Dynamic Control of Response Criterion in Premotor Cortex during Perceptual Detection under Temporal Uncertainty

Chaotic recurrent neural networks for brain modelling: A review

Even in the absence of external stimuli, the brain is spontaneously active. Indeed, most cortical activity is internally generated by recurrence. Both theoretical and experimental studies suggest that chaotic dynamics characterize this spontaneous activity. While the precise function of brain chaotic activity is still puzzling, we know that chaos confers many advantages. From a computational perspective, chaos enhances the complexity of network dynamics. From a behavioural point of view, chaotic activity could generate the variability required for exploration. Furthermore, information storage and transfer are maximized at the critical border between order and chaos. Despite these benefits, many computational brain models avoid incorporating spontaneous chaotic activity due to the challenges it poses for learning algorithms. In recent years, however, multiple approaches have been proposed to overcome this limitation. As a result, many different algorithms have been developed, initially within the reservoir computing paradigm. Over time, the field has evolved to increase the biological plausibility and performance of the algorithms, sometimes going beyond the reservoir computing framework. In this review article, we examine the computational benefits of chaos and the unique properties of chaotic recurrent neural networks, with a particular focus on those typically utilized in reservoir computing. We also provide a detailed analysis of the algorithms designed to train chaotic RNNs, tracing their historical evolution and highlighting key milestones in their development. Finally, we explore the applications and limitations of chaotic RNNs for brain modelling, consider their potential broader impacts beyond neuroscience, and outline promising directions for future research.

Neural signatures of temporal anticipation in human cortex represent event probability density

Temporal prediction is a fundamental function of neural systems. Recent results show that humans anticipate future events by calculating probability density functions, rather than hazard rates. However, direct neural evidence for this hypothesized mechanism is lacking. We recorded neural activity using magnetoencephalography as participants anticipated auditory and visual events distributed in time. We show that temporal anticipation, measured as reaction times, approximates the event probability density function, but not hazard rate. Temporal anticipation manifests as spatiotemporally patterned activity in three anatomically and functionally distinct parieto-temporal and sensorimotor cortical areas. Each of these areas revealed a marked neural signature of anticipation: Prior to sensory cues, activity in a specific frequency range of neural oscillations, spanning alpha and beta ranges, encodes the event probability density function. These neural signals predicted reaction times to imminent sensory cues. These results demonstrate that supra-modal representations of probability density across cortex underlie the anticipation of future events.

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.

Rapid calibration to dynamic temporal contexts

The prediction of future events and the preparation of appropriate behavioural reactions rely on an accurate perception of temporal regularities. In dynamic environments, temporal regularities are subject to slow and sudden changes, and adaptation to these changes is an important requirement for efficient behaviour. Bayesian models have proven a useful tool to understand the processing of temporal regularities in humans; yet an open question pertains to the degree of flexibility of the prior that is required for optimal modelling of behaviour. Here we directly compare dynamic models (with continuously changing prior expectations) and static models (a stable prior for each experimental session) with their ability to describe regression effects in interval timing. Our results show that dynamic Bayesian models are superior when describing the responses to slow, continuous environmental changes, whereas static models are more suitable to describe responses to sudden changes. In time perception research, these results will be informative for the choice of adequate computational models and enhance our understanding of the neuronal computations underlying human timing behaviour.

Constructing neural networks with pre-specified dynamics

A main goal in neuroscience is to understand the computations carried out by neural populations that give animals their cognitive skills. Neural network models allow to formulate explicit hypotheses regarding the algorithms instantiated in the dynamics of a neural population, its firing statistics, and the underlying connectivity. Neural networks can be defined by a small set of parameters, carefully chosen to procure specific capabilities, or by a large set of free parameters, fitted with optimization algorithms that minimize a given loss function. In this work we alternatively propose a method to make a detailed adjustment of the network dynamics and firing statistic to better answer questions that link dynamics, structure, and function. Our algorithm-termed generalised Firing-to-Parameter (gFTP)-provides a way to construct binary recurrent neural networks whose dynamics strictly follows a user pre-specified transition graph that details the transitions between population firing states triggered by stimulus presentations. Our main contribution is a procedure that detects when a transition graph is not realisable in terms of a neural network, and makes the necessary modifications in order to obtain a new transition graph that is realisable and preserves all the information encoded in the transitions of the original graph. With a realisable transition graph, gFTP assigns values to the network firing states associated with each node in the graph, and finds the synaptic weight matrices by solving a set of linear separation problems. We test gFTP performance by constructing networks with random dynamics, continuous attractor-like dynamics that encode position in 2-dimensional space, and discrete attractor dynamics. We then show how gFTP can be employed as a tool to explore the link between structure, function, and the algorithms instantiated in the network dynamics.

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.

