Motor primitives in space and time via targeted gain modulation in cortical networks

Descending networks transform command signals into population motor control

To convert intentions into actions, movement instructions must pass from the brain to downstream motor circuits through descending neurons (DNs). These include small sets of command-like neurons that are sufficient to drive behaviours1-the circuit mechanisms for which remain unclear. Here we show that command-like DNs in Drosophila directly recruit networks of additional DNs to orchestrate behaviours that require the active control of numerous body parts. Specifically, we found that command-like DNs previously thought to drive behaviours alone2-4 in fact co-activate larger populations of DNs. Connectome analyses and experimental manipulations revealed that this functional recruitment can be explained by direct excitatory connections between command-like DNs and networks of interconnected DNs in the brain. Descending population recruitment is necessary for behavioural control: DNs with many downstream descending partners require network co-activation to drive complete behaviours and drive only simple stereotyped movements in their absence. These DN networks reside within behaviour-specific clusters that inhibit one another. These results support a mechanism for command-like descending control in which behaviours are generated through the recruitment of increasingly large DN networks that compose behaviours by combining multiple motor subroutines.

Motor cortex latent dynamics encode spatial and temporal arm movement parameters independently

The fluid movement of an arm requires multiple spatiotemporal parameters to be set independently. Recent studies have argued that arm movements are generated by the collective dynamics of neurons in motor cortex. An untested prediction of this hypothesis is that independent parameters of movement must map to independent components of the neural dynamics. Using a task where monkeys made a sequence of reaching movements to randomly placed targets, we show that the spatial and temporal parameters of arm movements are independently encoded in the low-dimensional trajectories of population activity in motor cortex: Each movement's direction corresponds to a fixed neural trajectory through neural state space and its speed to how quickly that trajectory is traversed. Recurrent neural network models show this coding allows independent control over the spatial and temporal parameters of movement by separate network parameters. Our results support a key prediction of the dynamical systems view of motor cortex, but also argue that not all parameters of movement are defined by different trajectories of population activity.

Unified control of temporal and spatial scales of sensorimotor behavior through neuromodulation of short-term synaptic plasticity

Neuromodulators have been shown to alter the temporal profile of short-term synaptic plasticity (STP); however, the computational function of this neuromodulation remains unexplored. Here, we propose that the neuromodulation of STP provides a general mechanism to scale neural dynamics and motor outputs in time and space. We trained recurrent neural networks that incorporated STP to produce complex motor trajectories-handwritten digits-with different temporal (speed) and spatial (size) scales. Neuromodulation of STP produced temporal and spatial scaling of the learned dynamics and enhanced temporal or spatial generalization compared to standard training of the synaptic weights in the absence of STP. The model also accounted for the results of two experimental studies involving flexible sensorimotor timing. Neuromodulation of STP provides a unified and biologically plausible mechanism to control the temporal and spatial scales of neural dynamics and sensorimotor behaviors.

The computational foundations of dynamic coding in working memory

Working memory (WM) is a fundamental aspect of cognition. WM maintenance is classically thought to rely on stable patterns of neural activities. However, recent evidence shows that neural population activities during WM maintenance undergo dynamic variations before settling into a stable pattern. Although this has been difficult to explain theoretically, neural network models optimized for WM typically also exhibit such dynamics. Here, we examine stable versus dynamic coding in neural data, classical models, and task-optimized networks. We review principled mathematical reasons for why classical models do not, while task-optimized models naturally do exhibit dynamic coding. We suggest an update to our understanding of WM maintenance, in which dynamic coding is a fundamental computational feature rather than an epiphenomenon.

Temporal scaling of motor cortical dynamics reveals hierarchical control of vocal production

Neocortical activity is thought to mediate voluntary control over vocal production, but the underlying neural mechanisms remain unclear. In a highly vocal rodent, the male Alston's singing mouse, we investigate neural dynamics in the orofacial motor cortex (OMC), a structure critical for vocal behavior. We first describe neural activity that is modulated by component notes (~100 ms), probably representing sensory feedback. At longer timescales, however, OMC neurons exhibit diverse and often persistent premotor firing patterns that stretch or compress with song duration (~10 s). Using computational modeling, we demonstrate that such temporal scaling, acting through downstream motor production circuits, can enable vocal flexibility. These results provide a framework for studying hierarchical control circuits, a common design principle across many natural and artificial systems.

Dynamic predictive coding: A model of hierarchical sequence learning and prediction in the neocortex

We introduce dynamic predictive coding, a hierarchical model of spatiotemporal prediction and sequence learning in the neocortex. The model assumes that higher cortical levels modulate the temporal dynamics of lower levels, correcting their predictions of dynamics using prediction errors. As a result, lower levels form representations that encode sequences at shorter timescales (e.g., a single step) while higher levels form representations that encode sequences at longer timescales (e.g., an entire sequence). We tested this model using a two-level neural network, where the top-down modulation creates low-dimensional combinations of a set of learned temporal dynamics to explain input sequences. When trained on natural videos, the lower-level model neurons developed space-time receptive fields similar to those of simple cells in the primary visual cortex while the higher-level responses spanned longer timescales, mimicking temporal response hierarchies in the cortex. Additionally, the network's hierarchical sequence representation exhibited both predictive and postdictive effects resembling those observed in visual motion processing in humans (e.g., in the flash-lag illusion). When coupled with an associative memory emulating the role of the hippocampus, the model allowed episodic memories to be stored and retrieved, supporting cue-triggered recall of an input sequence similar to activity recall in the visual cortex. When extended to three hierarchical levels, the model learned progressively more abstract temporal representations along the hierarchy. Taken together, our results suggest that cortical processing and learning of sequences can be interpreted as dynamic predictive coding based on a hierarchical spatiotemporal generative model of the visual world.

