Local Recurrent Connections Research Articles

Neural network architectures in data sequence analysis: diagnosis of Reinke's oedema and Laryngeal polyps

In this review paper, we focus our attention on presenting selected neural network architectures dedicated to the analysis of sequential data, in particular to support the diagnosis of Reinke's oedema and laryngeal polyps. The research discussed here is located in the area of clinical computer decision support systems (CDS) based on the use of artificial recurrent neural networks (RNNs) for speech signal analysis. RNNs are able to predict time series due to their memory and local recurrent connections. In the experimental part, Elman-Jordan artificial neural networks are used, whose characteristics are speed and accuracy in pattern learning allowing real-time decision-making. In the review presented here, one important theme is the use of Bezier curves for preprocessing the speech signal, leading to data reduction and noise elimination. Elman-Jordan networks significantly speed up the learning process and show high classification accuracy in laryngopathy diagnosis.

The logic of recurrent circuits in the primary visual cortex

Recurrent cortical activity sculpts visual perception by refining, amplifying or suppressing visual input. However, the rules that govern the influence of recurrent activity remain enigmatic. We used ensemble-specific two-photon optogenetics in the mouse visual cortex to isolate the impact of recurrent activity from external visual input. We found that the spatial arrangement and the visual feature preference of the stimulated ensemble and the neighboring neurons jointly determine the net effect of recurrent activity. Photoactivation of these ensembles drives suppression in all cells beyond 30 µm but uniformly drives activation in closer similarly tuned cells. In nonsimilarly tuned cells, compact, cotuned ensembles drive net suppression, while diffuse, cotuned ensembles drive activation. Computational modeling suggests that highly local recurrent excitatory connectivity and selective convergence onto inhibitory neurons explain these effects. Our findings reveal a straightforward logic in which space and feature preference of cortical ensembles determine their impact on local recurrent activity.

Heterogeneous encoding of temporal stimuli in the cerebellar cortex

Local feedforward and recurrent connectivity are rife in the frontal areas of the cerebral cortex, which gives rise to rich heterogeneous dynamics observed in such areas. Recently, similar local connectivity motifs have been discovered among Purkinje and molecular layer interneurons of the cerebellar cortex, however, task-related activity in these neurons has often been associated with relatively simple facilitation and suppression dynamics. Here, we show that the rodent cerebellar cortex supports heterogeneity in task-related neuronal activity at a scale similar to the cerebral cortex. We provide a computational model that inculcates recent anatomical insights into local microcircuit motifs to show the putative basis for such heterogeneity. We also use cell-type specific chronic viral lesions to establish the involvement of cerebellar lobules in associative learning behaviors. Functional heterogeneity in neuronal profiles may not merely be the remit of the associative cerebral cortex, similar principles may be at play in subcortical areas, even those with seemingly crystalline and homogenous cytoarchitectures like the cerebellum.

Neurochemistry-enriched dynamic causal models of magnetoencephalography, using magnetic resonance spectroscopy

We present a hierarchical empirical Bayesian framework for testing hypotheses about neurotransmitters’ concertation as empirical prior for synaptic physiology using ultra-high field magnetic resonance spectroscopy (7T-MRS) and magnetoencephalography data (MEG). A first level dynamic causal modelling of cortical microcircuits is used to infer the connectivity parameters of a generative model of individuals’ neurophysiological observations. At the second level, individuals’ 7T-MRS estimates of regional neurotransmitter concentration supply empirical priors on synaptic connectivity. We compare the group-wise evidence for alternative empirical priors, defined by monotonic functions of spectroscopic estimates, on subsets of synaptic connections. For efficiency and reproducibility, we used Bayesian model reduction (BMR), parametric empirical Bayes and variational Bayesian inversion. In particular, we used Bayesian model reduction to compare alternative model evidence of how spectroscopic neurotransmitter measures inform estimates of synaptic connectivity. This identifies the subset of synaptic connections that are influenced by individual differences in neurotransmitter levels, as measured by 7T-MRS. We demonstrate the method using resting-state MEG (i.e., task-free recording) and 7T-MRS data from healthy adults. Our results confirm the hypotheses that GABA concentration influences local recurrent inhibitory intrinsic connectivity in deep and superficial cortical layers, while glutamate influences the excitatory connections between superficial and deep layers and connections from superficial to inhibitory interneurons. Using within-subject split-sampling of the MEG dataset (i.e., validation by means of a held-out dataset), we show that model comparison for hypothesis testing can be highly reliable. The method is suitable for applications with magnetoencephalography or electroencephalography, and is well-suited to reveal the mechanisms of neurological and psychiatric disorders, including responses to psychopharmacological interventions.

