Flexible Sensorimotor Computations through Rapid Reconfiguration of Cortical Dynamics

Reward influences movement vigor through multiple motor cortical mechanisms

The prospect of greater rewards often invigorates movements. What neural mechanisms support this increase of movement vigor for greater rewards? We had three rhesus monkeys perform reaching movements to targets worth different magnitudes of reward. We recorded neural population activity from primary motor and dorsal premotor cortex, brain areas at the output of cortical processing for voluntary movements, and asked how neural activity mediated the translation of reward into increased vigor. We identified features of neural activity during movement preparation, initiation, and execution that were both correlated with vigor and modulated by reward. We also found that the neural metrics that correlate with different aspects of movement vigor exhibit only limited correlation with one another, suggesting that there are multiple mechanisms through which reward modulates vigor. Finally, we note that the majority of reward's modulation of motor cortical activity cannot be accounted for by reward-mediated vigor differences in behavior, indicating that reward modulations within motor cortex may serve roles in addition to affecting vigor. Overall, our results provide insight into the neural mechanisms that link reward-driven motivation to the modulation of the details of movement.

Visual target and task-critical feedback uncertainty impair different stages of reach planning in motor cortex

Sensory uncertainty jeopardizes accurate movement. During reaching, visual uncertainty can affect the estimation of hand position (feedback) and the desired movement endpoint (target). While impairing motor learning, it is unclear how either form of uncertainty affects cortical reach goal encoding. We show that reach trajectories vary more with higher visual uncertainty of the target, but not the feedback. Accordingly, cortical motor goal activities in male rhesus monkeys are less accurate during planning and movement initiation under target but not feedback uncertainty. Yet, when monkeys critically depend on visual feedback to conduct reaches via a brain-computer interface, then visual feedback uncertainty impairs reach accuracy and neural motor goal encoding around movement initiation. Neural state space analyses reveal a dimension that separates population activity by uncertainty level in all tested conditions. Our findings demonstrate that while both target and feedback uncertainty always reflect in neural activity, uncertain feedback only deteriorates neural reach goal information and behavior when it is task-critical, i.e., when having to rely on the sensory feedback and no other more reliable sensory modalities are available. Further, uncertain target and feedback impair reach goal encoding in a time-dependent manner, suggesting that they are integrated during different stages of reach planning.

A mechanism linking dopamine's roles in reinforcement, movement and motivation

Dopamine neurons (DANs) play seemingly distinct roles in reinforcement, 1-3 motivation, 4,5 and movement, 6,7 and DA-modulating therapies relieve symptoms across a puzzling spectrum of neurologic and psychiatric symptoms. 8 Yet, the mechanistic relationship among these roles is unknown. Here, we show DA's tripartite roles are causally linked by a process in which phasic striatal DA rapidly and persistently recalibrates the propensity to move, a measure of vigor. Using a self-timed movement task, we found that single exposures to reward-related DA transients (both endogenous and exogenously-induced) exerted one-shot updates to movement timing-but in a surprising fashion. Rather than reinforce specific movement times, DA transients quantitatively changed movement timing on the next trial, with larger transients leading to earlier movements (and smaller to later), consistent with a stochastic search process that calibrates the frequency of movement. Both abrupt and gradual changes in external and internal contingencies-such as timing criterion, reward content, and satiety state-caused changes to the amplitude of DA transients that causally altered movement timing. The rapidity and bidirectionality of the one-shot effects are difficult to reconcile with gradual synaptic plasticity, and instead point to more flexible cellular mechanisms, such as DA-dependent modulation of neuronal excitability. Our findings shed light on how natural reinforcement, as well as DA-related disorders such as Parkinson's disease, could affect behavioral vigor.

Individual variability of neural computations underlying flexible decisions

The ability to flexibly switch our responses to external stimuli according to contextual information is critical for successful interactions with a complex world. Context-dependent computations are necessary across many domains1-3, yet their neural implementations remain poorly understood. Here we developed a novel behavioural task in rats to study context-dependent selection and accumulation of evidence for decision-making4-6. Under assumptions supported by both monkey and rat data, we first show mathematically that this computation can be supported by three dynamical solutions and that all networks performing the task implement a combination of these solutions. These solutions can be identified and tested directly with experimental data. We further show that existing electrophysiological and modelling data are compatible with the full variety of possible combinations of these solutions, suggesting that different individuals could use different combinations. To study variability across individual subjects, we developed automated, high-throughput methods to train rats on our task and trained many subjects using these methods. Consistent with theoretical predictions, neural and behavioural analyses revealed substantial heterogeneity across rats, despite uniformly good task performance. Our theory further predicts a specific link between behavioural and neural signatures, which was robustly supported in the data. In summary, our results provide an experimentally supported theoretical framework to analyse individual variability in biological and artificial systems that perform flexible decision-making tasks, open the door to cellular-resolution studies of individual variability in higher cognition, and provide insights into neural mechanisms of context-dependent computation more generally.

The information bottleneck as a principle underlying multi-area cortical representations during decision-making

Decision-making emerges from distributed computations across multiple brain areas, but it is unclear why the brain distributes the computation. In deep learning, artificial neural networks use multiple areas (or layers) and form optimal representations of task inputs. These optimal representations are sufficient to perform the task well, but minimal so they are invariant to other irrelevant variables. We recorded single neurons and multiunits in dorsolateral prefrontal cortex (DLPFC) and dorsal premotor cortex (PMd) in monkeys during a perceptual decision-making task. We found that while DLPFC represents task-related inputs required to compute the choice, the downstream PMd contains a minimal sufficient, or optimal, representation of the choice. To identify a mechanism for how cortex may form these optimal representations, we trained a multi-area recurrent neural network (RNN) to perform the task. Remarkably, DLPFC and PMd resembling representations emerged in the early and late areas of the multi-area RNN, respectively. The DLPFC-resembling area partially orthogonalized choice information and task inputs and this choice information was preferentially propagated to downstream areas through selective alignment with inter-area connections, while remaining task information was not. Our results suggest that cortex uses multi-area computation to form minimal sufficient representations by preferential propagation of relevant information between areas.