Active Predictive Coding: A Unifying Neural Model for Active Perception, Compositional Learning, and Hierarchical Planning

There is growing interest in predictive coding as a model of how the brain learns through predictions and prediction errors. Predictive coding models have traditionally focused on sensory coding and perception. Here we introduce active predictive coding (APC) as a unifying model for perception, action, and cognition. The APC model addresses important open problems in cognitive science and AI, including (1) how we learn compositional representations (e.g., part-whole hierarchies for equivariant vision) and (2) how we solve large-scale planning problems, which are hard for traditional reinforcement learning, by composing complex state dynamics and abstract actions from simpler dynamics and primitive actions. By using hypernetworks, self-supervised learning, and reinforcement learning, APC learns hierarchical world models by combining task-invariant state transition networks and task-dependent policy networks at multiple abstraction levels. We illustrate the applicability of the APC model to active visual perception and hierarchical planning. Our results represent, to our knowledge, the first proof-of-concept demonstration of a unified approach to addressing the part-whole learning problem in vision, the nested reference frames learning problem in cognition, and the integrated state-action hierarchy learning problem in reinforcement learning.

Silences, spikes and bursts: Three-part knot of the neural code

When a neuron breaks silence, it can emit action potentials in a number of patterns. Some responses are so sudden and intense that electrophysiologists felt the need to single them out, labelling action potentials emitted at a particularly high frequency with a metonym - bursts. Is there more to bursts than a figure of speech? After all, sudden bouts of high-frequency firing are expected to occur whenever inputs surge. The burst coding hypothesis advances that the neural code has three syllables: silences, spikes and bursts. We review evidence supporting this ternary code in terms of devoted mechanisms for burst generation, synaptic transmission and synaptic plasticity. We also review the learning and attention theories for which such a triad is beneficial.

Optimal information loading into working memory explains dynamic coding in the prefrontal cortex

Working memory involves the short-term maintenance of information and is critical in many tasks. The neural circuit dynamics underlying working memory remain poorly understood, with different aspects of prefrontal cortical (PFC) responses explained by different putative mechanisms. By mathematical analysis, numerical simulations, and using recordings from monkey PFC, we investigate a critical but hitherto ignored aspect of working memory dynamics: information loading. We find that, contrary to common assumptions, optimal loading of information into working memory involves inputs that are largely orthogonal, rather than similar, to the late delay activities observed during memory maintenance, naturally leading to the widely observed phenomenon of dynamic coding in PFC. Using a theoretically principled metric, we show that PFC exhibits the hallmarks of optimal information loading. We also find that optimal information loading emerges as a general dynamical strategy in task-optimized recurrent neural networks. Our theory unifies previous, seemingly conflicting theories of memory maintenance based on attractor or purely sequential dynamics and reveals a normative principle underlying dynamic coding.

Recursive neural programs: A differentiable framework for learning compositional part-whole hierarchies and image grammars

Human vision, thought, and planning involve parsing and representing objects and scenes using structured representations based on part-whole hierarchies. Computer vision and machine learning researchers have recently sought to emulate this capability using neural networks, but a generative model formulation has been lacking. Generative models that leverage compositionality, recursion, and part-whole hierarchies are thought to underlie human concept learning and the ability to construct and represent flexible mental concepts. We introduce Recursive Neural Programs (RNPs), a neural generative model that addresses the part-whole hierarchy learning problem by modeling images as hierarchical trees of probabilistic sensory-motor programs. These programs recursively reuse learned sensory-motor primitives to model an image within different spatial reference frames, enabling hierarchical composition of objects from parts and implementing a grammar for images. We show that RNPs can learn part-whole hierarchies for a variety of image datasets, allowing rich compositionality and intuitive parts-based explanations of objects. Our model also suggests a cognitive framework for understanding how human brains can potentially learn and represent concepts in terms of recursively defined primitives and their relations with each other.

Initial conditions combine with sensory evidence to induce decision-related dynamics in premotor cortex

We used a dynamical systems perspective to understand decision-related neural activity, a fundamentally unresolved problem. This perspective posits that time-varying neural activity is described by a state equation with an initial condition and evolves in time by combining at each time step, recurrent activity and inputs. We hypothesized various dynamical mechanisms of decisions, simulated them in models to derive predictions, and evaluated these predictions by examining firing rates of neurons in the dorsal premotor cortex (PMd) of monkeys performing a perceptual decision-making task. Prestimulus neural activity (i.e., the initial condition) predicted poststimulus neural trajectories, covaried with RT and the outcome of the previous trial, but not with choice. Poststimulus dynamics depended on both the sensory evidence and initial condition, with easier stimuli and fast initial conditions leading to the fastest choice-related dynamics. Together, these results suggest that initial conditions combine with sensory evidence to induce decision-related dynamics in PMd.

The concepts of muscle activity generation driven by upper limb kinematics

BACKGROUND

The underlying motivation of this work is to demonstrate that artificial muscle activity of known and unknown motion can be generated based on motion parameters, such as angular position, acceleration, and velocity of each joint (or the end-effector instead), which are similarly represented in our brains. This model is motivated by the known motion planning process in the central nervous system. That process incorporates the current body state from sensory systems and previous experiences, which might be represented as pre-learned inverse dynamics that generate associated muscle activity.

