Mapping Low-Dimensional Dynamics to High-Dimensional Neural Activity: A Derivation of the Ring Model From the Neural Engineering Framework

Empirical estimates of the dimensionality of neural population activity are often much lower than the population size. Similar phenomena are also observed in trained and designed neural network models. These experimental and computational results suggest that mapping low-dimensional dynamics to high-dimensional neural space is a common feature of cortical computation. Despite the ubiquity of this observation, the constraints arising from such mapping are poorly understood. Here we consider a specific example of mapping low-dimensional dynamics to high-dimensional neural activity—the neural engineering framework. We analytically solve the framework for the classic ring model—a neural network encoding a static or dynamic angular variable. Our results provide a complete characterization of the success and failure modes for this model. Based on similarities between this and other frameworks, we speculate that these results could apply to more general scenarios.

Multiscale low-dimensional motor cortical state dynamics predict naturalistic reach-and-grasp behavior

Motor function depends on neural dynamics spanning multiple spatiotemporal scales of population activity, from spiking of neurons to larger-scale local field potentials (LFP). How multiple scales of low-dimensional population dynamics are related in control of movements remains unknown. Multiscale neural dynamics are especially important to study in naturalistic reach-and-grasp movements, which are relatively under-explored. We learn novel multiscale dynamical models for spike-LFP network activity in monkeys performing naturalistic reach-and-grasps. We show low-dimensional dynamics of spiking and LFP activity exhibited several principal modes, each with a unique decay-frequency characteristic. One principal mode dominantly predicted movements. Despite distinct principal modes existing at the two scales, this predictive mode was multiscale and shared between scales, and was shared across sessions and monkeys, yet did not simply replicate behavioral modes. Further, this multiscale mode’s decay-frequency explained behavior. We propose that multiscale, low-dimensional motor cortical state dynamics reflect the neural control of naturalistic reach-and-grasp behaviors.

Low-dimensional dynamics for working memory and time encoding

Our decisions often depend on multiple sensory experiences separated by time delays. The brain can remember these experiences and, simultaneously, estimate the timing between events. To understand the mechanisms underlying working memory and time encoding, we analyze neural activity recorded during delays in four experiments on nonhuman primates. To disambiguate potential mechanisms, we propose two analyses, namely, decoding the passage of time from neural data and computing the cumulative dimensionality of the neural trajectory over time. Time can be decoded with high precision in tasks where timing information is relevant and with lower precision when irrelevant for performing the task. Neural trajectories are always observed to be low-dimensional. In addition, our results further constrain the mechanisms underlying time encoding as we find that the linear “ramping” component of each neuron’s firing rate strongly contributes to the slow timescale variations that make decoding time possible. These constraints rule out working memory models that rely on constant, sustained activity and neural networks with high-dimensional trajectories, like reservoir networks. Instead, recurrent networks trained with backpropagation capture the time-encoding properties and the dimensionality observed in the data.

Complementary roles of dimensionality and population structure in neural computations

Neural computations are currently investigated using two competing approaches: sorting neurons into functional classes, or examining the low-dimensional dynamics of collective activity. Whether and how these two aspects interact to shape computations is currently unclear. Using a novel approach to extract computational mechanisms from networks trained with machine-learning tools on neuroscience tasks, here we show that the dimensionality of the dynamics and cell-class structure play fundamentally complementary roles. While various tasks can be implemented by increasing the dimensionality in networks consisting of a single global population, flexible input-output mappings instead required networks to be organized into several sub-populations. Our analyses revealed that the subpopulation structure enabled flexible computations through a mechanism based on gain-controlled modulations that flexibly shape the dynamical landscape of collective dynamics. Our results lead to task-specific predictions for the structure of neural selectivity and inactivation experiments.

Optimal anticipatory control as a theory of motor preparation: a thalamo-cortical circuit model

SummaryAcross a range of motor and cognitive tasks, cortical activity can be accurately described by low-dimensional dynamics unfolding from specific initial conditions on every trial. These “preparatory states” largely determine the subsequent evolution of both neural activity and behaviour, and their importance raises questions regarding how they are — or ought to be — set. Here, we formulate motor preparation as optimal prospective control of future movements. The solution is a form of internal control of cortical circuit dynamics, which can be implemented as a thalamo-cortical loop gated by the basal ganglia. Critically, optimal control predicts selective quenching of variability in components of preparatory population activity that have future motor consequences, but not in others. This is consistent with recent perturbation experiments performed in mice, and with our novel analysis of monkey motor cortex activity during reaching. Together, these results suggest optimal anticipatory control of movement.