Excitation-Inhibition Balance Controls Information Encoding in Neural Populations

Understanding how the complex connectivity structure of the brain shapes its information-processing capabilities is a long-standing question. By focusing on a paradigmatic architecture, we study how the neural activity of excitatory and inhibitory populations encodes information on external signals. We show that at long times information is maximized at the edge of stability, where inhibition balances excitation, both in linear and nonlinear regimes. In the presence of multiple external signals, this maximum corresponds to the entropy of the input dynamics. By analyzing the case of a prolonged stimulus, we find that stronger inhibition is instead needed to maximize the instantaneous sensitivity, revealing an intrinsic tradeoff between short-time responses and long-time accuracy. In agreement with recent experimental findings, our results pave the way for a deeper information-theoretic understanding of how the balance between excitation and inhibition controls optimal information-processing in neural populations.

Contextual neural dynamics during time perception in the primate ventral premotor cortex

Understanding how time perception adapts to cognitive demands remains a significant challenge. In some contexts, the brain encodes time categorically (as "long" or "short"), while in others, it encodes precise time intervals on a continuous scale. Although the ventral premotor cortex (VPC) is known for its role in complex temporal processes, such as speech, its specific involvement in time estimation remains underexplored. In this study, we investigated how the VPC processes temporal information during a time interval comparison task (TICT) and a time interval categorization task (TCT) in primates. We found a notable heterogeneity in neuronal responses associated with time perception across both tasks. While most neurons responded during time interval presentation, a smaller subset retained this information during the working memory periods. Population-level analysis revealed distinct dynamics between tasks: In the TICT, population activity exhibited a linear and parametric relationship with interval duration, whereas in the TCT, neuronal activity diverged into two distinct dynamics corresponding to the interval categories. During delay periods, these categorical or parametric representations remained consistent within each task context. This contextual shift underscores the VPC's adaptive role in interval estimation and highlights how temporal representations are modulated by cognitive demands.

An emerging view of neural geometry in motor cortex supports high-performance decoding

Decoders for brain-computer interfaces (BCIs) assume constraints on neural activity, chosen to reflect scientific beliefs while yielding tractable computations. Recent scientific advances suggest that the true constraints on neural activity, especially its geometry, may be quite different from those assumed by most decoders. We designed a decoder, MINT, to embrace statistical constraints that are potentially more appropriate. If those constraints are accurate, MINT should outperform standard methods that explicitly make different assumptions. Additionally, MINT should be competitive with expressive machine learning methods that can implicitly learn constraints from data. MINT performed well across tasks, suggesting its assumptions are well-matched to the data. MINT outperformed other interpretable methods in every comparison we made. MINT outperformed expressive machine learning methods in 37 of 42 comparisons. MINT's computations are simple, scale favorably with increasing neuron counts, and yield interpretable quantities such as data likelihoods. MINT's performance and simplicity suggest it may be a strong candidate for many BCI applications.

Behaviorally Irrelevant Feature Matching Increases Neural and Behavioral Working Memory Readout

There is an ongoing debate about whether working memory (WM) maintenance relies on persistent activity and/or short-term synaptic plasticity. This is a challenging question, because neuroimaging techniques in cognitive neuroscience measure activity only. Recently, neural perturbation techniques have been developed to tackle this issue, such as visual impulse perturbation or "pinging," which reveals (un)attended WM content during maintenance. There are contrasting explanations of how pinging reveals WM content, which is central to the debate. Pinging could reveal mnemonic representations by perturbing content-specific networks or by increasing the neural signal-to-noise ratio of active neural states. Here we tested the extent to which the neural impulse response is patterned by the WM network, by presenting two different impulse stimuli. If the impulse interacts with WM networks, the WM-specific impulse response should be enhanced by physical overlap between the initial memory item and the subsequent external perturbation stimulus. This prediction was tested in a working memory task by matching or mismatching task-irrelevant spatial frequencies between memory items and impulse stimuli, as well as probes. Matching probe spatial frequency with memory items resulted in faster behavioral response times and matching impulse spatial frequency with memory items increased the specificity of the neural impulse response as measured from EEG. Matching spatial frequencies did neither result in globally stronger neural responses nor in a larger decrease in trial-to-trial variability compared to mismatching spatial frequencies. The improved neural and behavioral readout of irrelevant feature matching provide evidence that impulse perturbation interacts directly with the memory representations.

Role of short-term plasticity and slow temporal dynamics in enhancing time series prediction with a brain-inspired recurrent neural network

Typical reservoir networks are based on random connectivity patterns that differ from brain circuits in two important ways. First, traditional reservoir networks lack synaptic plasticity among recurrent units, whereas cortical networks exhibit plasticity across all neuronal types and cortical layers. Second, reservoir networks utilize random Gaussian connectivity, while cortical networks feature a heavy-tailed distribution of synaptic strengths. It is unclear what are the computational advantages of these features for predicting complex time series. In this study, we integrated short-term plasticity (STP) and lognormal connectivity into a novel recurrent neural network (RNN) framework. The model exhibited rich patterns of population activity characterized by slow coordinated fluctuations. Using graph spectral decomposition, we show that weighted networks with lognormal connectivity and STP yield higher complexity than several graph types. When tested on various tasks involving the prediction of complex time series data, the RNN model outperformed a baseline model with random connectivity as well as several other network architectures. Overall, our results underscore the potential of incorporating brain-inspired features such as STP and heavy-tailed connectivity to enhance the robustness and performance of artificial neural networks in complex data prediction and signal processing tasks.

Dynamic tracking of objects in the macaque dorsomedial frontal cortex

A central tenet of cognitive neuroscience is that humans build an internal model of the external world and use mental simulation of the model to perform physical inferences. Decades of human experiments have shown that behaviors in many physical reasoning tasks are consistent with predictions from the mental simulation theory. However, evidence for the defining feature of mental simulation - that neural population dynamics reflect simulations of physical states in the environment - is limited. We test the mental simulation hypothesis by combining a naturalistic ball-interception task, large-scale electrophysiology in non-human primates, and recurrent neural network modeling. We find that neurons in the monkeys' dorsomedial frontal cortex (DMFC) represent task-relevant information about the ball position in a multiplexed fashion. At a population level, the activity pattern in DMFC comprises a low-dimensional neural embedding that tracks the ball both when it is visible and invisible, serving as a neural substrate for mental simulation. A systematic comparison of different classes of task-optimized RNN models with the DMFC data provides further evidence supporting the mental simulation hypothesis. Our findings provide evidence that neural dynamics in the frontal cortex are consistent with internal simulation of external states in the environment.