METHODS

We develop a novel approach utilizing recurrent neural networks that are able to predict muscle activity of the upper limbs associated with complex 3D human arm motions. Therefore, motion parameters such as joint angle, velocity, acceleration, hand position, and orientation, serve as input for the models. In addition, these models are trained on multiple subjects (n=5 including , 3 male in the age of 26±2 years) and thus can generalize across individuals. In particular, we distinguish between a general model that has been trained on several subjects, a subject-specific model, and a specific fine-tuned model using a transfer learning approach to adapt the model to a new subject. Estimators such as mean square error MSE, correlation coefficient r, and coefficient of determination R² are used to evaluate the goodness of fit. We additionally assess performance by developing a new score called the zero-line score. The present approach was compared with multiple other architectures.

RESULTS

The presented approach predicts the muscle activity for previously through different subjects with remarkable high precision and generalizing nicely for new motions that have not been trained before. In an exhausting comparison, our recurrent network outperformed all other architectures. In addition, the high inter-subject variation of the recorded muscle activity was successfully handled using a transfer learning approach, resulting in a good fit for the muscle activity for a new subject.

CONCLUSIONS

The ability of this approach to efficiently predict muscle activity contributes to the fundamental understanding of motion control. Furthermore, this approach has great potential for use in rehabilitation contexts, both as a therapeutic approach and as an assistive device. The predicted muscle activity can be utilized to guide functional electrical stimulation, allowing specific muscles to be targeted and potentially improving overall rehabilitation outcomes.

Neuromodulatory control of complex adaptive dynamics in the brain

How is the massive dimensionality and complexity of the microscopic constituents of the nervous system brought under sufficiently tight control so as to coordinate adaptive behaviour? A powerful means for striking this balance is to poise neurons close to the critical point of a phase transition, at which a small change in neuronal excitability can manifest a nonlinear augmentation in neuronal activity. How the brain could mediate this critical transition is a key open question in neuroscience. Here, I propose that the different arms of the ascending arousal system provide the brain with a diverse set of heterogeneous control parameters that can be used to modulate the excitability and receptivity of target neurons-in other words, to act as control parameters for mediating critical neuronal order. Through a series of worked examples, I demonstrate how the neuromodulatory arousal system can interact with the inherent topological complexity of neuronal subsystems in the brain to mediate complex adaptive behaviour.

Rapid adaptation of brain-computer interfaces to new neuronal ensembles or participants via generative modelling

For brain-computer interfaces (BCIs), obtaining sufficient training data for algorithms that map neural signals onto actions can be difficult, expensive or even impossible. Here we report the development and use of a generative model-a model that synthesizes a virtually unlimited number of new data distributions from a learned data distribution-that learns mappings between hand kinematics and the associated neural spike trains. The generative spike-train synthesizer is trained on data from one recording session with a monkey performing a reaching task and can be rapidly adapted to new sessions or monkeys by using limited additional neural data. We show that the model can be adapted to synthesize new spike trains, accelerating the training and improving the generalization of BCI decoders. The approach is fully data-driven, and hence, applicable to applications of BCIs beyond motor control.

Neural dynamics in the rodent motor cortex enables flexible control of vocal timing

Neocortical activity is thought to mediate voluntary control over vocal production, but the underlying neural mechanisms remain unclear. In a highly vocal rodent, the Alston's singing mouse, we investigate neural dynamics in the orofacial motor cortex (OMC), a structure critical for vocal behavior. We first describe neural activity that is modulated by component notes (approx. 100 ms), likely representing sensory feedback. At longer timescales, however, OMC neurons exhibit diverse and often persistent premotor firing patterns that stretch or compress with song duration (approx. 10 s). Using computational modeling, we demonstrate that such temporal scaling, acting via downstream motor production circuits, can enable vocal flexibility. These results provide a framework for studying hierarchical control circuits, a common design principle across many natural and artificial systems.

Contextual inference in learning and memory

Context is widely regarded as a major determinant of learning and memory across numerous domains, including classical and instrumental conditioning, episodic memory, economic decision-making, and motor learning. However, studies across these domains remain disconnected due to the lack of a unifying framework formalizing the concept of context and its role in learning. Here, we develop a unified vernacular allowing direct comparisons between different domains of contextual learning. This leads to a Bayesian model positing that context is unobserved and needs to be inferred. Contextual inference then controls the creation, expression, and updating of memories. This theoretical approach reveals two distinct components that underlie adaptation, proper and apparent learning, respectively referring to the creation and updating of memories versus time-varying adjustments in their expression. We review a number of extensions of the basic Bayesian model that allow it to account for increasingly complex forms of contextual learning.

Sampling motion trajectories during hippocampal theta sequences

Efficient planning in complex environments requires that uncertainty associated with current inferences and possible consequences of forthcoming actions is represented. Representation of uncertainty has been established in sensory systems during simple perceptual decision making tasks but it remains unclear if complex cognitive computations such as planning and navigation are also supported by probabilistic neural representations. Here, we capitalized on gradually changing uncertainty along planned motion trajectories during hippocampal theta sequences to capture signatures of uncertainty representation in population responses. In contrast with prominent theories, we found no evidence of encoding parameters of probability distributions in the momentary population activity recorded in an open-field navigation task in rats. Instead, uncertainty was encoded sequentially by sampling motion trajectories randomly and efficiently in subsequent theta cycles from the distribution of potential trajectories. Our analysis is the first to demonstrate that the hippocampus is well equipped to contribute to optimal planning by representing uncertainty.