Paradoxical self-sustained dynamics emerge from orchestrated excitatory and inhibitory homeostatic plasticity rules

Self-sustained neural activity maintained through local recurrent connections is of fundamental importance to cortical function. Converging theoretical and experimental evidence indicates that cortical circuits generating self-sustained dynamics operate in an inhibition-stabilized regime. Theoretical work has established that four sets of weights (WE←E, WE←I, WI←E, and WI←I) must obey specific relationships to produce inhibition-stabilized dynamics, but it is not known how the brain can appropriately set the values of all four weight classes in an unsupervised manner to be in the inhibition-stabilized regime. We prove that standard homeostatic plasticity rules are generally unable to generate inhibition-stabilized dynamics and that their instability is caused by a signature property of inhibition-stabilized networks: the paradoxical effect. In contrast, we show that a family of "cross-homeostatic" rules overcome the paradoxical effect and robustly lead to the emergence of stable dynamics. This work provides a model of how-beginning from a silent network-self-sustained inhibition-stabilized dynamics can emerge from learning rules governing all four synaptic weight classes in an orchestrated manner.

The Generation and Modulation of Distinct Gamma Oscillations with Local, Horizontal, and Feedback Connections in the Primary Visual Cortex: A Model Study on Large-Scale Networks.

Gamma oscillation (GAMMA) in the local field potential (LFP) is a synchronized activity commonly found in many brain regions, and it has been thought as a functional signature of network connectivity in the brain, which plays important roles in information processing. Studies have shown that the response property of GAMMA is related to neural interaction through local recurrent connections (RC), feed-forward (FF), and feedback (FB) connections. However, the relationship between GAMMA and long-range horizontal connections (HC) in the brain remains unclear. Here, we aimed to understand this question in a large-scale network model for the primary visual cortex (V1). We created a computational model composed of multiple excitatory and inhibitory units with biologically plausible connectivity patterns for RC, FF, FB, and HC in V1; then, we quantitated GAMMA in network models at different strength levels of HC and other connection types. Surprisingly, we found that HC and FB, the two types of large-scale connections, play very different roles in generating and modulating GAMMA. While both FB and HC modulate a fast gamma oscillation (around 50-60 Hz) generated by FF and RC, HC generates a new GAMMA oscillating around 30 Hz, whose power and peak frequency can also be modulated by FB. Furthermore, response properties of the two GAMMAs in a network with both HC and FB are different in a way that is highly consistent with a recent experimental finding for distinct GAMMAs in macaque V1. The results suggest that distinct GAMMAs are signatures for neural connections in different spatial scales and they might be related to different functions for information integration. Our study, for the first time, pinpoints the underlying circuits for distinct GAMMAs in a mechanistic model for macaque V1, which might provide a new framework to study multiple gamma oscillations in other cortical regions.

Circuit-Specific Dendritic Development in the Piriform Cortex.

Dendritic geometry is largely determined during postnatal development and has a substantial impact on neural function. In sensory processing, postnatal development of the dendritic tree is affected by two dominant circuit motifs, ascending sensory feedforward inputs and descending and local recurrent connections. In the three-layered anterior piriform cortex (aPCx), neurons in the sublayers 2a and 2b display vertical segregation of these two circuit motifs. Here, we combined electrophysiology, detailed morphometry, and Ca2+ imaging in acute mouse brain slices and modeling to study circuit-specific aspects of dendritic development. We observed that determination of branching complexity, dendritic length increases, and pruning occurred in distinct developmental phases. Layer 2a and layer 2b neurons displayed developmental phase-specific differences between their apical and basal dendritic trees related to differences in circuit incorporation. We further identified functional candidate mechanisms for circuit-specific differences in postnatal dendritic growth in sublayers 2a and 2b at the mesoscale and microscale levels. Already in the first postnatal week, functional connectivity of layer 2a and layer 2b neurons during early spontaneous network activity scales with differences in basal dendritic growth. During the early critical period of sensory plasticity in the piriform cortex, our data are consistent with a model that proposes a role for dendritic NMDA-spikes in selecting branches for survival during developmental pruning in apical dendrites. The different stages of the morphologic and functional developmental pattern differences between layer 2a and layer 2b neurons demonstrate the complex interplay between dendritic development and circuit specificity.