Representation of a perceptual bias in the prefrontal cortex

Perception is influenced by sensory stimulation, prior knowledge, and contextual cues, which collectively contribute to the emergence of perceptual biases. However, the precise neural mechanisms underlying these biases remain poorly understood. This study aims to address this gap by analyzing neural recordings from the prefrontal cortex (PFC) of monkeys performing a vibrotactile frequency discrimination task. Our findings provide empirical evidence supporting the hypothesis that perceptual biases can be reflected in the neural activity of the PFC. We found that the state-space trajectories of PFC neuronal activity encoded a warped representation of the first frequency presented during the task. Remarkably, this distorted representation of the frequency aligned with the predictions of its Bayesian estimator. The identification of these neural correlates expands our understanding of the neural basis of perceptual biases and highlights the involvement of the PFC in shaping perceptual experiences. Similar analyses could be employed in other delayed comparison tasks and in various brain regions to explore where and how neural activity reflects perceptual biases during different stages of the trial.

Dynamic tuning of neural stability for cognitive control

The brain is thought to execute cognitive control by actively maintaining and flexibly updating patterns of neural activity that represent goals and rules. However, while actively maintaining patterns of activity requires robustness against noise and distractors, updating the activity requires sensitivity to task-relevant inputs. How these conflicting demands can be reconciled in a single neural system remains unclear. Here, we study the prefrontal cortex of monkeys maintaining a covert rule and integrating sensory inputs toward a choice. Following the onset of neural responses, sensory integration evolves with a 70 ms delay. Using a stability analysis and a recurrent neural network model trained to perform the task, we show that this delay enables a transient, system-level destabilization, opening a temporal window to selectively incorporate new information. This mechanism allows robustness and sensitivity to coexist in a neural system and hierarchically updates patterns of neural activity, providing a general framework for cognitive control. Furthermore, it reveals a learned, explicit rule representation, suggesting a reconciliation between the symbolic and connectionist approaches for building intelligent machines.

Brain-inspired multisensory integration neural network for cross-modal recognition through spatiotemporal dynamics and deep learning

The integration and interaction of cross-modal senses in brain neural networks can facilitate high-level cognitive functionalities. In this work, we proposed a bioinspired multisensory integration neural network (MINN) that integrates visual and audio senses for recognizing multimodal information across different sensory modalities. This deep learning-based model incorporates a cascading framework of parallel convolutional neural networks (CNNs) for extracting intrinsic features from visual and audio inputs, and a recurrent neural network (RNN) for multimodal information integration and interaction. The network was trained using synthetic training data generated for digital recognition tasks. It was revealed that the spatial and temporal features extracted from visual and audio inputs by CNNs were encoded in subspaces orthogonal with each other. In integration epoch, network state evolved along quasi-rotation-symmetric trajectories and a structural manifold with stable attractors was formed in RNN, supporting accurate cross-modal recognition. We further evaluated the robustness of the MINN algorithm with noisy inputs and asynchronous digital inputs. Experimental results demonstrated the superior performance of MINN for flexible integration and accurate recognition of multisensory information with distinct sense properties. The present results provide insights into the computational principles governing multisensory integration and a comprehensive neural network model for brain-inspired intelligence.

Ramping cells in the rodent medial prefrontal cortex encode time to past and future events via real Laplace transform

In interval reproduction tasks, animals must remember the event starting the interval and anticipate the time of the planned response to terminate the interval. The interval reproduction task thus allows for studying both memory for the past and anticipation of the future. We analyzed previously published recordings from the rodent medial prefrontal cortex [J. Henke et al., eLife10, e71612 (2021)] during an interval reproduction task and identified two cell groups by modeling their temporal receptive fields using hierarchical Bayesian models. The firing in the "past cells" group peaked at the start of the interval and relaxed exponentially back to baseline. The firing in the "future cells" group increased exponentially and peaked right before the planned action at the end of the interval. Contrary to the previous assumption that timing information in the brain has one or two time scales for a given interval, we found strong evidence for a continuous distribution of the exponential rate constants for both past and future cell populations. The real Laplace transformation of time predicts exponential firing with a continuous distribution of rate constants across the population. Therefore, the firing pattern of the past cells can be identified with the Laplace transform of time since the past event while the firing pattern of the future cells can be identified with the Laplace transform of time until the planned future event.

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 three male 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 that 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, and also argue that not all parameters of movement are defined by different trajectories of population activity.

Learning to use landmarks for navigation amplifies their representation in retrosplenial cortex

Visual landmarks provide powerful reference signals for efficient navigation by altering the activity of spatially tuned neurons, such as place cells, head direction cells, and grid cells. To understand the neural mechanism by which landmarks exert such strong influence, it is necessary to identify how these visual features gain spatial meaning. In this study, we characterized visual landmark representations in mouse retrosplenial cortex (RSC) using chronic two-photon imaging of the same neuronal ensembles over the course of spatial learning. We found a pronounced increase in landmark-referenced activity in RSC neurons that, once established, remained stable across days. Changing behavioral context by uncoupling treadmill motion from visual feedback systematically altered neuronal responses associated with the coherence between visual scene flow speed and self-motion. To explore potential underlying mechanisms, we modeled how burst firing, mediated by supralinear somatodendritic interactions, could efficiently mediate context- and coherence-dependent integration of landmark information. Our results show that visual encoding shifts to landmark-referenced and context-dependent codes as these cues take on spatial meaning during learning.

Recall tempo of Hebbian sequences depends on the interplay of Hebbian kernel with tutor signal timing

Understanding how neural circuits generate sequential activity is a longstanding challenge. While foundational theoretical models have shown how sequences can be stored as memories in neural networks with Hebbian plasticity rules, these models considered only a narrow range of Hebbian rules. Here, we introduce a model for arbitrary Hebbian plasticity rules, capturing the diversity of spike-timing-dependent synaptic plasticity seen in experiments, and show how the choice of these rules and of neural activity patterns influences sequence memory formation and retrieval. In particular, we derive a general theory that predicts the tempo of sequence replay. This theory lays a foundation for explaining how cortical tutor signals might give rise to motor actions that eventually become "automatic." Our theory also captures the impact of changing the tempo of the tutor signal. Beyond shedding light on biological circuits, this theory has relevance in artificial intelligence by laying a foundation for frameworks whereby slow and computationally expensive deliberation can be stored as memories and eventually replaced by inexpensive recall.

