Computation Through Neural Population Dynamics.

Significant experimental, computational, and theoretical work has identified rich structure within the coordinated activity of interconnected neural populations. An emerging challenge now is to uncover the nature of the associated computations, how they are implemented, and what role they play in driving behavior. We term this computation through neural population dynamics. If successful, this framework will reveal general motifs of neural population activity and quantitatively describe how neural population dynamics implement computations necessary for driving goal-directed behavior. Here, we start with a mathematical primer on dynamical systems theory and analytical tools necessary to apply this perspective to experimental data. Next, we highlight some recent discoveries resulting from successful application of dynamical systems. We focus on studies spanning motor control, timing, decision-making, and working memory. Finally, we briefly discuss promising recent lines of investigation and future directions for the computation through neural population dynamics framework.

Cortical preparatory activity indexes learned motor memories.

The brain's remarkable ability to learn and execute various motor behaviours harnesses the capacity of neural populations to generate a variety of activity patterns. Here we explore systematic changes in preparatory activity in motor cortex that accompany motor learning. We trained rhesus monkeys to learn an arm-reaching task1 in a curl force field that elicited new muscle forces for some, but not all, movement directions2,3. We found that in a neural subspace predictive of hand forces, changes in preparatory activity tracked the learned behavioural modifications and reassociated4 existing activity patterns with updated movements. Along a neural population dimension orthogonal to the force-predictive subspace, we discovered that preparatory activity shifted uniformly for all movement directions, including those unaltered by learning. During a washout period when the curl field was removed, preparatory activity gradually reverted in the force-predictive subspace, but the uniform shift persisted. These persistent preparatory activity patterns may retain a motor memory of the learned field5,6 and support accelerated relearning of the same curl field. When a set of distinct curl fields was learned in sequence, we observed a corresponding set of field-specific uniform shifts which separated the associated motor memories in the neural state space7-9. The precise geometry of these uniform shifts in preparatory activity could serve to index motor memories, facilitating the acquisition, retention and retrieval of a broad motor repertoire.

New neural activity patterns emerge with long-term learning.

Learning has been associated with changes in the brain at every level of organization. However, it remains difficult to establish a causal link between specific changes in the brain and new behavioral abilities. We establish that new neural activity patterns emerge with learning. We demonstrate that these new neural activity patterns cause the new behavior. Thus, the formation of new patterns of neural population activity can underlie the learning of new skills.

Neural constraints on learning.

Learning, whether motor, sensory or cognitive, requires networks of neurons to generate new activity patterns. As some behaviours are easier to learn than others, we asked if some neural activity patterns are easier to generate than others. Here we investigate whether an existing network constrains the patterns that a subset of its neurons is capable of exhibiting, and if so, what principles define this constraint. We employed a closed-loop intracortical brain-computer interface learning paradigm in which Rhesus macaques (Macaca mulatta) controlled a computer cursor by modulating neural activity patterns in the primary motor cortex. Using the brain-computer interface paradigm, we could specify and alter how neural activity mapped to cursor velocity. At the start of each session, we observed the characteristic activity patterns of the recorded neural population. The activity of a neural population can be represented in a high-dimensional space (termed the neural space), wherein each dimension corresponds to the activity of one neuron. These characteristic activity patterns comprise a low-dimensional subspace (termed the intrinsic manifold) within the neural space. The intrinsic manifold presumably reflects constraints imposed by the underlying neural circuitry. Here we show that the animals could readily learn to proficiently control the cursor using neural activity patterns that were within the intrinsic manifold. However, animals were less able to learn to proficiently control the cursor using activity patterns that were outside of the intrinsic manifold. These results suggest that the existing structure of a network can shape learning. On a timescale of hours, it seems to be difficult to learn to generate neural activity patterns that are not consistent with the existing network structure. These findings offer a network-level explanation for the observation that we are more readily able to learn new skills when they are related to the skills that we already possess.

Motor cortical control of movement speed with implications for brain-machine interface control.

Motor cortex plays a substantial role in driving movement, yet the details underlying this control remain unresolved. We analyzed the extent to which movement-related information could be extracted from single-trial motor cortical activity recorded while monkeys performed center-out reaching. Using information theoretic techniques, we found that single units carry relatively little speed-related information compared with direction-related information. This result is not mitigated at the population level: simultaneously recorded population activity predicted speed with significantly lower accuracy relative to direction predictions. Furthermore, a unit-dropping analysis revealed that speed accuracy would likely remain lower than direction accuracy, even given larger populations. These results suggest that the instantaneous details of single-trial movement speed are difficult to extract using commonly assumed coding schemes. This apparent paucity of speed information takes particular importance in the context of brain-machine interfaces (BMIs), which rely on extracting kinematic information from motor cortex. Previous studies have highlighted subjects' difficulties in holding a BMI cursor stable at targets. These studies, along with our finding of relatively little speed information in motor cortex, inspired a speed-dampening Kalman filter (SDKF) that automatically slows the cursor upon detecting changes in decoded movement direction. Effectively, SDKF enhances speed control by using prevalent directional signals, rather than requiring speed to be directly decoded from neural activity. SDKF improved success rates by a factor of 1.7 relative to a standard Kalman filter in a closed-loop BMI task requiring stable stops at targets. BMI systems enabling stable stops will be more effective and user-friendly when translated into clinical applications.