Intrinsic temporal tuning of neurons in the optic tectum is shaped by multisensory experience.

For a biological neural network to be functional, its neurons need to be connected with synapses of appropriate strength, and each neuron needs to appropriately respond to its synaptic inputs. This second aspect of network tuning is maintained by intrinsic plasticity; yet it is often considered secondary to changes in connectivity and mostly limited to adjustments of overall excitability of each neuron. Here we argue that even nonoscillatory neurons can be tuned to inputs of different temporal dynamics and that they can routinely adjust this tuning to match the statistics of their synaptic activation. Using the dynamic clamp technique, we show that, in the tectum of Xenopus tadpole, neurons become selective for faster inputs when animals are exposed to fast visual stimuli but remain responsive to longer inputs in animals exposed to slower, looming, or multisensory stimulation. We also report a homeostatic cotuning between synaptic and intrinsic temporal properties of individual tectal cells. These results expand our understanding of intrinsic plasticity in the brain and suggest that there may exist an additional dimension of network tuning that has been so far overlooked.NEW & NOTEWORTHY We use dynamic clamp to show that individual neurons in the tectum of Xenopus tadpoles are selectively tuned to either shorter (more synchronous) or longer (less synchronous) synaptic inputs. We also demonstrate that this intrinsic temporal tuning is strongly shaped by sensory experiences. This new phenomenon, which is likely to be mediated by changes in sodium channel inactivation, is bound to have important consequences for signal processing and the development of local recurrent connections.

Beyond core object recognition: Recurrent processes account for object recognition under occlusion.

Core object recognition, the ability to rapidly recognize objects despite variations in their appearance, is largely solved through the feedforward processing of visual information. Deep neural networks are shown to achieve human-level performance in these tasks, and explain the primate brain representation. On the other hand, object recognition under more challenging conditions (i.e. beyond the core recognition problem) is less characterized. One such example is object recognition under occlusion. It is unclear to what extent feedforward and recurrent processes contribute in object recognition under occlusion. Furthermore, we do not know whether the conventional deep neural networks, such as AlexNet, which were shown to be successful in solving core object recognition, can perform similarly well in problems that go beyond the core recognition. Here, we characterize neural dynamics of object recognition under occlusion, using magnetoencephalography (MEG), while participants were presented with images of objects with various levels of occlusion. We provide evidence from multivariate analysis of MEG data, behavioral data, and computational modelling, demonstrating an essential role for recurrent processes in object recognition under occlusion. Furthermore, the computational model with local recurrent connections, used here, suggests a mechanistic explanation of how the human brain might be solving this problem.

Selective Strengthening of Intracortical Excitatory Input Leads to Receptive Field Refinement during Auditory Cortical Development.

In the primary auditory cortex (A1) of rats, refinement of excitatory input to layer (L)4 neurons contributes to the sharpening of their frequency selectivity during postnatal development. L4 neurons receive both feedforward thalamocortical and recurrent intracortical inputs, but how potential developmental changes of each component can account for the sharpening of excitatory input tuning remains unclear. By combining in vivo whole-cell recording and pharmacological silencing of cortical spiking in young rats of both sexes, we examined developmental changes at three hierarchical stages: output of auditory thalamic neurons, thalamocortical input and recurrent excitatory input to an A1 L4 neuron. In the thalamus, the tonotopic map matured with an expanded range of frequency representations, while the frequency tuning of output responses was unchanged. On the other hand, the tuning shape of both thalamocortical and intracortical excitatory inputs to a L4 neuron became sharpened. In particular, the intracortical input became better tuned than thalamocortical excitation. Moreover, the weight of intracortical excitation around the optimal frequency was selectively strengthened, resulting in a dominant role of intracortical excitation in defining the total excitatory input tuning. Our modeling work further demonstrates that the frequency-selective strengthening of local recurrent excitatory connections plays a major role in the refinement of excitatory input tuning of L4 neurons.SIGNIFICANCE STATEMENT During postnatal development, sensory cortex undergoes functional refinement, through which the size of sensory receptive field is reduced. In the rat primary auditory cortex, such refinement in layer (L)4 is mainly attributed to improved selectivity of excitatory input a L4 neuron receives. In this study, we further examined three stages along the hierarchical neural pathway where excitatory input refinement might occur. We found that developmental refinement takes place at both thalamocortical and intracortical circuit levels, but not at the thalamic output level. Together with modeling results, we revealed that the optimal-frequency-selective strengthening of intracortical excitation plays a dominant role in the refinement of excitatory input tuning.