The role of astrocytes in place cell formation: A computational modeling study

Place cells develop spatially-tuned receptive fields during the early stages of novel environment exploration. The generative mechanism underlying these spatially-selective responses remains largely elusive, but has been associated with theta rhythmicity. An important factor implicating the transformation of silent cells to place cells is a spatially-uniform depolarization that is mediated by a persistent sodium current. This neuronal current is modulated by extracellular calcium concentration, which, in turn, is actively controlled by astrocytes. However, there is no established relationship between the neuronal depolarization and astrocytic activity. To consider this link, we designed a bioplausible computational model of a neuronal-astrocytic network, where astrocytes induced the transient emergence of place fields in silent cells, and accelerated the plasticity-induced consolidation of place cells. Interestingly, theta oscillations emerged naturally at the network level, resulting from the astrocytic modulation of subcellular neuronal properties. Our results suggest that astrocytes participate in spatial mapping and exploration, and further highlight the computational roles of these cells in the brain.

Movement is governed by rotational neural dynamics in spinal motor networks

Although the generation of movements is a fundamental function of the nervous system, the underlying neural principles remain unclear. As flexor and extensor muscle activities alternate during rhythmic movements such as walking, it is often assumed that the responsible neural circuitry is similarly exhibiting alternating activity¹. Here we present ensemble recordings of neurons in the lumbar spinal cord that indicate that, rather than alternating, the population is performing a low-dimensional 'rotation' in neural space, in which the neural activity is cycling through all phases continuously during the rhythmic behaviour. The radius of rotation correlates with the intended muscle force, and a perturbation of the low-dimensional trajectory can modify the motor behaviour. As existing models of spinal motor control do not offer an adequate explanation of rotation^1,2, we propose a theory of neural generation of movements from which this and other unresolved issues, such as speed regulation, force control and multifunctionalism, are readily explained.

Connectivity concepts in neuronal network modeling

Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic implementations, or parameterizations hinder progress. Such flaws are unfortunately frequent and one reason is a lack of readily applicable standards and tools for model description. Our work aims to advance complete and concise descriptions of network connectivity but also to guide the implementation of connection routines in simulation software and neuromorphic hardware systems. We first review models made available by the computational neuroscience community in the repositories ModelDB and Open Source Brain, and investigate the corresponding connectivity structures and their descriptions in both manuscript and code. The review comprises the connectivity of networks with diverse levels of neuroanatomical detail and exposes how connectivity is abstracted in existing description languages and simulator interfaces. We find that a substantial proportion of the published descriptions of connectivity is ambiguous. Based on this review, we derive a set of connectivity concepts for deterministically and probabilistically connected networks and also address networks embedded in metric space. Beside these mathematical and textual guidelines, we propose a unified graphical notation for network diagrams to facilitate an intuitive understanding of network properties. Examples of representative network models demonstrate the practical use of the ideas. We hope that the proposed standardizations will contribute to unambiguous descriptions and reproducible implementations of neuronal network connectivity in computational neuroscience.

Small, correlated changes in synaptic connectivity may facilitate rapid motor learning

Animals rapidly adapt their movements to external perturbations, a process paralleled by changes in neural activity in the motor cortex. Experimental studies suggest that these changes originate from altered inputs (H_input) rather than from changes in local connectivity (H_local), as neural covariance is largely preserved during adaptation. Since measuring synaptic changes in vivo remains very challenging, we used a modular recurrent neural network to qualitatively test this interpretation. As expected, H_input resulted in small activity changes and largely preserved covariance. Surprisingly given the presumed dependence of stable covariance on preserved circuit connectivity, H_local led to only slightly larger changes in activity and covariance, still within the range of experimental recordings. This similarity is due to H_local only requiring small, correlated connectivity changes for successful adaptation. Simulations of tasks that impose increasingly larger behavioural changes revealed a growing difference between H_input and H_local, which could be exploited when designing future experiments.

Regimes and mechanisms of transient amplification in abstract and biological neural networks

Neuronal networks encode information through patterns of activity that define the networks’ function. The neurons’ activity relies on specific connectivity structures, yet the link between structure and function is not fully understood. Here, we tackle this structure-function problem with a new conceptual approach. Instead of manipulating the connectivity directly, we focus on upper triangular matrices, which represent the network dynamics in a given orthonormal basis obtained by the Schur decomposition. This abstraction allows us to independently manipulate the eigenspectrum and feedforward structures of a connectivity matrix. Using this method, we describe a diverse repertoire of non-normal transient amplification, and to complement the analysis of the dynamical regimes, we quantify the geometry of output trajectories through the effective rank of both the eigenvector and the dynamics matrices. Counter-intuitively, we find that shrinking the eigenspectrum’s imaginary distribution leads to highly amplifying regimes in linear and long-lasting dynamics in nonlinear networks. We also find a trade-off between amplification and dimensionality of neuronal dynamics, i.e., trajectories in neuronal state-space. Networks that can amplify a large number of orthogonal initial conditions produce neuronal trajectories that lie in the same subspace of the neuronal state-space. Finally, we examine networks of excitatory and inhibitory neurons. We find that the strength of global inhibition is directly linked with the amplitude of amplification, such that weakening inhibitory weights also decreases amplification, and that the eigenspectrum’s imaginary distribution grows with an increase in the ratio between excitatory-to-inhibitory and excitatory-to-excitatory connectivity strengths. Consequently, the strength of global inhibition reveals itself as a strong signature for amplification and a potential control mechanism to switch dynamical regimes. Our results shed a light on how biological networks, i.e., networks constrained by Dale’s law, may be optimised for specific dynamical regimes.

