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Sequential activity reflecting previously experienced temporal sequences is considered a hallmark of learning across cortical areas. However, it is unknown how cortical circuits avoid the converse problem: producing spurious sequences that are not reflecting sequences in their inputs. We develop methods to quantify and study sequentiality in neural responses. We show that recurrent circuit responses generally include spurious sequences, which are specifically prevented in circuits that obey two widely known features of cortical microcircuit organization: Dale's law and Hebbian connectivity. In particular, spike-timing-dependent plasticity in excitation-inhibition networks leads to an adaptive erasure of spurious sequences. We tested our theory in multielectrode recordings from the visual cortex of awake ferrets. Although responses to natural stimuli were largely non-sequential, responses to artificial stimuli initially included spurious sequences, which diminished over extended exposure. These results reveal an unexpected role for Hebbian experience-dependent plasticity and Dale's law in sensory cortical circuits.

Understanding how neural dynamics give rise to behaviour is one of the most fundamental questions in systems neuroscience. To achieve this, a common approach is to record neural populations in behaving animals, and model these data as emanating from a latent dynamical system whose state trajectories can then be related back to behavioural observations via some form of decoding. As recordings are typically performed in localized circuits that form only a part of the wider implicated network, it is important to simultaneously learn the local dynamics and infer any unobserved external input that might drive them. Here, we introduce iLQR-VAE, a control-based approach to variational inference in nonlinear dynamical systems, capable of learning both latent dynamics, initial conditions, and ongoing external inputs. As in recent deep learning approaches, our method is based on an input-driven sequential variational autoencoder (VAE). The main novelty lies in the use of the powerful iterative linear quadratic regulator algorithm (iLQR) in the recognition model. Optimization of the standard evidence lower-bound requires differentiating through iLQR solutions, which is made possible by recent advances in differentiable control. Importantly, the recognition model is naturally tied to the generative model, greatly reducing the number of free parameters and ensuring high-quality inference throughout the course of learning. Moreover, iLQR can be used to perform inference flexibly on heterogeneous trials of varying lengths. This allows for instance to evaluate the model on a single long trial after training on smaller chunks. We demonstrate the effectiveness of iLQR-VAE on a range of synthetic systems, with autonomous as well as input-driven dynamics. We further apply it to neural and behavioural recordings in non-human primates performing two different reaching tasks, and show that iLQR-VAE yields high-quality kinematic reconstructions from the neural data.

Latent variable models are ubiquitous in the exploratory analysis of neural population recordings, where they allow researchers to summarize the activity of large populations of neurons in lower dimensional ‘latent’ spaces. Existing methods can generally be categorized into (i) Bayesian methods that facilitate flexible incorporation of prior knowledge and uncertainty estimation, but which typically do not scale to large datasets; and (ii) highly parameterized methods without explicit priors that scale better but often struggle in the low-data regime. Here, we bridge this gap by developing a fully Bayesian yet scalable version of Gaussian process factor analysis (bGPFA), which models neural data as arising from a set of inferred latent processes with a prior that encourages smoothness over time. Additionally, bGPFA uses automatic relevance determination to infer the dimensionality of neural activity directly from the training data during optimization. To enable the analysis of continuous recordings without trial structure, we introduce a novel variational inference strategy that scales near-linearly in time and also allows for non-Gaussian noise models appropriate for electrophysiological recordings. We apply bGPFA to continuous recordings spanning 30 minutes with over 14 million data points from primate motor and somatosensory cortices during a self-paced reaching task. We show that neural activity progresses from an initial state at target onset to a reach-specific preparatory state well before movement onset. The distance between these initial and preparatory latent states is predictive of reaction times across reaches, suggesting that such preparatory dynamics have behavioral relevance despite the lack of externally imposed delay periods. Additionally, bGPFA discovers latent processes that evolve over slow timescales on the order of several seconds and contain complementary information about reaction time. These timescales are longer than those revealed by methods which focus on individual movement epochs and may reflect fluctuations in e.g. task engagement.