Integrator dynamics in the cortico-basal ganglia loop underlie flexible motor timing

Flexible control of motor timing is crucial for behavior. Before volitional movement begins, the frontal cortex and striatum exhibit ramping spiking activity, with variable ramp slopes anticipating movement onsets. This activity in the cortico-basal ganglia loop may function as an adjustable 'timer,' triggering actions at the desired timing. However, because the frontal cortex and striatum share similar ramping dynamics and are both necessary for timing behaviors, distinguishing their individual roles in this timer function remains challenging. To address this, we conducted perturbation experiments combined with multi-regional electrophysiology in mice performing a flexible lick-timing task. Following transient silencing of the frontal cortex, cortical and striatal activity swiftly returned to pre-silencing levels and resumed ramping, leading to a shift in lick timing close to the silencing duration. Conversely, briefly inhibiting the striatum caused a gradual decrease in ramping activity in both regions, with ramping resuming from post-inhibition levels, shifting lick timing beyond the inhibition duration. Thus, inhibiting the frontal cortex and striatum effectively paused and rewound the timer, respectively. These findings suggest the striatum is a part of the network that temporally integrates input from the frontal cortex and generates ramping activity that regulates motor timing.

Emergent perceptual biases from state-space geometry in trained spiking recurrent neural networks

A stimulus held in working memory is perceived as contracted toward the average stimulus. This contraction bias has been extensively studied in psychophysics, but little is known about its origin from neural activity. By training recurrent networks of spiking neurons to discriminate temporal intervals, we explored the causes of this bias and how behavior relates to population firing activity. We found that the trained networks exhibited animal-like behavior. Various geometric features of neural trajectories in state space encoded warped representations of the durations of the first interval modulated by sensory history. Formulating a normative model, we showed that these representations conveyed a Bayesian estimate of the interval durations, thus relating activity and behavior. Importantly, our findings demonstrate that Bayesian computations already occur during the sensory phase of the first stimulus and persist throughout its maintenance in working memory, until the time of stimulus comparison.

Orthogonality of sensory and contextual categorical dynamics embedded in a continuum of responses from the second somatosensory cortex

How does the brain simultaneously process signals that bring complementary information, like raw sensory signals and their transformed counterparts, without any disruptive interference? Contemporary research underscores the brain's adeptness in using decorrelated responses to reduce such interference. Both neurophysiological findings and artificial neural networks support the notion of orthogonal representation for signal differentiation and parallel processing. Yet, where, and how raw sensory signals are transformed into more abstract representations remains unclear. Using a temporal pattern discrimination task in trained monkeys, we revealed that the second somatosensory cortex (S2) efficiently segregates faithful and transformed neural responses into orthogonal subspaces. Importantly, S2 population encoding for transformed signals, but not for faithful ones, disappeared during a nondemanding version of this task, which suggests that signal transformation and their decoding from downstream areas are only active on-demand. A mechanistic computation model points to gain modulation as a possible biological mechanism for the observed context-dependent computation. Furthermore, individual neural activities that underlie the orthogonal population representations exhibited a continuum of responses, with no well-determined clusters. These findings advocate that the brain, while employing a continuum of heterogeneous neural responses, splits population signals into orthogonal subspaces in a context-dependent fashion to enhance robustness, performance, and improve coding efficiency.

Context-invariant beliefs are supported by dynamic reconfiguration of single unit functional connectivity in prefrontal cortex of male macaques

Natural behaviors occur in closed action-perception loops and are supported by dynamic and flexible beliefs abstracted away from our immediate sensory milieu. How this real-world flexibility is instantiated in neural circuits remains unknown. Here, we have male macaques navigate in a virtual environment by primarily leveraging sensory (optic flow) signals, or by more heavily relying on acquired internal models. We record single-unit spiking activity simultaneously from the dorsomedial superior temporal area (MSTd), parietal area 7a, and the dorso-lateral prefrontal cortex (dlPFC). Results show that while animals were able to maintain adaptive task-relevant beliefs regardless of sensory context, the fine-grain statistical dependencies between neurons, particularly in 7a and dlPFC, dynamically remapped with the changing computational demands. In dlPFC, but not 7a, destroying these statistical dependencies abolished the area's ability for cross-context decoding. Lastly, correlational analyses suggested that the more unit-to-unit couplings remapped in dlPFC, and the less they did so in MSTd, the less were population codes and behavior impacted by the loss of sensory evidence. We conclude that dynamic functional connectivity between neurons in prefrontal cortex maintain a stable population code and context-invariant beliefs during naturalistic behavior.

Flexible multitask computation in recurrent networks utilizes shared dynamical motifs

Flexible computation is a hallmark of intelligent behavior. However, little is known about how neural networks contextually reconfigure for different computations. In the present work, we identified an algorithmic neural substrate for modular computation through the study of multitasking artificial recurrent neural networks. Dynamical systems analyses revealed learned computational strategies mirroring the modular subtask structure of the training task set. Dynamical motifs, which are recurring patterns of neural activity that implement specific computations through dynamics, such as attractors, decision boundaries and rotations, were reused across tasks. For example, tasks requiring memory of a continuous circular variable repurposed the same ring attractor. We showed that dynamical motifs were implemented by clusters of units when the unit activation function was restricted to be positive. Cluster lesions caused modular performance deficits. Motifs were reconfigured for fast transfer learning after an initial phase of learning. This work establishes dynamical motifs as a fundamental unit of compositional computation, intermediate between neuron and network. As whole-brain studies simultaneously record activity from multiple specialized systems, the dynamical motif framework will guide questions about specialization and generalization.