The architecture of neuronal networks lies at the heart of its dynamic behaviour, or in other words, the function of the system. However, the relationship between changes in the architecture and their effect on the dynamics, a structure-function problem, is still poorly understood. Here, we approach this problem by studying a rotated connectivity matrix that is easier to manipulate and interpret. We focus our analysis on a dynamical regime that arises from the biological property that neurons are usually not connected symmetrically, which may result in a non-normal connectivity matrix. Our techniques unveil distinct expressions of the dynamical regime of non-normal amplification. Moreover, we devise a way to analyse the geometry of the dynamics: we assign a single number to a network that quantifies how dissimilar its repertoire of behaviours can be. Finally, using our approach, we can close the loop back to the original neuronal architecture and find that biologically plausible networks use the strength of inhibition and excitatory-to-inhibitory connectivity strength to navigate the different dynamical regimes of non-normal amplification.

Neural mechanisms underlying the temporal organization of naturalistic animal behavior

Naturalistic animal behavior exhibits a strikingly complex organization in the temporal domain, with variability arising from at least three sources: hierarchical, contextual, and stochastic. What neural mechanisms and computational principles underlie such intricate temporal features? In this review, we provide a critical assessment of the existing behavioral and neurophysiological evidence for these sources of temporal variability in naturalistic behavior. Recent research converges on an emergent mechanistic theory of temporal variability based on attractor neural networks and metastable dynamics, arising via coordinated interactions between mesoscopic neural circuits. We highlight the crucial role played by structural heterogeneities as well as noise from mesoscopic feedback loops in regulating flexible behavior. We assess the shortcomings and missing links in the current theoretical and experimental literature and propose new directions of investigation to fill these gaps.

BiCoSS: Toward Large-Scale Cognition Brain With Multigranular Neuromorphic Architecture

The further exploration of the neural mechanisms underlying the biological activities of the human brain depends on the development of large-scale spiking neural networks (SNNs) with different categories at different levels, as well as the corresponding computing platforms. Neuromorphic engineering provides approaches to high-performance biologically plausible computational paradigms inspired by neural systems. In this article, we present a biological-inspired cognitive supercomputing system (BiCoSS) that integrates multiple granules (GRs) of SNNs to realize a hybrid compatible neuromorphic platform. A scalable hierarchical heterogeneous multicore architecture is presented, and a synergistic routing scheme for hybrid neural information is proposed. The BiCoSS system can accommodate different levels of GRs and biological plausibility of SNN models in an efficient and scalable manner. Over four million neurons can be realized on BiCoSS with a power efficiency of 2.8k larger than the GPU platform, and the average latency of BiCoSS is 3.62 and 2.49 times higher than conventional architectures of digital neuromorphic systems. For the verification, BiCoSS is used to replicate various biological cognitive activities, including motor learning, action selection, context-dependent learning, and movement disorders. Comprehensively considering the programmability, biological plausibility, learning capability, computational power, and scalability, BiCoSS is shown to outperform the alternative state-of-the-art works for large-scale SNN, while its real-time computational capability enables a wide range of potential applications.

The role of population structure in computations through neural dynamics

Neural computations are currently investigated using two separate approaches: sorting neurons into functional subpopulations 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 on neuroscience tasks, here we show that the dimensionality of the dynamics and subpopulation structure play fundamentally complementary roles. Although various tasks can be implemented by increasing the dimensionality in networks with fully random population structure, flexible input-output mappings instead require a non-random population structure that can be described in terms of multiple subpopulations. Our analyses revealed that such a subpopulation structure enables flexible computations through a mechanism based on gain-controlled modulations that flexibly shape the collective dynamics. Our results lead to task-specific predictions for the structure of neural selectivity, for inactivation experiments and for the implication of different neurons in multi-tasking.

Invariant neural subspaces maintained by feedback modulation

Sensory systems reliably process incoming stimuli in spite of changes in context. Most recent models accredit this context invariance to an extraction of increasingly complex sensory features in hierarchical feedforward networks. Here, we study how context-invariant representations can be established by feedback rather than feedforward processing. We show that feedforward neural networks modulated by feedback can dynamically generate invariant sensory representations. The required feedback can be implemented as a slow and spatially diffuse gain modulation. The invariance is not present on the level of individual neurons, but emerges only on the population level. Mechanistically, the feedback modulation dynamically reorients the manifold of neural activity and thereby maintains an invariant neural subspace in spite of contextual variations. Our results highlight the importance of population-level analyses for understanding the role of feedback in flexible sensory processing.

From Parametric Representation to Dynamical System: Shifting Views of the Motor Cortex in Motor Control

In contrast to traditional representational perspectives in which the motor cortex is involved in motor control via neuronal preference for kinetics and kinematics, a dynamical system perspective emerging in the last decade views the motor cortex as a dynamical machine that generates motor commands by autonomous temporal evolution. In this review, we first look back at the history of the representational and dynamical perspectives and discuss their explanatory power and controversy from both empirical and computational points of view. Here, we aim to reconcile the above perspectives, and evaluate their theoretical impact, future direction, and potential applications in brain-machine interfaces.

Complementary encoding of spatial information in hippocampal astrocytes

Calcium dynamics into astrocytes influence the activity of nearby neuronal structures. However, because previous reports show that astrocytic calcium signals largely mirror neighboring neuronal activity, current information coding models neglect astrocytes. Using simultaneous two-photon calcium imaging of astrocytes and neurons in the hippocampus of mice navigating a virtual environment, we demonstrate that astrocytic calcium signals encode (i.e., statistically reflect) spatial information that could not be explained by visual cue information. Calcium events carrying spatial information occurred in topographically organized astrocytic subregions. Importantly, astrocytes encoded spatial information that was complementary and synergistic to that carried by neurons, improving spatial position decoding when astrocytic signals were considered alongside neuronal ones. These results suggest that the complementary place dependence of localized astrocytic calcium signals may regulate clusters of nearby synapses, enabling dynamic, context-dependent variations in population coding within brain circuits.