Neocortical inhibitory imbalance predicts successful sensory detection

Perceptual success depends on fast-spiking, parvalbumin-positive interneurons (FS/PVs). However, competing theories of optimal rate and correlation in pyramidal (PYR) firing make opposing predictions regarding the underlying FS/PV dynamics. We addressed this with population calcium imaging of FS/PVs and putative PYR neurons during threshold detection. In primary somatosensory and visual neocortex, a distinct PYR subset shows increased rate and spike-count correlations on detected trials ("hits"), while most show no rate change and decreased correlations. A larger fraction of FS/PVs predicts hits with either rate increases or decreases. Using computational modeling, we found that inhibitory imbalance, created by excitatory "feedback" and interactions between FS/PV pools, can account for the data. Rate-decreasing FS/PVs increase rate and correlation in a PYR subset, while rate-increasing FS/PVs reduce correlations and offset enhanced excitation in PYR neurons. These findings indicate that selection of informative PYR ensembles, through transient inhibitory imbalance, is a common motif of optimal neocortical processing.

Thalamocortical interactions shape hierarchical neural variability during stimulus perception

The brain is organized hierarchically to process sensory signals. But, how do functional connections within and across areas contribute to this hierarchical order? We addressed this problem in the thalamocortical network, while monkeys detected vibrotactile stimulus. During this task, we quantified neural variability and directed functional connectivity in simultaneously recorded neurons sharing the cutaneous receptive field within and across VPL and areas 3b and 1. Before stimulus onset, VPL and area 3b exhibited similar fast dynamics while area 1 showed slower timescales. During the stimulus presence, inter-trial neural variability increased along the network VPL-3b-1 while VPL established two main feedforward pathways with areas 3b and 1 to process the stimulus. This lower variability of VPL and area 3b was found to regulate feedforward thalamocortical pathways. Instead, intra-cortical interactions were only anticipated by higher intrinsic timescales in area 1. Overall, our results provide evidence of hierarchical functional roles along the thalamocortical network.

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.

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.

Sequential neuronal processing of number values, abstract decision, and action in the primate prefrontal cortex

Decision-making requires processing of sensory information, comparing the gathered evidence to make a judgment, and performing the action to communicate it. How neuronal representations transform during this cascade of representations remains a matter of debate. Here, we studied the succession of neuronal representations in the primate prefrontal cortex (PFC). We trained monkeys to judge whether a pair of sequentially presented displays had the same number of items. We used a combination of single neuron and population-level analyses and discovered a sequential transformation of represented information with trial progression. While numerical values were initially represented with high precision and in conjunction with detailed information such as order, the decision was encoded in a low-dimensional subspace of neural activity. This decision encoding was invariant to both retrospective numerical values and prospective motor plans, representing only the binary judgment of "same number" versus "different number," thus facilitating the generalization of decisions to novel number pairs. We conclude that this transformation of neuronal codes within the prefrontal cortex supports cognitive flexibility and generalizability of decisions to new conditions.

A recurrent Hopfield network for estimating meso-scale effective connectivity in MEG

The architecture of communication within the brain, represented by the human connectome, has gained a paramount role in the neuroscience community. Several features of this communication, e.g., the frequency content, spatial topology, and temporal dynamics are currently well established. However, identifying generative models providing the underlying patterns of inhibition/excitation is very challenging. To address this issue, we present a novel generative model to estimate large-scale effective connectivity from MEG. The dynamic evolution of this model is determined by a recurrent Hopfield neural network with asymmetric connections, and thus denoted Recurrent Hopfield Mass Model (RHoMM). Since RHoMM must be applied to binary neurons, it is suitable for analyzing Band Limited Power (BLP) dynamics following a binarization process. We trained RHoMM to predict the MEG dynamics through a gradient descent minimization and we validated it in two steps. First, we showed a significant agreement between the similarity of the effective connectivity patterns and that of the interregional BLP correlation, demonstrating RHoMM's ability to capture individual variability of BLP dynamics. Second, we showed that the simulated BLP correlation connectomes, obtained from RHoMM evolutions of BLP, preserved some important topological features, e.g, the centrality of the real data, assuring the reliability of RHoMM. Compared to other biophysical models, RHoMM is based on recurrent Hopfield neural networks, thus, it has the advantage of being data-driven, less demanding in terms of hyperparameters and scalable to encompass large-scale system interactions. These features are promising for investigating the dynamics of inhibition/excitation at different spatial scales.

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.

Multimodal Temporal Pattern Discrimination Is Encoded in Visual Cortical Dynamics

Discriminating between temporal features in sensory stimuli is critical to complex behavior and decision-making. However, how sensory cortical circuit mechanisms contribute to discrimination between subsecond temporal components in sensory events is unclear. To elucidate the mechanistic underpinnings of timing in primary visual cortex (V1), we recorded from V1 using two-photon calcium imaging in awake-behaving mice performing a go/no-go discrimination timing task, which was composed of patterns of subsecond audiovisual stimuli. In both conditions, activity during the early stimulus period was temporally coordinated with the preferred stimulus. However, while network activity increased in the preferred condition, network activity was increasingly suppressed in the nonpreferred condition over the stimulus period. Multiple levels of analyses suggest that discrimination between subsecond intervals that are contained in rhythmic patterns can be accomplished by local neural dynamics in V1.