Rule-based modulation of a sensorimotor transformation across cortical areas

Flexible responses to sensory stimuli based on changing rules are critical for adapting to a dynamic environment. However, it remains unclear how the brain encodes and uses rule information to guide behavior. Here, we made single-unit recordings while head-fixed mice performed a cross-modal sensory selection task where they switched between two rules: licking in response to tactile stimuli while rejecting visual stimuli, or vice versa. Along a cortical sensorimotor processing stream including the primary (S1) and secondary (S2) somatosensory areas, and the medial (MM) and anterolateral (ALM) motor areas, single-neuron activity distinguished between the two rules both prior to and in response to the tactile stimulus. We hypothesized that neural populations in these areas would show rule-dependent preparatory states, which would shape the subsequent sensory processing and behavior. This hypothesis was supported for the motor cortical areas (MM and ALM) by findings that (1) the current task rule could be decoded from pre-stimulus population activity; (2) neural subspaces containing the population activity differed between the two rules; and (3) optogenetic disruption of pre-stimulus states impaired task performance. Our findings indicate that flexible action selection in response to sensory input can occur via configuration of preparatory states in the motor cortex.

Effect in the spectra of eigenvalues and dynamics of RNNs trained with excitatory-inhibitory constraint

In order to comprehend and enhance models that describes various brain regions it is important to study the dynamics of trained recurrent neural networks. Including Dale's law in such models usually presents several challenges. However, this is an important aspect that allows computational models to better capture the characteristics of the brain. Here we present a framework to train networks using such constraint. Then we have used it to train them in simple decision making tasks. We characterized the eigenvalue distributions of the recurrent weight matrices of such networks. Interestingly, we discovered that the non-dominant eigenvalues of the recurrent weight matrix are distributed in a circle with a radius less than 1 for those whose initial condition before training was random normal and in a ring for those whose initial condition was random orthogonal. In both cases, the radius does not depend on the fraction of excitatory and inhibitory units nor the size of the network. Diminution of the radius, compared to networks trained without the constraint, has implications on the activity and dynamics that we discussed here.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-09956-w.

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.

Neural dynamics of robust legged robots

Legged robot control has improved in recent years with the rise of deep reinforcement learning, however, much of the underlying neural mechanisms remain difficult to interpret. Our aim is to leverage bio-inspired methods from computational neuroscience to better understand the neural activity of robust robot locomotion controllers. Similar to past work, we observe that terrain-based curriculum learning improves agent stability. We study the biomechanical responses and neural activity within our neural network controller by simultaneously pairing physical disturbances with targeted neural ablations. We identify an agile hip reflex that enables the robot to regain its balance and recover from lateral perturbations. Model gradients are employed to quantify the relative degree that various sensory feedback channels drive this reflexive behavior. We also find recurrent dynamics are implicated in robust behavior, and utilize sampling-based ablation methods to identify these key neurons. Our framework combines model-based and sampling-based methods for drawing causal relationships between neural network activity and robust embodied robot behavior.

Motor cortex retains and reorients neural dynamics during motor imagery

The most prominent characteristic of motor cortex is its activation during movement execution, but it is also active when we simply imagine movements in the absence of actual motor output. Despite decades of behavioural and imaging studies, it is unknown how the specific activity patterns and temporal dynamics in motor cortex during covert motor imagery relate to those during motor execution. Here we recorded intracortical activity from the motor cortex of two people who retain some residual wrist function following incomplete spinal cord injury as they performed both actual and imagined isometric wrist extensions. We found that we could decompose the population activity into three orthogonal subspaces, where one was similarly active during both action and imagery, and the others were active only during a single task type-action or imagery. Although they inhabited orthogonal neural dimensions, the action-unique and imagery-unique subspaces contained a strikingly similar set of dynamic features. Our results suggest that during motor imagery, motor cortex maintains the same overall population dynamics as during execution by reorienting the components related to motor output and/or feedback into a unique, output-null imagery subspace.

The mediodorsal thalamus in executive control

Executive control, the ability to organize thoughts and action plans in real time, is a defining feature of higher cognition. Classical theories have emphasized cortical contributions to this process, but recent studies have reinvigorated interest in the role of the thalamus. Although it is well established that local thalamic damage diminishes cognitive capacity, such observations have been difficult to inform functional models. Recent progress in experimental techniques is beginning to enrich our understanding of the anatomical, physiological, and computational substrates underlying thalamic engagement in executive control. In this review, we discuss this progress and particularly focus on the mediodorsal thalamus, which regulates the activity within and across frontal cortical areas. We end with a synthesis that highlights frontal thalamocortical interactions in cognitive computations and discusses its functional implications in normal and pathological conditions.

Rule-based modulation of a sensorimotor transformation across cortical areas

Flexible responses to sensory stimuli based on changing rules are critical for adapting to a dynamic environment. However, it remains unclear how the brain encodes rule information and uses this information to guide behavioral responses to sensory stimuli. Here, we made single-unit recordings while head-fixed mice performed a cross-modal sensory selection task in which they switched between two rules in different blocks of trials: licking in response to tactile stimuli applied to a whisker while rejecting visual stimuli, or licking to visual stimuli while rejecting the tactile stimuli. Along a cortical sensorimotor processing stream including the primary (S1) and secondary (S2) somatosensory areas, and the medial (MM) and anterolateral (ALM) motor areas, the single-trial activity of individual neurons distinguished between the two rules both prior to and in response to the tactile stimulus. Variable rule-dependent responses to identical stimuli could in principle occur via appropriate configuration of pre-stimulus preparatory states of a neural population, which would shape the subsequent response. We hypothesized that neural populations in S1, S2, MM and ALM would show preparatory activity states that were set in a rule-dependent manner to cause processing of sensory information according to the current rule. This hypothesis was supported for the motor cortical areas by findings that (1) the current task rule could be decoded from pre-stimulus population activity in ALM and MM; (2) neural subspaces containing the population activity differed between the two rules; and (3) optogenetic disruption of pre-stimulus states within ALM and MM impaired task performance. Our findings indicate that flexible selection of an appropriate action in response to a sensory input can occur via configuration of preparatory states in the motor cortex.

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.

