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Correlations in state space can cause sub-optimal adaptation of optimal feedback control models.

ABSTRACT: Control of our movements is apparently facilitated by an adaptive internal model in the cerebellum. It was long thought that this internal model implemented an adaptive inverse model and generated motor commands, but recently many reject that idea in favor of a forward model hypothesis. In theory, the forward model predicts upcoming state during reaching movements so the motor cortex can generate appropriate motor commands. Recent computational models of this process rely on the optimal feedback control (OFC) framework of control theory. OFC is a powerful tool for describing motor control, it does not describe adaptation. Some assume that adaptation of the forward model alone could explain motor adaptation, but this is widely understood to be overly simplistic. However, an adaptive optimal controller is difficult to implement. A reasonable alternative is to allow forward model adaptation to 're-tune' the controller. Our simulations show that, as expected, forward model adaptation alone does not produce optimal trajectories during reaching movements perturbed by force fields. However, they also show that re-optimizing the controller from the forward model can be sub-optimal. This is because, in a system with state correlations or redundancies, accurate prediction requires different information than optimal control. We find that adding noise to the movements that matches noise found in human data is enough to overcome this problem. However, since the state space for control of real movements is far more complex than in our simple simulations, the effects of correlations on re-adaptation of the controller from the forward model cannot be overlooked.

SUBMITTER: Aprasoff J

PROVIDER: S-EPMC3304072 | biostudies-literature | 2012 Apr

REPOSITORIES: biostudies-literature

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Correlations in state space can cause sub-optimal adaptation of optimal feedback control models.

Aprasoff Jonathan J Donchin Opher O

Journal of computational neuroscience 20110727 2

Control of our movements is apparently facilitated by an adaptive internal model in the cerebellum. It was long thought that this internal model implemented an adaptive inverse model and generated motor commands, but recently many reject that idea in favor of a forward model hypothesis. In theory, the forward model predicts upcoming state during reaching movements so the motor cortex can generate appropriate motor commands. Recent computational models of this process rely on the optimal feedback ...[more]

PMID: 21792671

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Project description:The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel's time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

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Correlations in state space can cause sub-optimal adaptation of optimal feedback control models.

Publications

Correlations in state space can cause sub-optimal adaptation of optimal feedback control models.

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