Motor cortex (M1) exhibits a rich repertoire of activities to support the generation of complex movements. Recent network models capture many qualitative aspects of M1 dynamics, but they can generate only a few distinct movements (all of the same duration). We demonstrate that simple modulation of neuronal input–output gains in recurrent neuronal network models with fixed connectivity can dramatically reorganize neuronal activity and consequently downstream muscle outputs. We show that a relatively small number of modulatory control units provide sufficient flexibility to adjust high-dimensional network activity using a simple reward-based learning rule. Furthermore, novel movements can be assembled from previously-learned primitives and we can separately change movement speed while preserving movement shape. Our results provide a new perspective on the role of modulatory systems in controlling recurrent cortical activity., Our work was supported by grants from the Wellcome Trust (TPV and JPS WT100000, 246 GH 202111/Z/16/Z) and the Engineering and Physical Sciences Research Council (JPS).

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.

A major challenge in systems neuroscience is to understand how the dynamics of neural circuits give rise to behaviour. Analysis of complex dynamical systems is also at the heart of control engineering, where it is central to the design of robust control strategies. Although a rich engineering literature has grown over decades to facilitate the analysis of such systems, little of it has percolated into neuroscience so far. Here, we give a brief introduction to a number of core control-theoretic concepts that provide useful perspectives on neural circuit dynamics. We introduce important mathematical tools related to these concepts, and establish connections to neural circuit analysis, focusing on a number of themes that have arisen from the modern ‘state-space’ view on neural population dynamics.

Sensory cortices display a suite of ubiquitous dynamical features, such as ongoing noise variability, transient overshoots and oscillations, that have so far escaped a common, principled theoretical account. We developed a unifying model for these phenomena by training a recurrent excitatory?inhibitory neural circuit model of a visual cortical hypercolumn to perform sampling-based probabilistic inference. The optimized network displayed several key biological properties, including divisive normalization and stimulus-modulated noise variability, inhibition-dominated transients at stimulus onset and strong gamma oscillations. These dynamical features had distinct functional roles in speeding up inferences and made predictions that we confirmed in novel analyses of recordings from awake monkeys. Our results suggest that the basic motifs of cortical dynamics emerge as a consequence of the efficient implementation of the same computational function?fast sampling-based inference?and predict further properties of these motifs that can be tested in future experiments. Fil: Echeveste, Rodrigo Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hídricas. Instituto de Investigación en Señales, Sistemas e Inteligencia Computacional; Argentina Fil: Aitchison, Laurence. University of Cambridge; Reino Unido Fil: Hennequin, Guillaume. University of Cambridge; Estados Unidos Fil: Lengyel, Máté. University of Cambridge; Reino Unido

In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media requires understanding of how they propagate and transform information in the face of noise. Here, we develop a framework that enables us to examine how network structure, noise, and interference between consecutive packets jointly determine transmission performance in networks with linear dynamics at single nodes and arbitrary topologies. Mathematically normal networks, which can be decomposed into separate low-dimensional information channels, suffer greatly from readout and interference noise. Interestingly, most details of their wiring have no impact on transmission quality. Non-normal networks, however, can largely cancel the effect of noise by transiently amplifying select input dimensions while ignoring others, resulting in higher net information throughput. Our theory could inform the design of new communication networks, as well as the optimal use of existing ones., 29 pages, 11 figures. Main text and supplementary material. To appear in Science Advances

Reliable information processing is a hallmark of many physical and biological networked systems. In this paper, we propose a novel framework for modelling information transmission within a linear dynamical network. Information propagation is modelled by means of a digital communication protocol that takes into account the realistic phenomenon of inter-symbol interference. Building on this framework, we adopt Shannon information rate to quantify the amount of information that can be reliably sent over the network within a fixed time window. We investigate how the latter information metric is affected by the connectivity structure of the network. Here, we focus in particular on networks characterized by a normal adjacency matrix. We show that for such networks the maximum achievable information rate depends only on the spectrum of the adjacency matrix. We then provide numerical results suggesting that non-normal network architectures could benefit information transmission in our framework.

