can recover qualitative features of the phase portrait such as attractors, slow points, and bifurcations, while also producing reliable longterm future predictions in a variety of dynamical models and in real neural data.
Interpretable Nonlinear Dynamic Modeling of Neural Trajectories
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model assumes low-dimensional continuous dynamics in a finite volume. It incorporates a prior assumption about globally contractional dynamics to avoid overly enthusiastic extrapolation outside of the support of observed trajectories. We show that our model can recover qualitative features of the phase portrait such as attractors, slow points, and bifurcations, while also producing reliable long-term future predictions in a variety of dynamical models and in real neural data.
Interpretable Nonlinear Dynamic Modeling of Neural Trajectories
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model assumes low-dimensional continuous dynamics in a finite volume. It incorporates a prior assumption about globally contractional dynamics to avoid overly enthusiastic extrapolation outside of the support of observed trajectories. We show that our model can recover qualitative features of the phase portrait such as attractors, slow points, and bifurcations, while also producing reliable long-term future predictions in a variety of dynamical models and in real neural data.