Differential Formation of Motor Cortical Dynamics during Movement Preparation According to the Predictability of Go Timing

The motor cortex not only executes but also prepares movement, as motor cortical neurons exhibit preparatory activity that predicts upcoming movements. In movement preparation, animals adopt different strategies in response to uncertainties existing in nature such as the unknown timing of when a predator will attack-an environmental cue informing "go." However, how motor cortical neurons cope with such uncertainties is less understood. In this study, we aim to investigate whether and how preparatory activity is altered depending on the predictability of "go" timing. We analyze firing activities of the anterior lateral motor cortex in male mice during two auditory delayed-response tasks each with predictable or unpredictable go timing. When go timing is unpredictable, preparatory activities immediately reach and stay in a neural state capable of producing movement anytime to a sudden go cue. When go timing is predictable, preparation activity reaches the movement-producible state more gradually, to secure more accurate decisions. Surprisingly, this preparation process entails a longer reaction time. We find that as preparatory activity increases in accuracy, it takes longer for a neural state to transition from the end of preparation to the start of movement. Our results suggest that the motor cortex fine-tunes preparatory activity for more accurate movement using the predictability of go timing.

Ramping cells in rodent mPFC encode time to past and future events via real Laplace transform

In interval reproduction tasks, animals must remember the event starting the interval and anticipate the time of the planned response to terminate the interval. The interval reproduction task thus allows for studying both memory for the past and anticipation of the future. We analyzed previously published recordings from rodent mPFC (Henke et al., 2021) during an interval reproduction task and identified two cell groups by modeling their temporal receptive fields using hierarchical Bayesian models. The firing in the "past cells" group peaked at the start of the interval and relaxed exponentially back to baseline. The firing in the "future cells" group increased exponentially and peaked right before the planned action at the end of the interval. Contrary to the previous assumption that timing information in the brain has one or two time scales for a given interval, we found strong evidence for a continuous distribution of the exponential rate constants for both past and future cell populations. The real Laplace transformation of time predicts exponential firing with a continuous distribution of rate constants across the population. Therefore, the firing pattern of the past cells can be identified with the Laplace transform of time since the past event while the firing pattern of the future cells can be identified with the Laplace transform of time until the planned future event.

Neuronal travelling waves explain rotational dynamics in experimental datasets and modelling

Spatiotemporal properties of neuronal population activity in cortical motor areas have been subjects of experimental and theoretical investigations, generating numerous interpretations regarding mechanisms for preparing and executing limb movements. Two competing models, representational and dynamical, strive to explain the relationship between movement parameters and neuronal activity. A dynamical model uses the jPCA method that holistically characterizes oscillatory activity in neuron populations by maximizing the data rotational dynamics. Different rotational dynamics interpretations revealed by the jPCA approach have been proposed. Yet, the nature of such dynamics remains poorly understood. We comprehensively analyzed several neuronal-population datasets and found rotational dynamics consistently accounted for by a traveling wave pattern. For quantifying rotation strength, we developed a complex-valued measure, the gyration number. Additionally, we identified parameters influencing rotation extent in the data. Our findings suggest that rotational dynamics and traveling waves are typically the same phenomena, so reevaluation of the previous interpretations where they were considered separate entities is needed.

Identifying Interpretable Latent Factors with Sparse Component Analysis

In many neural populations, the computationally relevant signals are posited to be a set of 'latent factors' - signals shared across many individual neurons. Understanding the relationship between neural activity and behavior requires the identification of factors that reflect distinct computational roles. Methods for identifying such factors typically require supervision, which can be suboptimal if one is unsure how (or whether) factors can be grouped into distinct, meaningful sets. Here, we introduce Sparse Component Analysis (SCA), an unsupervised method that identifies interpretable latent factors. SCA seeks factors that are sparse in time and occupy orthogonal dimensions. With these simple constraints, SCA facilitates surprisingly clear parcellations of neural activity across a range of behaviors. We applied SCA to motor cortex activity from reaching and cycling monkeys, single-trial imaging data from C. elegans, and activity from a multitask artificial network. SCA consistently identified sets of factors that were useful in describing network computations.

Neural manifolds carry reactivation of phonetic representations during semantic processing

Traditional models of speech perception posit that neural activity encodes speech through a hierarchy of cognitive processes, from low-level representations of acoustic and phonetic features to high-level semantic encoding. Yet it remains unknown how neural representations are transformed across levels of the speech hierarchy. Here, we analyzed unique microelectrode array recordings of neuronal spiking activity from the human left anterior superior temporal gyrus, a brain region at the interface between phonetic and semantic speech processing, during a semantic categorization task and natural speech perception. We identified distinct neural manifolds for semantic and phonetic features, with a functional separation of the corresponding low-dimensional trajectories. Moreover, phonetic and semantic representations were encoded concurrently and reflected in power increases in the beta and low-gamma local field potentials, suggesting top-down predictive and bottom-up cumulative processes. Our results are the first to demonstrate mechanisms for hierarchical speech transformations that are specific to neuronal population dynamics.

Emergence of Universal Computations Through Neural Manifold Dynamics

There is growing evidence that many forms of neural computation may be implemented by low-dimensional dynamics unfolding at the population scale. However, neither the connectivity structure nor the general capabilities of these embedded dynamical processes are currently understood. In this work, the two most common formalisms of firing-rate models are evaluated using tools from analysis, topology, and nonlinear dynamics in order to provide plausible explanations for these problems. It is shown that low-rank structured connectivities predict the formation of invariant and globally attracting manifolds in all these models. Regarding the dynamics arising in these manifolds, it is proved they are topologically equivalent across the considered formalisms. This letter also shows that under the low-rank hypothesis, the flows emerging in neural manifolds, including input-driven systems, are universal, which broadens previous findings. It explores how low-dimensional orbits can bear the production of continuous sets of muscular trajectories, the implementation of central pattern generators, and the storage of memory states. These dynamics can robustly simulate any Turing machine over arbitrary bounded memory strings, virtually endowing rate models with the power of universal computation. In addition, the letter shows how the low-rank hypothesis predicts the parsimonious correlation structure observed in cortical activity. Finally, it discusses how this theory could provide a useful tool from which to study neuropsychological phenomena using mathematical methods.