Recurrent networks endowed with structural priors explain suboptimal animal behavior

The strategies found by animals facing a new task are determined both by individual experience and by structural priors evolved to leverage the statistics of natural environments. Rats quickly learn to capitalize on the trial sequence correlations of two-alternative forced choice (2AFC) tasks after correct trials but consistently deviate from optimal behavior after error trials. To understand this outcome-dependent gating, we first show that recurrent neural networks (RNNs) trained in the same 2AFC task outperform rats as they can readily learn to use across-trial information both after correct and error trials. We hypothesize that, although RNNs can optimize their behavior in the 2AFC task without any a priori restrictions, rats' strategy is constrained by a structural prior adapted to a natural environment in which rewarded and non-rewarded actions provide largely asymmetric information. When pre-training RNNs in a more ecological task with more than two possible choices, networks develop a strategy by which they gate off the across-trial evidence after errors, mimicking rats' behavior. Population analyses show that the pre-trained networks form an accurate representation of the sequence statistics independently of the outcome in the previous trial. After error trials, gating is implemented by a change in the network dynamics that temporarily decouple the categorization of the stimulus from the across-trial accumulated evidence. Our results suggest that the rats' suboptimal behavior reflects the influence of a structural prior that reacts to errors by isolating the network decision dynamics from the context, ultimately constraining the performance in a 2AFC laboratory task.

A Recurrent Neural Network Model Accounts for Both Timing and Working Memory Components of an Interval Discrimination Task

Interval discrimination is of fundamental importance to many forms of sensory processing, including speech and music. Standard interval discrimination tasks require comparing two intervals separated in time, and thus include both working memory (WM) and timing components. Models of interval discrimination invoke separate circuits for the timing and WM components. Here we examine if, in principle, the same recurrent neural network can implement both. Using human psychophysics, we first explored the role of the WM component by varying the interstimulus delay. Consistent with previous studies, discrimination was significantly worse for a 250 ms delay, compared to 750 and 1500 ms delays, suggesting that the first interval is stably stored in WM for longer delays. We next successfully trained a recurrent neural network (RNN) on the task, demonstrating that the same network can implement both the timing and WM components. Many units in the RNN were tuned to specific intervals during the sensory epoch, and others encoded the first interval during the delay period. Overall, the encoding strategy was consistent with the notion of mixed selectivity. Units generally encoded more interval information during the sensory epoch than in the delay period, reflecting categorical encoding of short versus long in WM, rather than encoding of the specific interval. Our results demonstrate that, in contrast to standard models of interval discrimination that invoke a separate memory module, the same network can, in principle, solve the timing, WM, and comparison components of an interval discrimination task.

The neural bases for timing of durations

Durations are defined by a beginning and an end, and a major distinction is drawn between durations that start in the present and end in the future ('prospective timing') and durations that start in the past and end either in the past or the present ('retrospective timing'). Different psychological processes are thought to be engaged in each of these cases. The former is thought to engage a clock-like mechanism that accurately tracks the continuing passage of time, whereas the latter is thought to engage a reconstructive process that utilizes both temporal and non-temporal information from the memory of past events. We propose that, from a biological perspective, these two forms of duration 'estimation' are supported by computational processes that are both reliant on population state dynamics but are nevertheless distinct. Prospective timing is effectively carried out in a single step where the ongoing dynamics of population activity directly serve as the computation of duration, whereas retrospective timing is carried out in two steps: the initial generation of population state dynamics through the process of event segmentation and the subsequent computation of duration utilizing the memory of those dynamics.

Encoding time in neural dynamic regimes with distinct computational tradeoffs

Converging evidence suggests the brain encodes time in dynamic patterns of neural activity, including neural sequences, ramping activity, and complex dynamics. Most temporal tasks, however, require more than just encoding time, and can have distinct computational requirements including the need to exhibit temporal scaling, generalize to novel contexts, or robustness to noise. It is not known how neural circuits can encode time and satisfy distinct computational requirements, nor is it known whether similar patterns of neural activity at the population level can exhibit dramatically different computational or generalization properties. To begin to answer these questions, we trained RNNs on two timing tasks based on behavioral studies. The tasks had different input structures but required producing identically timed output patterns. Using a novel framework we quantified whether RNNs encoded two intervals using either of three different timing strategies: scaling, absolute, or stimulus-specific dynamics. We found that similar neural dynamic patterns at the level of single intervals, could exhibit fundamentally different properties, including, generalization, the connectivity structure of the trained networks, and the contribution of excitatory and inhibitory neurons. Critically, depending on the task structure RNNs were better suited for generalization or robustness to noise. Further analysis revealed different connection patterns underlying the different regimes. Our results predict that apparently similar neural dynamic patterns at the population level (e.g., neural sequences) can exhibit fundamentally different computational properties in regards to their ability to generalize to novel stimuli and their robustness to noise—and that these differences are associated with differences in network connectivity and distinct contributions of excitatory and inhibitory neurons. We also predict that the task structure used in different experimental studies accounts for some of the experimentally observed variability in how networks encode time.

The ability to tell time and anticipate when external events will occur are among the most fundamental computations the brain performs. Converging evidence suggests the brain encodes time through changing patterns of neural activity. Different temporal tasks, however, have distinct computational requirements, such as the need to flexibly scale temporal patterns or generalize to novel inputs. To understand how networks can encode time and satisfy different computational requirements we trained recurrent neural networks (RNNs) on two timing tasks that have previously been used in behavioral studies. Both tasks required producing identically timed output patterns. Using a novel framework to quantify how networks encode different intervals, we found that similar patterns of neural activity—neural sequences—were associated with fundamentally different underlying mechanisms, including the connectivity patterns of the RNNs. Critically, depending on the task the RNNs were trained on, they were better suited for generalization or robustness to noise. Our results predict that similar patterns of neural activity can be produced by distinct RNN configurations, which in turn have fundamentally different computational tradeoffs. Our results also predict that differences in task structure account for some of the experimentally observed variability in how networks encode time.

