The neuron as a direct data-driven controller

Abstract

In the quest to model neuronal function amid gaps in physiological data, a promising strategy is to develop a normative theory that interprets neuronal physiology as optimizing a computational objective. This study extends current normative models, which primarily optimize prediction, by conceptualizing neurons as optimal feedback controllers. We posit that neurons, especially those beyond early sensory areas, steer their environment toward a specific desired state through their output. This environment comprises both synaptically interlinked neurons and external motor sensory feedback loops, enabling neurons to evaluate the effectiveness of their control via synaptic feedback. To model neurons as biologically feasible controllers which implicitly identify loop dynamics, infer latent states, and optimize control we utilize the contemporary direct data-driven control (DD-DC) framework. Our DD-DC neuron model explains various neurophysiological phenomena: the shift from potentiation to depression in spike-timing-dependent plasticity with its asymmetry, the duration and adaptive nature of feedforward and feedback neuronal filters, the imprecision in spike generation under constant stimulation, and the characteristic operational variability and noise in the brain. Our model presents a significant departure from the traditional, feedforward, instant-response McCulloch-Pitts-Rosenblatt neuron, offering a modern, biologically informed fundamental unit for constructing neural networks.

Keywords: control; dynamics; neuron.

Fig. 1.

(A) A schematic representation of the neuron as a feedback controller in a closed loop. (B) A scalar fully observed dynamical system controlled by tuning the weight of a synapse, $w$, in the control law. (C) The subspace of valid pairings of observations and controls (blue plane) is spanned by the previously observed states (blue vectors). The intersection of the valid dynamical subspace with the $x_{t+1}=0$ plane defines the control law (red line). (D) STDP: the relative change in the synaptic weight, $\mathrm{\Delta }w/w$, vs. the time interval between the pre- and postsynaptic spikes, $t_x-t_u$, showing the potentiation (causal) and depression (anticausal) windows (–29). Adapted from ref. . Copyright 1998 Society for Neuroscience.

Fig. 2.

The gain, $w$, of the online DD-DC LQR controller (Top) and the state variable, $x$, of the scalar dynamical plant (Bottom) as a function of time for switching system dynamics parameters. Left: In the absence of noise in control, the DD-DC controller fails to adapt to the changing conditions because of the loss of persistence of excitation. Each of the five colored lines represents a different simulation trial. Right: Adding noise to the control law Eq. 16 enables exploration that restores the persistence of excitation and performance of the controller (also see SI Appendix, section B). The dashed line shows optimal LQR values of weights for every time step. The white bands within the gray shaded areas in the $w$ plots represent regions of stability and instability respectively. Insets plot $|x|$ on a log scale–representative of the control loss.

Fig. 3.

(A) Illustration of the neuron modeled as an ARMA controller, characterized by feedforward, ${\mathbf{K}}_{\mathit{ff}}$, and feedback, ${\mathbf{K}}_{\mathit{fb}}$, temporal filters. (B–D) Adaptation of experimentally measured temporal filters (depicted in black, yellow, and blue) to input signal statistics. Solid lines represent mean values, while thin dotted lines denote standard errors of the mean. Regions where differences are statistically significant ($P<0.05$, Wilcoxon rank-sum test with Bonferroni correction for multiple comparisons) are highlighted in red. (B) Variation in feedforward (akin to decorrelated spike-triggered average, STA) and feedback (analogous to spike-history dependence) filters of the blowfly H1 neuron (54), responding to visual motion against different background luminance levels. (C) Feedforward and feedback filters in pyramidal cells from the mouse primary visual cortex (55) responding to current injections with varying mean levels. (D) Feedback filters in a salamander retinal ganglion cell (8) for stimuli comprising a drifting bar and a fish movie (meta data for the feedforward filter is unavailable, see SI Appendix). (E) Adaptation of feedforward and feedback filters in a Drosophila olfactory receptor neuron (ORN) (56) to odorant concentrations with varying variances. (F) Feedback filters in rat somatosensory cortex pyramidal neurons (57), responding to current injections modulated by an Ornstein–Uhlenbeck process atop a DC component. Feedforward filters are provided in SI Appendix.

Fig. 4.

High-variance current injections into a neuron yield remarkably consistent spike trains over multiple trials, showcasing the precision of the spike-generation mechanism. Right: In contrast, a constant current input leads to notably variable spike trains, revealing a significant reduction in spike-timing precision. This dichotomy highlights the neuron’s differential response to varying and constant stimuli. Adapted with permission from ref. .

Fig. 5.

Left: Illustration of controlling a nonlinear dynamical system using multiple switching DD-DCs. Right: Depiction of a deep network model where each neuron exerts control over its immediate environment, contributing to the broader control exerted by the entire brain over the external environment.