Keeping time and rhythm by internal simulation of sensory stimuli and behavioral actions

Effective behavior often requires synchronizing our actions with changes in the environment. Rhythmic changes in the environment are easy to predict, and we can readily time our actions to them. Yet, how the brain encodes and maintains rhythms is not known. Here, we trained primates to internally maintain rhythms of different tempos and performed large-scale recordings of neuronal activity across the sensory-motor hierarchy. Results show that maintaining rhythms engages multiple brain areas, including visual, parietal, premotor, prefrontal, and hippocampal regions. Each recorded area displayed oscillations in firing rates and oscillations in broadband local field potential power that reflected the temporal and spatial characteristics of an internal metronome, which flexibly encoded fast, medium, and slow tempos. The presence of widespread metronome-related activity, in the absence of stimuli and motor activity, suggests that internal simulation of stimuli and actions underlies timekeeping and rhythm maintenance.

Modelling and Controlling System Dynamics of the Brain: An Intersection of Machine Learning and Control Theory

The human brain, as a complex system, has long captivated multidisciplinary researchers aiming to decode its intricate structure and function. This intricate network has driven scientific pursuits to advance our understanding of cognition, behavior, and neurological disorders by delving into the complex mechanisms underlying brain function and dysfunction. Modelling brain dynamics using machine learning techniques deepens our comprehension of brain dynamics from a computational perspective. These computational models allow researchers to simulate and analyze neural interactions, facilitating the identification of dysfunctions in connectivity or activity patterns. Additionally, the trained dynamical system, serving as a surrogate model, optimizes neurostimulation strategies under the guidelines of control theory. In this chapter, we discuss the recent studies on modelling and controlling brain dynamics at the intersection of machine learning and control theory, providing a framework to understand and improve cognitive function, and treat neurological and psychiatric disorders.

Neural Sequences and the Encoding of Time

Converging experimental and computational evidence indicate that on the scale of seconds the brain encodes time through changing patterns of neural activity. Experimentally, two general forms of neural dynamic regimes that can encode time have been observed: neural population clocks and ramping activity. Neural population clocks provide a high-dimensional code to generate complex spatiotemporal output patterns, in which each neuron exhibits a nonlinear temporal profile. A prototypical example of neural population clocks are neural sequences, which have been observed across species, brain areas, and behavioral paradigms. Additionally, neural sequences emerge in artificial neural networks trained to solve time-dependent tasks. Here, we examine the role of neural sequences in the encoding of time, and how they may emerge in a biologically plausible manner. We conclude that neural sequences may represent a canonical computational regime to perform temporal computations.

Estimating Time and Rhythm by Predicting External Stimuli

In this chapter, we present recent findings from our group showing that elapsed time, interval timing, and rhythm maintenance might be achieved by the well-known ability of the brain to predict the future states of the world. The difference between predictions and actual sensory evidence is used to generate perceptual and behavioral adjustments that help subjects achieve desired behavioral goals. Concretely, we show that (1) accumulating prediction errors is a plausible strategy humans could use to determine whether a train of consecutive stimuli arrives at regular or irregular intervals. By analyzing the behavior of human and non-human primate subjects performing rhythm perception tasks, we demonstrate that (2) the ability to estimate elapsed time and internally maintain rhythms is shared across primates and humans. Neurophysiological recordings show that (3) the medial premotor cortex engages in rhythm entrainment and maintains oscillatory activity that reveals an internal metronome's spatial and temporal characteristics. Finally, we demonstrate that (4) the amplitude of gamma oscillations within this cortex increases proportionally to the total elapsed time. In conjunction with our most recent experiments, our results suggest that timing might be achieved by an internal simulation of the sensory stimuli and the motor commands that define the timing task that needs to be performed.

Dynamical flexible inference of nonlinear latent factors and structures in neural population activity

Modelling the spatiotemporal dynamics in the activity of neural populations while also enabling their flexible inference is hindered by the complexity and noisiness of neural observations. Here we show that the lower-dimensional nonlinear latent factors and latent structures can be computationally modelled in a manner that allows for flexible inference causally, non-causally and in the presence of missing neural observations. To enable flexible inference, we developed a neural network that separates the model into jointly trained manifold and dynamic latent factors such that nonlinearity is captured through the manifold factors and the dynamics can be modelled in tractable linear form on this nonlinear manifold. We show that the model, which we named 'DFINE' (for 'dynamical flexible inference for nonlinear embeddings') achieves flexible inference in simulations of nonlinear dynamics and across neural datasets representing a diversity of brain regions and behaviours. Compared with earlier neural-network models, DFINE enables flexible inference, better predicts neural activity and behaviour, and better captures the latent neural manifold structure. DFINE may advance the development of neurotechnology and investigations in neuroscience.

Diverse Time Encoding Strategies Within the Medial Premotor Areas of the Primate

The measurement of time in the subsecond scale is critical for many sophisticated behaviors, yet its neural underpinnings are largely unknown. Recent neurophysiological experiments from our laboratory have shown that the neural activity in the medial premotor areas (MPC) of macaques can represent different aspects of temporal processing. During single interval categorization, we found that preSMA encodes a subjective category limit by reaching a peak of activity at a time that divides the set of test intervals into short and long. We also observed neural signals associated with the category selected by the subjects and the reward outcomes of the perceptual decision. On the other hand, we have studied the behavioral and neurophysiological basis of rhythmic timing. First, we have shown in different tapping tasks that macaques are able to produce predictively and accurately intervals that are cued by auditory or visual metronomes or when intervals are produced internally without sensory guidance. In addition, we found that the rhythmic timing mechanism in MPC is governed by different layers of neural clocks. Next, the instantaneous activity of single cells shows ramping activity that encodes the elapsed or remaining time for a tapping movement. In addition, we found MPC neurons that build neural sequences, forming dynamic patterns of activation that flexibly cover all the produced interval depending on the tapping tempo. This rhythmic neural clock resets on every interval providing an internal representation of pulse. Furthermore, the MPC cells show mixed selectivity, encoding not only elapsed time, but also the tempo of the tapping and the serial order element in the rhythmic sequence. Hence, MPC can map different task parameters, including the passage of time, using different cell populations. Finally, the projection of the time varying activity of MPC hundreds of cells into a low dimensional state space showed circular neural trajectories whose geometry represented the internal pulse and the tapping tempo. Overall, these findings support the notion that MPC is part of the core timing mechanism for both single interval and rhythmic timing, using neural clocks with different encoding principles, probably to flexibly encode and mix the timing representation with other task parameters.