Multiple-Timescale Neural Networks: Generation of History-Dependent Sequences and Inference Through Autonomous Bifurcations

Sequential transitions between metastable states are ubiquitously observed in the neural system and underlying various cognitive functions such as perception and decision making. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences are generated, the focused sequences are simple Markov ones. On the other hand, fine recurrent neural networks trained with supervised machine learning methods can generate complex non-Markov sequences, but these sequences are vulnerable against perturbations and such learning methods are biologically implausible. How stable and complex sequences are generated in the neural system still remains unclear. We have developed a neural network with fast and slow dynamics, which are inspired by the hierarchy of timescales on neural activities in the cortex. The slow dynamics store the history of inputs and outputs and affect the fast dynamics depending on the stored history. We show that the learning rule that requires only local information can form the network generating the complex and robust sequences in the fast dynamics. The slow dynamics work as bifurcation parameters for the fast one, wherein they stabilize the next pattern of the sequence before the current pattern is destabilized depending on the previous patterns. This co-existence period leads to the stable transition between the current and the next pattern in the non-Markov sequence. We further find that timescale balance is critical to the co-existence period. Our study provides a novel mechanism generating robust complex sequences with multiple timescales. Considering the multiple timescales are widely observed, the mechanism advances our understanding of temporal processing in the neural system.

Computational mechanisms of distributed value representations and mixed learning strategies

Learning appropriate representations of the reward environment is challenging in the real world where there are many options, each with multiple attributes or features. Despite existence of alternative solutions for this challenge, neural mechanisms underlying emergence and adoption of value representations and learning strategies remain unknown. To address this, we measure learning and choice during a multi-dimensional probabilistic learning task in humans and trained recurrent neural networks (RNNs) to capture our experimental observations. We find that human participants estimate stimulus-outcome associations by learning and combining estimates of reward probabilities associated with the informative feature followed by those of informative conjunctions. Through analyzing representations, connectivity, and lesioning of the RNNs, we demonstrate this mixed learning strategy relies on a distributed neural code and opponency between excitatory and inhibitory neurons through value-dependent disinhibition. Together, our results suggest computational and neural mechanisms underlying emergence of complex learning strategies in naturalistic settings.

Towards the next generation of recurrent network models for cognitive neuroscience

Recurrent neural networks (RNNs) trained with machine learning techniques on cognitive tasks have become a widely accepted tool for neuroscientists. In this short opinion piece, we discuss fundamental challenges faced by the early work of this approach and recent steps to overcome such challenges and build next-generation RNN models for cognition. We propose several essential questions that practitioners of this approach should address to continue to build future generations of RNN models.

Differential Excitability of PV and SST Neurons Results in Distinct Functional Roles in Inhibition Stabilization of Up States

Up states are the best studied example of an emergent neural dynamic regime. Computational models based on a single class of inhibitory neurons indicate that Up states reflect bistable dynamic systems in which positive feedback is stabilized by strong inhibition and predict a paradoxical effect in which increased drive to inhibitory neurons results in decreased inhibitory activity. To date, however, computational models have not incorporated empirically defined properties of parvalbumin (PV) and somatostatin (SST) neurons. Here we first experimentally characterized the frequency-current (F-I) curves of pyramidal (Pyr), PV, and SST neurons from mice of either sex, and confirmed a sharp difference between the threshold and slopes of PV and SST neurons. The empirically defined F-I curves were incorporated into a three-population computational model that simulated the empirically derived firing rates of pyramidal, PV, and SST neurons. Simulations revealed that the intrinsic properties were sufficient to predict that PV neurons are primarily responsible for generating the nontrivial fixed points representing Up states. Simulations and analytical methods demonstrated that while the paradoxical effect is not obligatory in a model with two classes of inhibitory neurons, it is present in most regimes. Finally, experimental tests validated predictions of the model that the Pyr ↔ PV inhibitory loop is stronger than the Pyr ↔ SST loop.SIGNIFICANCE STATEMENT Many cortical computations, such as working memory, rely on the local recurrent excitatory connections that define cortical circuit motifs. Up states are among the best studied examples of neural dynamic regimes that rely on recurrent excitatory excitation. However, this positive feedback must be held in check by inhibition. To address the relative contribution of PV and SST neurons, we characterized the intrinsic input-output differences between these classes of inhibitory neurons and, using experimental and theoretical methods, show that the higher threshold and gain of PV leads to a dominant role in network stabilization.