A dynamical systems view of neuroethology: Uncovering stateful computation in natural behaviors

State-dependent computation is key to cognition in both biological and artificial systems. Alan Turing recognized the power of stateful computation when he created the Turing machine with theoretically infinite computational capacity in 1936. Independently, by 1950, ethologists such as Tinbergen and Lorenz also began to implicitly embed rudimentary forms of state-dependent computation to create qualitative models of internal drives and naturally occurring animal behaviors. Here, we reformulate core ethological concepts in explicitly dynamical systems terms for stateful computation. We examine, based on a wealth of recent neural data collected during complex innate behaviors across species, the neural dynamics that determine the temporal structure of internal states. We will also discuss the degree to which the brain can be hierarchically partitioned into nested dynamical systems and the need for a multi-dimensional state-space model of the neuromodulatory system that underlies motivational and affective states.

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

Across 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 behavior, and their importance raises questions regarding how they are, or ought to be, set. Here, we formulate motor preparation as optimal anticipatory control of future movements and show that the solution requires a form of internal feedback control of cortical circuit dynamics. In contrast to a simple feedforward strategy, feedback control enables fast movement preparation by selectively controlling the cortical state in the small subspace that matters for the upcoming movement. Feedback but not feedforward control explains the orthogonality between preparatory and movement activity observed in reaching monkeys. We propose a circuit model in which optimal preparatory control is implemented as a thalamo-cortical loop gated by the basal ganglia.

The Remarkable Robustness of Surrogate Gradient Learning for Instilling Complex Function in Spiking Neural Networks

Brains process information in spiking neural networks. Their intricate connections shape the diverse functions these networks perform. Yet how network connectivity relates to function is poorly understood, and the functional capabilities of models of spiking networks are still rudimentary. The lack of both theoretical insight and practical algorithms to find the necessary connectivity poses a major impediment to both studying information processing in the brain and building efficient neuromorphic hardware systems. The training algorithms that solve this problem for artificial neural networks typically rely on gradient descent. But doing so in spiking networks has remained challenging due to the nondifferentiable nonlinearity of spikes. To avoid this issue, one can employ surrogate gradients to discover the required connectivity. However, the choice of a surrogate is not unique, raising the question of how its implementation influences the effectiveness of the method. Here, we use numerical simulations to systematically study how essential design parameters of surrogate gradients affect learning performance on a range of classification problems. We show that surrogate gradient learning is robust to different shapes of underlying surrogate derivatives, but the choice of the derivative's scale can substantially affect learning performance. When we combine surrogate gradients with suitable activity regularization techniques, spiking networks perform robust information processing at the sparse activity limit. Our study provides a systematic account of the remarkable robustness of surrogate gradient learning and serves as a practical guide to model functional spiking neural networks.

Network dynamics underlying OFF responses in the auditory cortex

Across sensory systems, complex spatio-temporal patterns of neural activity arise following the onset (ON) and offset (OFF) of stimuli. While ON responses have been widely studied, the mechanisms generating OFF responses in cortical areas have so far not been fully elucidated. We examine here the hypothesis that OFF responses are single-cell signatures of recurrent interactions at the network level. To test this hypothesis, we performed population analyses of two-photon calcium recordings in the auditory cortex of awake mice listening to auditory stimuli, and compared them to linear single-cell and network models. While the single-cell model explained some prominent features of the data, it could not capture the structure across stimuli and trials. In contrast, the network model accounted for the low-dimensional organization of population responses and their global structure across stimuli, where distinct stimuli activated mostly orthogonal dimensions in the neural state-space.

Learning compositional sequences with multiple time scales through a hierarchical network of spiking neurons

Sequential behaviour is often compositional and organised across multiple time scales: a set of individual elements developing on short time scales (motifs) are combined to form longer functional sequences (syntax). Such organisation leads to a natural hierarchy that can be used advantageously for learning, since the motifs and the syntax can be acquired independently. Despite mounting experimental evidence for hierarchical structures in neuroscience, models for temporal learning based on neuronal networks have mostly focused on serial methods. Here, we introduce a network model of spiking neurons with a hierarchical organisation aimed at sequence learning on multiple time scales. Using biophysically motivated neuron dynamics and local plasticity rules, the model can learn motifs and syntax independently. Furthermore, the model can relearn sequences efficiently and store multiple sequences. Compared to serial learning, the hierarchical model displays faster learning, more flexible relearning, increased capacity, and higher robustness to perturbations. The hierarchical model redistributes the variability: it achieves high motif fidelity at the cost of higher variability in the between-motif timings.

A goal-driven modular neural network predicts parietofrontal neural dynamics during grasping

One of the primary ways we interact with the world is using our hands. In macaques, the circuit spanning the anterior intraparietal area, the hand area of the ventral premotor cortex, and the primary motor cortex is necessary for transforming visual information into grasping movements. However, no comprehensive model exists that links all steps of processing from vision to action. We hypothesized that a recurrent neural network mimicking the modular structure of the anatomical circuit and trained to use visual features of objects to generate the required muscle dynamics used by primates to grasp objects would give insight into the computations of the grasping circuit. Internal activity of modular networks trained with these constraints strongly resembled neural activity recorded from the grasping circuit during grasping and paralleled the similarities between brain regions. Network activity during the different phases of the task could be explained by linear dynamics for maintaining a distributed movement plan across the network in the absence of visual stimulus and then generating the required muscle kinematics based on these initial conditions in a module-specific way. These modular models also outperformed alternative models at explaining neural data, despite the absence of neural data during training, suggesting that the inputs, outputs, and architectural constraints imposed were sufficient for recapitulating processing in the grasping circuit. Finally, targeted lesioning of modules produced deficits similar to those observed in lesion studies of the grasping circuit, providing a potential model for how brain regions may coordinate during the visually guided grasping of objects.