Dopamine precursor depletion affects performance and confidence judgements when events are timed from an explicit, but not an implicit onset

Dopamine affects processing of temporal information, but most previous work has tested its role in prospective tasks, where participants know in advance when the event to be timed starts. However, we are often exposed to events whose onset we do not know in advance. We can evaluate their duration after they have elapsed, but mechanisms underlying this ability are still elusive. Here we contrasted effects of acute phenylalanine and tyrosine depletion (APTD) on both forms of timing in healthy volunteers, in a within-subject, placebo-controlled design. Participants were presented with a disc moving around a circular path and asked to reproduce the duration of one full revolution and to judge their confidence in performance. The onset of the revolution was either known in advance (explicit onset) or revealed only at the end of the trial (implicit onset). We found that APTD shortened reproduced durations in the explicit onset task but had no effect on temporal performance in the implicit onset task. This dissociation is corroborated by effects of APTD on confidence judgements in the explicit task only. Our findings suggest that dopamine has a specific role in prospective encoding of temporal intervals, rather than the processing of temporal information in general.

Cortico-spinal modularity in the parieto-frontal system: A new perspective on action control

Classical neurophysiology suggests that the motor cortex (MI) has a unique role in action control. In contrast, this review presents evidence for multiple parieto-frontal spinal command modules that can bypass MI. Five observations support this modular perspective: (i) the statistics of cortical connectivity demonstrate functionally-related clusters of cortical areas, defining functional modules in the premotor, cingulate, and parietal cortices; (ii) different corticospinal pathways originate from the above areas, each with a distinct range of conduction velocities; (iii) the activation time of each module varies depending on task, and different modules can be activated simultaneously; (iv) a modular architecture with direct motor output is faster and less metabolically expensive than an architecture that relies on MI, given the slow connections between MI and other cortical areas; (v) lesions of the areas composing parieto-frontal modules have different effects from lesions of MI. Here we provide examples of six cortico-spinal modules and functions they subserve: module 1) arm reaching, tool use and object construction; module 2) spatial navigation and locomotion; module 3) grasping and observation of hand and mouth actions; module 4) action initiation, motor sequences, time encoding; module 5) conditional motor association and learning, action plan switching and action inhibition; module 6) planning defensive actions. These modules can serve as a library of tools to be recombined when faced with novel tasks, and MI might serve as a recombinatory hub. In conclusion, the availability of locally-stored information and multiple outflow paths supports the physiological plausibility of the proposed modular perspective.

Phantom oscillations in principal component analysis

Principal component analysis (PCA) is a dimensionality reduction method that is known for being simple and easy to interpret. Principal components are often interpreted as low-dimensional patterns in high-dimensional space. However, this simple interpretation fails for timeseries, spatial maps, and other continuous data. In these cases, nonoscillatory data may have oscillatory principal components. Here, we show that two common properties of data cause oscillatory principal components: smoothness and shifts in time or space. These two properties implicate almost all neuroscience data. We show how the oscillations produced by PCA, which we call "phantom oscillations," impact data analysis. We also show that traditional cross-validation does not detect phantom oscillations, so we suggest procedures that do. Our findings are supported by a collection of mathematical proofs. Collectively, our work demonstrates that patterns which emerge from high-dimensional data analysis may not faithfully represent the underlying data.

Exploring weight initialization, diversity of solutions, and degradation in recurrent neural networks trained for temporal and decision-making tasks

Recurrent Neural Networks (RNNs) are frequently used to model aspects of brain function and structure. In this work, we trained small fully-connected RNNs to perform temporal and flow control tasks with time-varying stimuli. Our results show that different RNNs can solve the same task by converging to different underlying dynamics and also how the performance gracefully degrades as either network size is decreased, interval duration is increased, or connectivity damage is induced. For the considered tasks, we explored how robust the network obtained after training can be according to task parameterization. In the process, we developed a framework that can be useful to parameterize other tasks of interest in computational neuroscience. Our results are useful to quantify different aspects of the models, which are normally used as black boxes and need to be understood in order to model the biological response of cerebral cortex areas.

Reconstructing computational system dynamics from neural data with recurrent neural networks

Computational models in neuroscience usually take the form of systems of differential equations. The behaviour of such systems is the subject of dynamical systems theory. Dynamical systems theory provides a powerful mathematical toolbox for analysing neurobiological processes and has been a mainstay of computational neuroscience for decades. Recently, recurrent neural networks (RNNs) have become a popular machine learning tool for studying the non-linear dynamics of neural and behavioural processes by emulating an underlying system of differential equations. RNNs have been routinely trained on similar behavioural tasks to those used for animal subjects to generate hypotheses about the underlying computational mechanisms. By contrast, RNNs can also be trained on the measured physiological and behavioural data, thereby directly inheriting their temporal and geometrical properties. In this way they become a formal surrogate for the experimentally probed system that can be further analysed, perturbed and simulated. This powerful approach is called dynamical system reconstruction. In this Perspective, we focus on recent trends in artificial intelligence and machine learning in this exciting and rapidly expanding field, which may be less well known in neuroscience. We discuss formal prerequisites, different model architectures and training approaches for RNN-based dynamical system reconstructions, ways to evaluate and validate model performance, how to interpret trained models in a neuroscience context, and current challenges.

Amodal population clock in the primate medial premotor system for rhythmic tapping

The neural substrate for beat extraction and response entrainment to rhythms is not fully understood. Here we analyze the activity of medial premotor neurons in monkeys performing isochronous tapping guided by brief flashing stimuli or auditory tones. The population dynamics shared the following properties across modalities: the circular dynamics of the neural trajectories form a regenerating loop for every produced interval; the trajectories converge in similar state space at tapping times resetting the clock; and the tempo of the synchronized tapping is encoded in the trajectories by a combination of amplitude modulation and temporal scaling. Notably, the modality induces displacement in the neural trajectories in the auditory and visual subspaces without greatly altering the time-keeping mechanism. These results suggest that the interaction between the medial premotor cortex's amodal internal representation of pulse and a modality-specific external input generates a neural rhythmic clock whose dynamics govern rhythmic tapping execution across senses.