Attractor dynamics gate cortical information flow during decision-making

Decisions are held in memory until enacted, which makes them potentially vulnerable to distracting sensory input. Gating of information flow from sensory to motor areas could protect memory from interference during decision-making, but the underlying network mechanisms are not understood. Here, we trained mice to detect optogenetic stimulation of the somatosensory cortex, with a delay separating sensation and action. During the delay, distracting stimuli lost influence on behavior over time, even though distractor-evoked neural activity percolated through the cortex without attenuation. Instead, choice-encoding activity in the motor cortex became progressively less sensitive to the impact of distractors. Reverse engineering of neural networks trained to reproduce motor cortex activity revealed that the reduction in sensitivity to distractors was caused by a growing separation in the neural activity space between attractors that encode alternative decisions. Our results show that communication between brain regions can be gated via attractor dynamics, which control the degree of commitment to an action.

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.

Extracting single-trial neural interaction using latent dynamical systems model

In systems neuroscience, advances in simultaneous recording technology have helped reveal the population dynamics that underlie the complex neural correlates of animal behavior and cognitive processes. To investigate these correlates, neural interactions are typically abstracted from spike trains of pairs of neurons accumulated over the course of many trials. However, the resultant averaged values do not lead to understanding of neural computation in which the responses of populations are highly variable even under identical external conditions. Accordingly, neural interactions within the population also show strong fluctuations. In the present study, we introduce an analysis method reflecting the temporal variation of neural interactions, in which cross-correlograms on rate estimates are applied via a latent dynamical systems model. Using this method, we were able to predict time-varying neural interactions within a single trial. In addition, the pairwise connections estimated in our analysis increased along behavioral epochs among neurons categorized within similar functional groups. Thus, our analysis method revealed that neurons in the same groups communicate more as the population gets involved in the assigned task. We also showed that the characteristics of neural interaction from our model differ from the results of a typical model employing cross-correlation coefficients. This suggests that our model can extract nonoverlapping information about network topology, unlike the typical model.

Invariant timescale hierarchy across the cortical somatosensory network

The ability of cortical networks to integrate information from different sources is essential for cognitive processes. On one hand, sensory areas exhibit fast dynamics often phase-locked to stimulation; on the other hand, frontal lobe areas with slow response latencies to stimuli must integrate and maintain information for longer periods. Thus, cortical areas may require different timescales depending on their functional role. Studying the cortical somatosensory network while monkeys discriminated between two vibrotactile stimulus patterns, we found that a hierarchical order could be established across cortical areas based on their intrinsic timescales. Further, even though subareas (areas 3b, 1, and 2) of the primary somatosensory (S1) cortex exhibit analogous firing rate responses, a clear differentiation was observed in their timescales. Importantly, we observed that this inherent timescale hierarchy was invariant between task contexts (demanding vs. nondemanding). Even if task context severely affected neural coding in cortical areas downstream to S1, their timescales remained unaffected. Moreover, we found that these time constants were invariant across neurons with different latencies or coding. Although neurons had completely different dynamics, they all exhibited comparable timescales within each cortical area. Our results suggest that this measure is demonstrative of an inherent characteristic of each cortical area, is not a dynamical feature of individual neurons, and does not depend on task demands.

PsychRNN: An Accessible and Flexible Python Package for Training Recurrent Neural Network Models on Cognitive Tasks

Task-trained artificial recurrent neural networks (RNNs) provide a computational modeling framework of increasing interest and application in computational, systems, and cognitive neuroscience. RNNs can be trained, using deep-learning methods, to perform cognitive tasks used in animal and human experiments and can be studied to investigate potential neural representations and circuit mechanisms underlying cognitive computations and behavior. Widespread application of these approaches within neuroscience has been limited by technical barriers in use of deep-learning software packages to train network models. Here, we introduce PsychRNN, an accessible, flexible, and extensible Python package for training RNNs on cognitive tasks. Our package is designed for accessibility, for researchers to define tasks and train RNN models using only Python and NumPy, without requiring knowledge of deep-learning software. The training backend is based on TensorFlow and is readily extensible for researchers with TensorFlow knowledge to develop projects with additional customization. PsychRNN implements a number of specialized features to support applications in systems and cognitive neuroscience. Users can impose neurobiologically relevant constraints on synaptic connectivity patterns. Furthermore, specification of cognitive tasks has a modular structure, which facilitates parametric variation of task demands to examine their impact on model solutions. PsychRNN also enables task shaping during training, or curriculum learning, in which tasks are adjusted in closed-loop based on performance. Shaping is ubiquitous in training of animals in cognitive tasks, and PsychRNN allows investigation of how shaping trajectories impact learning and model solutions. Overall, the PsychRNN framework facilitates application of trained RNNs in neuroscience research.

Learning to select actions shapes recurrent dynamics in the corticostriatal system

Learning to select appropriate actions based on their values is fundamental to adaptive behavior. This form of learning is supported by fronto-striatal systems. The dorsal-lateral prefrontal cortex (dlPFC) and the dorsal striatum (dSTR), which are strongly interconnected, are key nodes in this circuitry. Substantial experimental evidence, including neurophysiological recordings, have shown that neurons in these structures represent key aspects of learning. The computational mechanisms that shape the neurophysiological responses, however, are not clear. To examine this, we developed a recurrent neural network (RNN) model of the dlPFC-dSTR circuit and trained it on an oculomotor sequence learning task. We compared the activity generated by the model to activity recorded from monkey dlPFC and dSTR in the same task. This network consisted of a striatal component which encoded action values, and a prefrontal component which selected appropriate actions. After training, this system was able to autonomously represent and update action values and select actions, thus being able to closely approximate the representational structure in corticostriatal recordings. We found that learning to select the correct actions drove action-sequence representations further apart in activity space, both in the model and in the neural data. The model revealed that learning proceeds by increasing the distance between sequence-specific representations. This makes it more likely that the model will select the appropriate action sequence as learning develops. Our model thus supports the hypothesis that learning in networks drives the neural representations of actions further apart, increasing the probability that the network generates correct actions as learning proceeds. Altogether, this study advances our understanding of how neural circuit dynamics are involved in neural computation, revealing how dynamics in the corticostriatal system support task learning.