Designing spontaneous behavioral switching via chaotic itinerancy

Chaotic itinerancy is a frequently observed phenomenon in high-dimensional nonlinear dynamical systems and is characterized by itinerant transitions among multiple quasi-attractors. Several studies have pointed out that high-dimensional activity in animal brains can be observed to exhibit chaotic itinerancy, which is considered to play a critical role in the spontaneous behavior generation of animals. Thus, how to design desired chaotic itinerancy is a topic of great interest, particularly for neurorobotics researchers who wish to understand and implement autonomous behavioral controls. However, it is generally difficult to gain control over high-dimensional nonlinear dynamical systems. In this study, we propose a method for implementing chaotic itinerancy reproducibly in a high-dimensional chaotic neural network. We demonstrate that our method enables us to easily design both the trajectories of quasi-attractors and the transition rules among them simply by adjusting the limited number of system parameters and by using the intrinsic high-dimensional chaos.

Theoretical distinction between functional states in working memory and their corresponding neural states

Working memory (WM) is important for guiding behaviour, but not always for the next possible action. Here we define a WM item that is currently relevant for guiding behaviour as the functionally "active" item; whereas items maintained in WM, but not immediately relevant to behaviour, are defined as functionally "latent". Traditional neurophysiological theories of WM proposed that content is maintained via persistent neural activity (e.g., stable attractors); however, more recent theories have highlighted the potential role for "activity-silent" mechanisms (e.g., short-term synaptic plasticity). Given these somewhat parallel dichotomies, functionally active and latent cognitive states of WM have been associated with storage based on persistent-activity and activity-silent neural mechanisms, respectively. However, in this article we caution against a one-to-one correspondence between functional and activity states. We argue that the principal theoretical requirement for active and latent WM is that the corresponding neural states play qualitatively different functional roles. We consider a number of candidate solutions, and conclude that the neurophysiological mechanisms for functionally active and latent WM items are theoretically independent of the distinction between persistent activity-based and activity-silent forms of WM storage.

Engineering recurrent neural networks from task-relevant manifolds and dynamics

Many cognitive processes involve transformations of distributed representations in neural populations, creating a need for population-level models. Recurrent neural network models fulfill this need, but there are many open questions about how their connectivity gives rise to dynamics that solve a task. Here, we present a method for finding the connectivity of networks for which the dynamics are specified to solve a task in an interpretable way. We apply our method to a working memory task by synthesizing a network that implements a drift-diffusion process over a ring-shaped manifold. We also use our method to demonstrate how inputs can be used to control network dynamics for cognitive flexibility and explore the relationship between representation geometry and network capacity. Our work fits within the broader context of understanding neural computations as dynamics over relatively low-dimensional manifolds formed by correlated patterns of neurons.

Achieving stable dynamics in neural circuits

The brain consists of many interconnected networks with time-varying, partially autonomous activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable, reproducible state (or sequence of states) for its computations to make sense. We approached this problem from a control-theory perspective by applying contraction analysis to recurrent neural networks. This allowed us to find mechanisms for achieving stability in multiple connected networks with biologically realistic dynamics, including synaptic plasticity and time-varying inputs. These mechanisms included inhibitory Hebbian plasticity, excitatory anti-Hebbian plasticity, synaptic sparsity and excitatory-inhibitory balance. Our findings shed light on how stable computations might be achieved despite biological complexity. Crucially, our analysis is not limited to analyzing the stability of fixed geometric objects in state space (e.g points, lines, planes), but rather the stability of state trajectories which may be complex and time-varying.

Basal Ganglia Circuits for Action Specification

Behavior is readily classified into patterns of movements with inferred common goals-actions. Goals may be discrete; movements are continuous. Through the careful study of isolated movements in laboratory settings, or via introspection, it has become clear that animals can exhibit exquisite graded specification to their movements. Moreover, graded control can be as fundamental to success as the selection of which action to perform under many naturalistic scenarios: a predator adjusting its speed to intercept moving prey, or a tool-user exerting the perfect amount of force to complete a delicate task. The basal ganglia are a collection of nuclei in vertebrates that extend from the forebrain (telencephalon) to the midbrain (mesencephalon), constituting a major descending extrapyramidal pathway for control over midbrain and brainstem premotor structures. Here we discuss how this pathway contributes to the continuous specification of movements that endows our voluntary actions with vigor and grace.

Neuronal mechanisms for sequential activation of memory items: Dynamics and reliability

In this article we present a biologically inspired model of activation of memory items in a sequence. Our model produces two types of sequences, corresponding to two different types of cerebral functions: activation of regular or irregular sequences. The switch between the two types of activation occurs through the modulation of biological parameters, without altering the connectivity matrix. Some of the parameters included in our model are neuronal gain, strength of inhibition, synaptic depression and noise. We investigate how these parameters enable the existence of sequences and influence the type of sequences observed. In particular we show that synaptic depression and noise drive the transitions from one memory item to the next and neuronal gain controls the switching between regular and irregular (random) activation.