Learning leaves a memory trace in motor cortex.

How are we able to learn new behaviors without disrupting previously learned ones? To understand how the brain achieves this, we used a brain-computer interface (BCI) learning paradigm, which enables us to detect the presence of a memory of one behavior while performing another. We found that learning to use a new BCI map altered the neural activity that monkeys produced when they returned to using a familiar BCI map in a way that was specific to the learning experience. That is, learning left a "memory trace" in the primary motor cortex. This memory trace coexisted with proficient performance under the familiar map, primarily by altering neural activity in dimensions that did not impact behavior. Forming memory traces might be how the brain is able to provide for the joint learning of multiple behaviors without interference.

Learning is shaped by abrupt changes in neural engagement.

Internal states such as arousal, attention and motivation modulate brain-wide neural activity, but how these processes interact with learning is not well understood. During learning, the brain modifies its neural activity to improve behavior. How do internal states affect this process? Using a brain-computer interface learning paradigm in monkeys, we identified large, abrupt fluctuations in neural population activity in motor cortex indicative of arousal-like internal state changes, which we term 'neural engagement.' In a brain-computer interface, the causal relationship between neural activity and behavior is known, allowing us to understand how neural engagement impacted behavioral performance for different task goals. We observed stereotyped changes in neural engagement that occurred regardless of how they impacted performance. This allowed us to predict how quickly different task goals were learned. These results suggest that changes in internal states, even those seemingly unrelated to goal-seeking behavior, can systematically influence how behavior improves with learning.

Universality and individuality in neural dynamics across large populations of recurrent networks.

Task-based modeling with recurrent neural networks (RNNs) has emerged as a popular way to infer the computational function of different brain regions. These models are quantitatively assessed by comparing the low-dimensional neural representations of the model with the brain, for example using canonical correlation analysis (CCA). However, the nature of the detailed neurobiological inferences one can draw from such efforts remains elusive. For example, to what extent does training neural networks to solve common tasks uniquely determine the network dynamics, independent of modeling architectural choices? Or alternatively, are the learned dynamics highly sensitive to different model choices? Knowing the answer to these questions has strong implications for whether and how we should use task-based RNN modeling to understand brain dynamics. To address these foundational questions, we study populations of thousands of networks, with commonly used RNN architectures, trained to solve neuroscientifically motivated tasks and characterize their nonlinear dynamics. We find the geometry of the RNN representations can be highly sensitive to different network architectures, yielding a cautionary tale for measures of similarity that rely on representational geometry, such as CCA. Moreover, we find that while the geometry of neural dynamics can vary greatly across architectures, the underlying computational scaffold-the topological structure of fixed points, transitions between them, limit cycles, and linearized dynamics-often appears universal across all architectures.

Reverse engineering recurrent networks for sentiment classification reveals line attractor dynamics.

Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it-to obtain a quantitative, interpretable description of how it solves a particular task. Even for simple tasks, a detailed understanding of how recurrent networks work, or a prescription for how to develop such an understanding, remains elusive. In this work, we use tools from dynamical systems analysis to reverse engineer recurrent networks trained to perform sentiment classification, a foundational natural language processing task. Given a trained network, we find fixed points of the recurrent dynamics and linearize the nonlinear system around these fixed points. Despite their theoretical capacity to implement complex, high-dimensional computations, we find that trained networks converge to highly interpretable, low-dimensional representations. In particular, the topological structure of the fixed points and corresponding linearized dynamics reveal an approximate line attractor within the RNN, which we can use to quantitatively understand how the RNN solves the sentiment analysis task. Finally, we find this mechanism present across RNN architectures (including LSTMs, GRUs, and vanilla RNNs) trained on multiple datasets, suggesting that our findings are not unique to a particular architecture or dataset. Overall, these results demonstrate that surprisingly universal and human interpretable computations can arise across a range of recurrent networks.

Computation through Cortical Dynamics.

Population dynamics is emerging as a language for understanding high-dimensional neural recordings. Remington et al. (2018) explore how inputs to frontal cortex modulate neural dynamics in order to implement a computation of interest.

Publisher Correction: Learning by neural reassociation.

In the version of this article initially published, equation (10) contained cos Θ instead of sin Θ as the bottom element of the right-hand vector. The error has been corrected in the HTML and PDF versions of the article.

Learning by neural reassociation.