Neural Sequences as an Optimal Dynamical Regime for the Readout of Time

Converging evidence suggests that the brain encodes time through dynamically changing patterns of neural activity, including neural sequences, ramping activity, and complex spatiotemporal dynamics. However, the potential computational significance and advantage of these different regimes have remained unaddressed. We combined large-scale recordings and modeling to compare population dynamics between premotor cortex and striatum in mice performing a two-interval timing task. Conventional decoders revealed that the dynamics within each area encoded time equally well; however, the dynamics in striatum exhibited a higher degree of sequentiality. Analysis of premotor and striatal dynamics, together with a large set of simulated prototypical dynamical regimes, revealed that regimes with higher sequentiality allowed a biologically constrained artificial downstream network to better read out time. These results suggest that, although different strategies exist for encoding time in the brain, neural sequences represent an ideal and flexible dynamical regime for enabling downstream areas to read out this information.

Low-dimensional dynamics for working memory and time encoding

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

Turning Touch into Perception

Many brain areas modulate their activity during vibrotactile tasks. The activity from these areas may code the stimulus parameters, stimulus perception, or perceptual reports. Here, we discuss findings obtained in behaving monkeys aimed to understand these processes. In brief, neurons from the somatosensory thalamus and primary somatosensory cortex (S1) only code the stimulus parameters during the stimulation periods. In contrast, areas downstream of S1 code the stimulus parameters during not only the task components but also perception. Surprisingly, the midbrain dopamine system is an actor not considered before in perception. We discuss the evidence that it codes the subjective magnitude of a sensory percept. The findings reviewed here may help us to understand where and how sensation transforms into perception in the brain.

Green model to adapt classical conditioning learning in the hippocampus

Compared with the biological paradigms of classical conditioning, non-adaptive computational models are not capable of realistically simulating the biological behavioural functions of the hippocampal regions, because of their implausible requirement for a large number of learning trials, which can be on the order of hundreds. Additionally, these models did not attain a unified, final stable state even after hundreds of learning trials. Conversely, the output response has a different threshold for similar tasks in various models with prolonged transient response of unspecified status via the training or even testing phases. Accordingly, a green model is a combination of adaptive neuro-computational hippocampal and cortical models that is proposed by adaptively updating the whole weights in all layers for both intact networks and lesion networks using instar and outstar learning rules with adaptive resonance theory (ART). The green model sustains and expands the classical conditioning biological paradigms of the non-adaptive models. The model also overcomes the irregular output response behaviour by using the proposed feature of adaptivity. Further, the model successfully simulates the hippocampal regions without passing the final output response back to the whole network, which is considered to be biologically implausible. The results of the Green model showed a significant improvement confirmed by empirical studies of different tasks. In addition, the results indicated that the model outperforms the previously published models. All the obtained results successfully and quickly attained a stable, desired final state (with a unified concluding state of either "1" or "0") with a significantly shorter transient duration.

Coding with transient trajectories in recurrent neural networks

Following a stimulus, the neural response typically strongly varies in time and across neurons before settling to a steady-state. While classical population coding theory disregards the temporal dimension, recent works have argued that trajectories of transient activity can be particularly informative about stimulus identity and may form the basis of computations through dynamics. Yet the dynamical mechanisms needed to generate a population code based on transient trajectories have not been fully elucidated. Here we examine transient coding in a broad class of high-dimensional linear networks of recurrently connected units. We start by reviewing a well-known result that leads to a distinction between two classes of networks: networks in which all inputs lead to weak, decaying transients, and networks in which specific inputs elicit amplified transient responses and are mapped onto output states during the dynamics. Theses two classes are simply distinguished based on the spectrum of the symmetric part of the connectivity matrix. For the second class of networks, which is a sub-class of non-normal networks, we provide a procedure to identify transiently amplified inputs and the corresponding readouts. We first apply these results to standard randomly-connected and two-population networks. We then build minimal, low-rank networks that robustly implement trajectories mapping a specific input onto a specific orthogonal output state. Finally, we demonstrate that the capacity of the obtained networks increases proportionally with their size.

Harnessing behavioral diversity to understand neural computations for cognition

With the increasing acquisition of large-scale neural recordings comes the challenge of inferring the computations they perform and understanding how these give rise to behavior. Here, we review emerging conceptual and technological advances that begin to address this challenge, garnering insights from both biological and artificial neural networks. We argue that neural data should be recorded during rich behavioral tasks, to model cognitive processes and estimate latent behavioral variables. Careful quantification of animal movements can also provide a more complete picture of how movements shape neural dynamics and reflect changes in brain state, such as arousal or stress. Artificial neural networks (ANNs) could serve as artificial model organisms to connect neural dynamics and rich behavioral data. ANNs have already begun to reveal how a wide range of different behaviors can be implemented, generating hypotheses about how observed neural activity might drive behavior and explaining diversity in behavioral strategies.