Neural Classifiers with Limited Connectivity and Recurrent Readouts.

For many neural network models in which neurons are trained to classify inputs like perceptrons, the number of inputs that can be classified is limited by the connectivity of each neuron, even when the total number of neurons is very large. This poses the problem of how the biological brain can take advantage of its huge number of neurons given that the connectivity is sparse. One solution is to combine multiple perceptrons together, as in committee machines. The number of classifiable random patterns would then grow linearly with the number of perceptrons, even when each perceptron has limited connectivity. However, the problem is moved to the downstream readout neurons, which would need a number of connections as large as the number of perceptrons. Here we propose a different approach in which the readout is implemented by connecting multiple perceptrons in a recurrent attractor neural network. We prove analytically that the number of classifiable random patterns can grow unboundedly with the number of perceptrons, even when the connectivity of each perceptron remains finite. Most importantly, both the recurrent connectivity and the connectivity of downstream readouts also remain finite. Our study shows that feedforward neural classifiers with numerous long-range afferent connections can be replaced by recurrent networks with sparse long-range connectivity without sacrificing the classification performance. Our strategy could be used to design more general scalable network architectures with limited connectivity, which resemble more closely the brain neural circuits that are dominated by recurrent connectivity.SIGNIFICANCE STATEMENT The mammalian brain has a huge number of neurons, but the connectivity is rather sparse. This observation seems to contrast with the theoretical studies showing that for many neural network models the performance scales with the number of connections per neuron and not with the total number of neurons. To solve this dilemma, we propose a model in which a recurrent network reads out multiple neural classifiers. Its performance scales with the total number of neurons even when each neuron of the network has limited connectivity. Our study reveals an important role of recurrent connections in neural systems like the hippocampus, in which the computational limitations due to sparse long-range feedforward connectivity might be compensated by local recurrent connections.

Data driven modelling based on Recurrent Interval-Valued Metacognitive Scaffolding Fuzzy Neural Network

The Metacognitive Scaffolding Learning Machine (McSLM), combining the concept of metacognition—what-to-learn, how-to-learn, and when-to-learn, and the Scaffolding theory—a tutoring theory for a learner to learn a complex task, has been successfully developed to enhance the capability of Evolving Intelligent Systems (EIS) in processing non-stationary data streams. Three issues, namely uncertainty, temporal behaviour, unknown system order, are however uncharted by any existing McSLMs and all McSLMs in the literature are designed for classification problems. This paper proposes a novel McSLM, called Recurrent Interval-Valued Metacognitive Scaffolding Fuzzy Neural Network (RIVMcSFNN) and used to solve regression and time-series modelling problems from data streams. RIVMcSFNN presents a novel recurrent network architecture as a cognitive constituent, which features double local recurrent connections at both the hidden layer and the consequent layer. The new recurrent network architecture is driven by the interval-valued multivariate Gaussian function in the hidden node and the nonlinear Wavelet function in the consequent node. As with its predecessors, the RIVMcSFNN characterises an open structure, where it can automatically grow, prune, adjust, merge, recall its hidden node and can select relevant data samples on the fly using an online active learning methodology. The RIVMcSFNN is also equipped with the online dimensionality reduction technique to cope with the curse of dimensionality. All learning mechanisms are carried out in the single-pass and local learning mode and actualise the plug-and-play learning principle, which aims to minimise the use of pre-and/or post-training steps. The efficacy of our algorithm was tested using numerous data-driven modelling problems and comprehensive comparisons with its counterparts. The RIVMcSFNN demonstrated substantial improvements in both accuracy and complexity against existing variants of the McSLMs and EISs.

Circuits and Mechanisms for Surround Modulation in Visual Cortex.

Surround modulation (SM) is a fundamental property of sensory neurons in many species and sensory modalities. SM is the ability of stimuli in the surround of a neuron's receptive field (RF) to modulate (typically suppress) the neuron's response to stimuli simultaneously presented inside the RF, a property thought to underlie optimal coding of sensory information and important perceptual functions. Understanding the circuit and mechanisms for SM can reveal fundamental principles of computations in sensory cortices, from mouse to human. Current debate is centered over whether feedforward or intracortical circuits generate SM, and whether this results from increased inhibition or reduced excitation. Here we present a working hypothesis, based on theoretical and experimental evidence, that SM results from feedforward, horizontal, and feedback interactions with local recurrent connections, via synaptic mechanisms involving both increased inhibition and reduced recurrent excitation. In particular, strong and balanced recurrent excitatory and inhibitory circuits play a crucial role in the computation of SM.