Behavior is driven by coordinated activity across a population of neurons. Learning requires the brain to change the neural population activity produced to achieve a given behavioral goal. How does population activity reorganize during learning? We studied intracortical population activity in the primary motor cortex of rhesus macaques during short-term learning in a brain-computer interface (BCI) task. In a BCI, the mapping between neural activity and behavior is exactly known, enabling us to rigorously define hypotheses about neural reorganization during learning. We found that changes in population activity followed a suboptimal neural strategy of reassociation: animals relied on a fixed repertoire of activity patterns and associated those patterns with different movements after learning. These results indicate that the activity patterns that a neural population can generate are even more constrained than previously thought and might explain why it is often difficult to quickly learn to a high level of proficiency.

Constraints on neural redundancy.

Millions of neurons drive the activity of hundreds of muscles, meaning many different neural population activity patterns could generate the same movement. Studies have suggested that these redundant (i.e. behaviorally equivalent) activity patterns may be beneficial for neural computation. However, it is unknown what constraints may limit the selection of different redundant activity patterns. We leveraged a brain-computer interface, allowing us to define precisely which neural activity patterns were redundant. Rhesus monkeys made cursor movements by modulating neural activity in primary motor cortex. We attempted to predict the observed distribution of redundant neural activity. Principles inspired by work on muscular redundancy did not accurately predict these distributions. Surprisingly, the distributions of redundant neural activity and task-relevant activity were coupled, which enabled accurate predictions of the distributions of redundant activity. This suggests limits on the extent to which redundancy may be exploited by the brain for computation.

Brain-computer interfaces for dissecting cognitive processes underlying sensorimotor control.

Sensorimotor control engages cognitive processes such as prediction, learning, and multisensory integration. Understanding the neural mechanisms underlying these cognitive processes with arm reaching is challenging because we currently record only a fraction of the relevant neurons, the arm has nonlinear dynamics, and multiple modalities of sensory feedback contribute to control. A brain-computer interface (BCI) is a well-defined sensorimotor loop with key simplifying advantages that address each of these challenges, while engaging similar cognitive processes. As a result, BCI is becoming recognized as a powerful tool for basic scientific studies of sensorimotor control. Here, we describe the benefits of BCI for basic scientific inquiries and review recent BCI studies that have uncovered new insights into the neural mechanisms underlying sensorimotor control.

Internal models for interpreting neural population activity during sensorimotor control.

To successfully guide limb movements, the brain takes in sensory information about the limb, internally tracks the state of the limb, and produces appropriate motor commands. It is widely believed that this process uses an internal model, which describes our prior beliefs about how the limb responds to motor commands. Here, we leveraged a brain-machine interface (BMI) paradigm in rhesus monkeys and novel statistical analyses of neural population activity to gain insight into moment-by-moment internal model computations. We discovered that a mismatch between subjects' internal models and the actual BMI explains roughly 65% of movement errors, as well as long-standing deficiencies in BMI speed control. We then used the internal models to characterize how the neural population activity changes during BMI learning. More broadly, this work provides an approach for interpreting neural population activity in the context of how prior beliefs guide the transformation of sensory input to motor output.

Learning an Internal Dynamics Model from Control Demonstration.

Much work in optimal control and inverse control has assumed that the controller has perfect knowledge of plant dynamics. However, if the controller is a human or animal subject, the subject's internal dynamics model may differ from the true plant dynamics. Here, we consider the problem of learning the subject's internal model from demonstrations of control and knowledge of task goals. Due to sensory feedback delay, the subject uses an internal model to generate an internal prediction of the current plant state, which may differ from the actual plant state. We develop a probabilistic framework and exact EM algorithm to jointly estimate the internal model, internal state trajectories, and feedback delay. We applied this framework to demonstrations by a nonhuman primate of brain-machine interface (BMI) control. We discovered that the subject's internal model deviated from the true BMI plant dynamics and provided significantly better explanation of the recorded neural control signals than did the true plant dynamics.

Internal models engaged by brain-computer interface control.

Internal models have been proposed to explain the brain's ability to compensate for sensory feedback delays by predicting the sensory consequences of movement commands. Single-neuron studies in the oculomotor and vestibulo-ocular systems have provided evidence of internal models, as have behavioral studies in the skeletomotor system. Here, we present evidence of internal models from simultaneously recorded population activity underlying closed-loop brain-computer interface (BCI) control. We studied cursor-based BCI control by a nonhuman primate implanted with a multi-electrode array in motor cortex. Using a novel BCI task, we measured the visual feedback processing delay to be about 130 milliseconds. By examining the task-based appropriateness of the population activity at different time lags, we found evidence that the subject compensates for the feedback delay by predicting upcoming cursor positions, suggesting the use of an internal forward model. Lastly, we examined the time course of internal model adaptation after altering the mapping between population activity and cursor movements. This study suggests that closed-loop BCI experiments combined with novel statistical analyses can provide insight into the neural substrates of feedback motor control and motor learning.