Flexible Sensorimotor Computations through Rapid Reconfiguration of Cortical Dynamics

Neural mechanisms that support flexible sensorimotor computations are not well understood. In a dynamical system whose state is determined by interactions among neurons, computations can be rapidly reconfigured by controlling the system's inputs and initial conditions. To investigate whether the brain employs such control mechanisms, we recorded from the dorsomedial frontal cortex of monkeys trained to measure and produce time intervals in two sensorimotor contexts. The geometry of neural trajectories during the production epoch was consistent with a mechanism wherein the measured interval and sensorimotor context exerted control over cortical dynamics by adjusting the system's initial condition and input, respectively. These adjustments, in turn, set the speed at which activity evolved in the production epoch, allowing the animal to flexibly produce different time intervals. These results provide evidence that the language of dynamical systems can be used to parsimoniously link brain activity to sensorimotor computations.

The Neural Basis of Timing: Distributed Mechanisms for Diverse Functions

Timing is critical to most forms of learning, behavior, and sensory-motor processing. Converging evidence supports the notion that, precisely because of its importance across a wide range of brain functions, timing relies on intrinsic and general properties of neurons and neural circuits; that is, the brain uses its natural cellular and network dynamics to solve a diversity of temporal computations. Many circuits have been shown to encode elapsed time in dynamically changing patterns of neural activity-so-called population clocks. But temporal processing encompasses a wide range of different computations, and just as there are different circuits and mechanisms underlying computations about space, there are a multitude of circuits and mechanisms underlying the ability to tell time and generate temporal patterns.

Beyond the Maximum Storage Capacity Limit in Hopfield Recurrent Neural Networks

In a neural network, an autapse is a particular kind of synapse that links a neuron onto itself. Autapses are almost always not allowed neither in artificial nor in biological neural networks. Moreover, redundant or similar stored states tend to interact destructively. This paper shows how autapses together with stable state redundancy can improve the storage capacity of a recurrent neural network. Recent research shows how, in an N-node Hopfield neural network with autapses, the number of stored patterns (P) is not limited to the well known bound 0.14N, as it is for networks without autapses. More precisely, it describes how, as the number of stored patterns increases well over the 0.14N threshold, for P much greater than N, the retrieval error asymptotically approaches a value below the unit. Consequently, the reduction of retrieval errors allows a number of stored memories, which largely exceeds what was previously considered possible. Unfortunately, soon after, new results showed that, in the thermodynamic limit, given a network with autapses in this high-storage regime, the basin of attraction of the stored memories shrinks to a single state. This means that, for each stable state associated with a stored memory, even a single bit error in the initial pattern would lead the system to a stationary state associated with a different memory state. This thus limits the potential use of this kind of Hopfield network as an associative memory. This paper presents a strategy to overcome this limitation by improving the error correcting characteristics of the Hopfield neural network. The proposed strategy allows us to form what we call an absorbing-neighborhood of state surrounding each stored memory. An absorbing-neighborhood is a set defined by a Hamming distance surrounding a network state, which is an absorbing because, in the long-time limit, states inside it are absorbed by stable states in the set. We show that this strategy allows the network to store an exponential number of memory patterns, each surrounded with an absorbing-neighborhood with an exponentially growing size.

Bayesian Computation through Cortical Latent Dynamics

Statistical regularities in the environment create prior beliefs that we rely on to optimize our behavior when sensory information is uncertain. Bayesian theory formalizes how prior beliefs can be leveraged and has had a major impact on models of perception, sensorimotor function, and cognition. However, it is not known how recurrent interactions among neurons mediate Bayesian integration. By using a time-interval reproduction task in monkeys, we found that prior statistics warp neural representations in the frontal cortex, allowing the mapping of sensory inputs to motor outputs to incorporate prior statistics in accordance with Bayesian inference. Analysis of recurrent neural network models performing the task revealed that this warping was enabled by a low-dimensional curved manifold and allowed us to further probe the potential causal underpinnings of this computational strategy. These results uncover a simple and general principle whereby prior beliefs exert their influence on behavior by sculpting cortical latent dynamics.

A Role for the Superior Colliculus in Decision Criteria

Simple decisions arise from the evaluation of sensory evidence. But decisions are determined by more than just evidence. Individuals establish internal decision criteria that influence how they respond. Where or how decision criteria are established in the brain remains poorly understood. Here, we show that neuronal activity in the superior colliculus (SC) predicts changes in decision criteria. Using a novel "Yes-No" task that isolates changes in decision criterion from changes in decision sensitivity, and computing neuronal measures of sensitivity and criterion, we find that SC neuronal activity correlates with the decision criterion regardless of the location of the choice report. We also show that electrical manipulation of activity within the SC produces changes in decisions consistent with changes in decision criteria and are largely independent of the choice report location. Our correlational and causal results together provide strong evidence that SC activity signals the position of a decision criterion. VIDEO ABSTRACT.