On Primitives in Motor Control

The concept of primitives has been used in motor control both as a theoretical construct and as a means of describing the results of experimental studies involving multiple moving elements. This concept is close to Bernstein’s notion of engrams and level of synergies. Performance primitives have been explored in spaces of peripheral variables but interpreted in terms of neural control primitives. Performance primitives reflect a variety of mechanisms ranging from body mechanics to spinal mechanisms and to supraspinal circuitry. This review suggests that primitives originate at the task level as preferred time functions of spatial referent coordinates or at mappings from higher level referent coordinates to lower level, frequently abundant, referent coordinate sets. Different patterns of performance primitives can emerge depending, in particular, on the external force field.

Towards a functional connectome in Drosophila

The full functionality of the brain is determined by its molecular, cellular and circuit structure. Modern neuroscience now prioritizes the mapping of whole brain connectomes by detecting all direct neuron to neuron synaptic connections, a feat first accomplished for C. elegans, a full reconstruction of a 302-neuron nervous system. Efforts at Janelia Research Campus will soon reconstruct the whole brain connectomes of a larval and an adult Drosophila. These connectomes will provide a framework for incorporating detailed neural circuit information that Drosophila neuroscientists have gathered over decades. But when viewed in the context of a whole brain, it becomes difficult to isolate the contributions of distinct circuits, whether sensory systems or higher brain regions. The complete wiring diagram tells us that sensory information is not only processed in separate channels, but that even the earliest sensory layers are strongly synaptically interconnected. In the higher brain, long-range projections densely interconnect major brain regions and convergence centers that integrate input from different sensory systems. Furthermore, we also need to understand the impact of neuronal communication beyond direct synaptic modulation. Nevertheless, all of this can be pursued with Drosophila, combining connectomics with a diverse array of genetic tools and behavioral paradigms that provide effective approaches to entire brain function.

Considerations in using recurrent neural networks to probe neural dynamics

Recurrent neural networks (RNNs) are increasingly being used to model complex cognitive and motor tasks performed by behaving animals. RNNs are trained to reproduce animal behavior while also capturing key statistics of empirically recorded neural activity. In this manner, the RNN can be viewed as an in silico circuit whose computational elements share similar motifs with the cortical area it is modeling. Furthermore, because the RNN's governing equations and parameters are fully known, they can be analyzed to propose hypotheses for how neural populations compute. In this context, we present important considerations when using RNNs to model motor behavior in a delayed reach task. First, by varying the network's nonlinear activation and rate regularization, we show that RNNs reproducing single-neuron firing rate motifs may not adequately capture important population motifs. Second, we find that even when RNNs reproduce key neurophysiological features on both the single neuron and population levels, they can do so through distinctly different dynamical mechanisms. To distinguish between these mechanisms, we show that an RNN consistent with a previously proposed dynamical mechanism is more robust to input noise. Finally, we show that these dynamics are sufficient for the RNN to generalize to tasks it was not trained on. Together, these results emphasize important considerations when using RNN models to probe neural dynamics.NEW & NOTEWORTHY Artificial neurons in a recurrent neural network (RNN) may resemble empirical single-unit activity but not adequately capture important features on the neural population level. Dynamics of RNNs can be visualized in low-dimensional projections to provide insight into the RNN's dynamical mechanism. RNNs trained in different ways may reproduce neurophysiological motifs but do so with distinctly different mechanisms. RNNs trained to only perform a delayed reach task can generalize to perform tasks where the target is switched or the target location is changed.

Oscillatory recurrent gated neural integrator circuits (ORGaNICs), a unifying theoretical framework for neural dynamics

Working memory is an example of a cognitive and neural process that is not static but evolves dynamically with changing sensory inputs; another example is motor preparation and execution. We introduce a theoretical framework for neural dynamics, based on oscillatory recurrent gated neural integrator circuits (ORGaNICs), and apply it to simulate key phenomena of working memory and motor control. The model circuits simulate neural activity with complex dynamics, including sequential activity and traveling waves of activity, that manipulate (as well as maintain) information during working memory. The same circuits convert spatial patterns of premotor activity to temporal profiles of motor control activity and manipulate (e.g., time warp) the dynamics. Derivative-like recurrent connectivity, in particular, serves to manipulate and update internal models, an essential feature of working memory and motor execution. In addition, these circuits incorporate recurrent normalization, to ensure stability over time and robustness with respect to perturbations of synaptic weights.

Constraining computational models using electron microscopy wiring diagrams

Numerous efforts to generate "connectomes," or synaptic wiring diagrams, of large neural circuits or entire nervous systems are currently underway. These efforts promise an abundance of data to guide theoretical models of neural computation and test their predictions. However, there is not yet a standard set of tools for incorporating the connectivity constraints that these datasets provide into the models typically studied in theoretical neuroscience. This article surveys recent approaches to building models with constrained wiring diagrams and the insights they have provided. It also describes challenges and the need for new techniques to scale these approaches to ever more complex datasets.

Brian 2, an intuitive and efficient neural simulator

Brian 2 allows scientists to simply and efficiently simulate spiking neural network models. These models can feature novel dynamical equations, their interactions with the environment, and experimental protocols. To preserve high performance when defining new models, most simulators offer two options: low-level programming or description languages. The first option requires expertise, is prone to errors, and is problematic for reproducibility. The second option cannot describe all aspects of a computational experiment, such as the potentially complex logic of a stimulation protocol. Brian addresses these issues using runtime code generation. Scientists write code with simple and concise high-level descriptions, and Brian transforms them into efficient low-level code that can run interleaved with their code. We illustrate this with several challenging examples: a plastic model of the pyloric network, a closed-loop sensorimotor model, a programmatic exploration of a neuron model, and an auditory model with real-time input.