Summary Correlated variability in cortical activity is ubiquitously quenched following stimulus onset, in a stimulus-dependent manner. These modulations have been attributed to circuit dynamics involving either multiple stable states (“attractors”) or chaotic activity. Here we show that a qualitatively different dynamical regime, involving fluctuations about a single, stimulus-driven attractor in a loosely balanced excitatory-inhibitory network (the stochastic “stabilized supralinear network”), best explains these modulations. Given the supralinear input/output functions of cortical neurons, increased stimulus drive strengthens effective network connectivity. This shifts the balance from interactions that amplify variability to suppressive inhibitory feedback, quenching correlated variability around more strongly driven steady states. Comparing to previously published and original data analyses, we show that this mechanism, unlike previous proposals, uniquely accounts for the spatial patterns and fast temporal dynamics of variability suppression. Specifying the cortical operating regime is key to understanding the computations underlying perception., Highlights • A simple network model explains stimulus-tuning of cortical variability suppression • Inhibition stabilizes recurrently interacting neurons with supralinear I/O functions • Stimuli strengthen inhibitory stabilization around a stable state, quenching variability • Single-trial V1 data are compatible with this model and rules out competing proposals, Stimuli suppress cortical correlated variability. Hennequin et al. show that a cortical operating regime of inhibitory stabilization around a single stable state—the “stabilized supralinear network”—explains this suppression’s tuning and timing, while alternative proposed regimes do not.

SummaryPopulations of neurons in motor cortex engage in complex transient dynamics of large amplitude during the execution of limb movements. Traditional network models with stochastically assigned synapses cannot reproduce this behavior. Here we introduce a class of cortical architectures with strong and random excitatory recurrence that is stabilized by intricate, fine-tuned inhibition, optimized from a control theory perspective. Such networks transiently amplify specific activity states and can be used to reliably execute multidimensional movement patterns. Similar to the experimental observations, these transients must be preceded by a steady-state initialization phase from which the network relaxes back into the background state by way of complex internal dynamics. In our networks, excitation and inhibition are as tightly balanced as recently reported in experiments across several brain areas, suggesting inhibitory control of complex excitatory recurrence as a generic organizational principle in cortex.

SummaryVariability and correlations in cortical activity are ubiquitously modulated by stimuli. Correlated variability is quenched following stimulus onset across multiple cortical areas, suppressing low-frequency components of the LFP and of Vm-LFP coherence. Modulation of Fano factors and correlations in area MT is tuned for stimulus direction. What circuit mechanisms underly these behaviors? We show that a simple model circuit, the stochastic Stabilized Supralinear Network (SSN), robustly explains these results. Stimuli modulate variability by modifying two forms of effective connectivity between activity patterns that characterize excitatory-inhibitory (E/I) circuits. Increases in the strength with which activity patterns inhibit themselves reduce correlated variability, while increases in feedforward connections between patterns (transforming E/I imbalance into balanced fluctuations) increase variability. These results suggest an operating regime of cortical dynamics that involves fast fluctuations and fast responses to stimulus changes, unlike previous models of variability suppression through suppression of chaos or networks with multiple attractors.

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In dynamical models of cortical networks, the recurrent connectivity can amplify the input given to the network in two distinct ways. One is induced by the presence of near-critical eigenvalues in the connectivity matrix W, producing large but slow activity fluctuations along the corresponding eigenvectors (dynamical slowing). The other relies on W being nonnormal, which allows the network activity to make large but fast excursions along specific directions. Here we investigate the tradeoff between nonnormal amplification and dynamical slowing in the spontaneous activity of large random neuronal networks composed of excitatory and inhibitory neurons. We use a Schur decomposition of W to separate the two amplification mechanisms. Assuming linear stochastic dynamics, we derive an exact expression for the expected amount of purely nonnormal amplification. We find that amplification is very limited if dynamical slowing must be kept weak. We conclude that, to achieve strong transient amplification with little slowing, the connectivity must be structured. We show that unidirectional connections between neurons of the same type together with reciprocal connections between neurons of different types, allow for amplification already in the fast dynamical regime. Finally, our results also shed light on the differences between balanced networks in which inhibition exactly cancels excitation, and those where inhibition dominates., 13 pages, 7 figures

Over the past 30 years, Bienenstock-Cooper-Munro (BCM) [1] type learning rules have shaped our understanding of synaptic plasticity. While they excel at explaining the emergence of receptive fields and stimulus selectivity in networks with feed-forward architecture, their impact on recurrent scenarios is less distinctive. Here, we analyze general BCM-type synaptic plasticity rules with a homeostatic sliding threshold in the framework of recurrent networks of rate-based and spiking neurons. We begin by considering the effects of learning rate and homeostatic timescales on network stability in a non-linear firing rate model. We show how a sensible choice of timescales leads to stable weight dynamics, but other seemingly sensible parameter choices will inevitably lead to catastrophic run-away potentiation. We discuss under which conditions a stable fixed-point in a regime of Hebbian learning exists. We then study the network's response to perturbations and quantify the critical point whereupon network stability is compromised. By viewing perturbation as a consequence of pattern storage in synaptic connections, we quantify the number of such patterns that can be learned safely in a given time. Our model could provide simple explanations as to why memory intake capacity is limited and why learning becomes increasingly inefficient during intensive learning periods. We confirm these findings in numerical simulations of spiking neural networks and show that our analytical results apply to synapses subject to additive triplet-STDP [2].