Models that learn how humans learn: The case of decision-making and its disorders

Popular computational models of decision-making make specific assumptions about learning processes that may cause them to underfit observed behaviours. Here we suggest an alternative method using recurrent neural networks (RNNs) to generate a flexible family of models that have sufficient capacity to represent the complex learning and decision- making strategies used by humans. In this approach, an RNN is trained to predict the next action that a subject will take in a decision-making task and, in this way, learns to imitate the processes underlying subjects' choices and their learning abilities. We demonstrate the benefits of this approach using a new dataset drawn from patients with either unipolar (n = 34) or bipolar (n = 33) depression and matched healthy controls (n = 34) making decisions on a two-armed bandit task. The results indicate that this new approach is better than baseline reinforcement-learning methods in terms of overall performance and its capacity to predict subjects' choices. We show that the model can be interpreted using off-policy simulations and thereby provides a novel clustering of subjects' learning processes-something that often eludes traditional approaches to modelling and behavioural analysis.

Local online learning in recurrent networks with random feedback

Recurrent neural networks (RNNs) enable the production and processing of time-dependent signals such as those involved in movement or working memory. Classic gradient-based algorithms for training RNNs have been available for decades, but are inconsistent with biological features of the brain, such as causality and locality. We derive an approximation to gradient-based learning that comports with these constraints by requiring synaptic weight updates to depend only on local information about pre- and postsynaptic activities, in addition to a random feedback projection of the RNN output error. In addition to providing mathematical arguments for the effectiveness of the new learning rule, we show through simulations that it can be used to train an RNN to perform a variety of tasks. Finally, to overcome the difficulty of training over very large numbers of timesteps, we propose an augmented circuit architecture that allows the RNN to concatenate short-duration patterns into longer sequences.

Temporal signals underlying a cognitive process in the dorsal premotor cortex

During discrimination between two sequential vibrotactile stimulus patterns, the primate dorsal premotor cortex (DPC) neurons exhibit a complex repertoire of coding dynamics associated with the working memory, comparison, and decision components of this task. In addition, these neurons and neurons with no coding responses show complex strong fluctuations in their firing rate associated with the temporal sequence of task events. Here, to make sense of this temporal complexity, we extracted the temporal signals that were latent in the population. We found a strong link between the individual and population response, suggesting a common neural substrate. Notably, in contrast to coding dynamics, these time-dependent responses were unaffected during error trials. However, in a nondemanding task in which monkeys did not require discrimination for reward, these time-dependent signals were largely reduced and changed. These results suggest that temporal dynamics in DPC reflect the underlying cognitive processes of this task.

Feed-forward information and zero-lag synchronization in the sensory thalamocortical circuit are modulated during stimulus perception

The direction of functional information flow in the sensory thalamocortical circuit may play a role in stimulus perception, but, surprisingly, this process is poorly understood. We addressed this problem by evaluating a directional information measure between simultaneously recorded neurons from somatosensory thalamus (ventral posterolateral nucleus, VPL) and somatosensory cortex (S1) sharing the same cutaneous receptive field while monkeys judged the presence or absence of a tactile stimulus. During stimulus presence, feed-forward information (VPL → S1) increased as a function of the stimulus amplitude, while pure feed-back information (S1 → VPL) was unaffected. In parallel, zero-lag interaction emerged with increasing stimulus amplitude, reflecting externally driven thalamocortical synchronization during stimulus processing. Furthermore, VPL → S1 information decreased during error trials. Also, VPL → S1 and zero-lag interaction decreased when monkeys were not required to report the stimulus presence. These findings provide evidence that both the direction of information flow and the instant synchronization in the sensory thalamocortical circuit play a role in stimulus perception.

Task representations in neural networks trained to perform many cognitive tasks

The brain has the ability to flexibly perform many tasks, but the underlying mechanism cannot be elucidated in traditional experimental and modeling studies designed for one task at a time. Here, we trained single network models to perform 20 cognitive tasks that depend on working memory, decision making, categorization, and inhibitory control. We found that after training, recurrent units can develop into clusters that are functionally specialized for different cognitive processes, and we introduce a simple yet effective measure to quantify relationships between single-unit neural representations of tasks. Learning often gives rise to compositionality of task representations, a critical feature for cognitive flexibility, whereby one task can be performed by recombining instructions for other tasks. Finally, networks developed mixed task selectivity similar to recorded prefrontal neurons after learning multiple tasks sequentially with a continual-learning technique. This work provides a computational platform to investigate neural representations of many cognitive tasks.

Bridging large-scale neuronal recordings and large-scale network models using dimensionality reduction

A long-standing goal in neuroscience has been to bring together neuronal recordings and neural network modeling to understand brain function. Neuronal recordings can inform the development of network models, and network models can in turn provide predictions for subsequent experiments. Traditionally, neuronal recordings and network models have been related using single-neuron and pairwise spike train statistics. We review here recent studies that have begun to relate neuronal recordings and network models based on the multi-dimensional structure of neuronal population activity, as identified using dimensionality reduction. This approach has been used to study working memory, decision making, motor control, and more. Dimensionality reduction has provided common ground for incisive comparisons and tight interplay between neuronal recordings and network models.