Spike-frequency adaptation is known to enhance the transmission of information in sensory spiking neurons, by rescaling the dynamic range for input processing, matching it to the temporal statistics of the sensory stimulus. Achieving maximal information transmission has also been recently postulated as a role for Spike-Timing Dependent Plasticity (STDP). However, the link between optimal plasticity and STDP in cortex remains loose, and so does the relationship between STDP and adaptation processes. We investigate how STDP, as described by recent minimal models derived from experimental data, influences the quality of information transmission in an adapting neuron. We show that a phenomenological model based on triplets of spikes yields almost the same information rate as an optimal model specially designed to this end. In contrast, the standard pair-based model of STDP does not improve information transmission as much. This result holds not only for additive STDP with hard weight bounds, known to produce bimodal distributions of synaptic weights, but also for weight-dependent STDP in the context of unimodal but skewed weight distributions. We analyze the similarities between the triplet model and the optimal learning rule, and find that the triplet effect is an important feature of the optimal model when the neuron is adaptive. If STDP is optimized for information transmission, it must take into account the dynamical properties of the postsynaptic cell, which might explain the target-cell specificity of STDP. In particular, it accounts for the differences found in vitro between STDP at excitatory synapses onto principal cells and those onto fast-spiking interneurons.

Spiking models of small areas of the neocortex have so far mainly been studied under the assumption that neurons are sparsely and randomly connected. The absence of structure allows for the use of powerful mean-field approximation techniques, whereby statistical properties of spike trains such as the average firing rate and the interspike interval coefficient of variation are described in terms of their distributions across neurons [1,2]. Such approaches cannot offer a more detailed description as to what patterns of activity the network spontaneously produces. The macroscopic state is unstructured with predictable mean, while during the asynchronous irregular firing the microscopic dynamics is chaotic. It therefore becomes hard to think of the representation of information in cortex if its activity is neither structured nor reproducible. Connectivity in cortex is not purely random: published data on synaptic connectivity suggests a model of cortical connectivity in which excitatory neurons make long-range patchy projections while inhibitory neurons only target their close neighbours [3]. How does this structure affect the dynamics of the network? Can we hope to describe it in terms of activity patterns, therefore going beyond the mean-field predictions mentioned above? Recent theoretical considerations [4] have suggested a positive answer, by showing that balanced networks should be expected to transiently amplify certain activity patterns without slowing the dynamics down (“balanced amplification”). Underlying this theory is the nature of the connectivity matrix, “nonnormal” in the mathematical sense [5]. The amplified patterns depend on the details of the connectivity and are best revealed by a Schur decomposition of the connectivity matrix. We examine the dynamics of linear networks with patchy connectivity structures. With long-range patchy inhibition, about 25% of the eigenvalues of the connectivity matrix have strictly positive real parts. Since real parts must be smaller than one for stability, the overall magnitude of the connections, and therefore also the amount of transient amplification, need to be constrained. The presence of eigenvalues with real parts close to one also predicts dynamical slowing with a small number of modes (typically < 5) completely dominating the dynamics and limiting the representational power. If inhibition is kept local, as it seems to be in nature, the connectivity matrix has the nice property that all its eigenvalues have negative real parts. The network can thus be arbitrarily rescaled and yet remain stable. Strong amplification can coexist with fast network dynamics that yields a rich repertoire of transient spatial states. Extensive simulations of the noise-driven linear networks confirm the theoretical insights. Importantly, we also ran large-scale simulations of conductance-based spiking neurons with sparse connectivity spatially organized as mentioned above. Despite the strong deviation from linearity, the network activity matches the linear predictions remarkably well, in terms of both speed and amplification of the Schur modes. We conclude that the activity in spatially organised networks is highly structured and can be described on the level of two-dimensional activity patterns. Local inhibition, but not long-range inhibition, enables rapid state switching on the time scale of a few milliseconds.