Operation and plasticity of hippocampal CA3 circuits: implications for memory encoding.

The CA3 region of the hippocampus is important for rapid encoding of memory. Computational theories have proposed specific roles in hippocampal function and memory for the sparse inputs from the dentate gyrus to CA3 and for the extended local recurrent connectivity that gives rise to the CA3 autoassociative network. Recently, we have gained considerable new insight into the operation and plasticity of CA3 circuits, including the identification of novel forms of synaptic plasticity and their underlying mechanisms, and structural plasticity in the GABAergic control of CA3 circuits. In addition, experimental links between synaptic plasticity of CA3 circuits and memory are starting to emerge.

Plasticity-Driven Self-Organization under Topological Constraints Accounts for Non-random Features of Cortical Synaptic Wiring.

Understanding the structure and dynamics of cortical connectivity is vital to understanding cortical function. Experimental data strongly suggest that local recurrent connectivity in the cortex is significantly non-random, exhibiting, for example, above-chance bidirectionality and an overrepresentation of certain triangular motifs. Additional evidence suggests a significant distance dependency to connectivity over a local scale of a few hundred microns, and particular patterns of synaptic turnover dynamics, including a heavy-tailed distribution of synaptic efficacies, a power law distribution of synaptic lifetimes, and a tendency for stronger synapses to be more stable over time. Understanding how many of these non-random features simultaneously arise would provide valuable insights into the development and function of the cortex. While previous work has modeled some of the individual features of local cortical wiring, there is no model that begins to comprehensively account for all of them. We present a spiking network model of a rodent Layer 5 cortical slice which, via the interactions of a few simple biologically motivated intrinsic, synaptic, and structural plasticity mechanisms, qualitatively reproduces these non-random effects when combined with simple topological constraints. Our model suggests that mechanisms of self-organization arising from a small number of plasticity rules provide a parsimonious explanation for numerous experimentally observed non-random features of recurrent cortical wiring. Interestingly, similar mechanisms have been shown to endow recurrent networks with powerful learning abilities, suggesting that these mechanism are central to understanding both structure and function of cortical synaptic wiring.

Self-organization of complex cortex-like wiring in a spiking neural network model

Understanding the structure and dynamics of cortical connectivity is vital to understanding cortical function. Experimental data strongly suggest that local recurrent connectivity in the cortex is significantly non-random, exhibiting above-chance bidirectionality, an overrepresentation of certain triangular motifs, and a heavy-tailed distribution of synaptic efficacies [1]. Additional evidence suggests a significant distance dependency to connectivity over a local scale of a few hundred microns [2], and particular patterns of synaptic turnover dynamics [3]. It is currently not understood how many of these non-random features arise. Gaining understanding, then, of the processes that lead to these complexities would provide valuable insights into the development and computational functionality of the cortex. While previous work has attempted to model some of the individual features of local cortical wiring, there is no model that comprehensively begins to account for all of them. Here we present a spiking network model of a Layer V-like cortical slice culture (panel B) that, via the interactions of a few simple biologically motivated plasticity mechanisms, qualitatively reproduces many of these non-random effects, such as synaptic weight (panel A) and triangular motif distribution (panel C) Additionally, it reproduced experimentally observed synaptic growth and efficacy dynamics [3]. These plasticity mechanisms include spike timing dependent plasticity, synaptic normalization, homeostatic firing threshold adaptation, pruning of zero-efficacy synaptic connections, and the distance-dependent generation of new synaptic connections. As a spiking, topographic extension to the previously developed SORN family of models [4,5], there is also evidence suggesting that these plasticity mechanisms endow recurrent networks with powerful learning abilities. Our model suggests that mechanisms of self-organization arising from a small number of plasticity rules provide a parsimonious explanation for numerous experimentally observed non-random features of recurrent cortical wiring. Figure 1 Panel A: Mature synaptic weight distribution (in logarithmic space) for a simulation run with associated Gaussian (lognormal in linear space) fit. Panel B: Topological graph of mature network for a simulation run. Panel C: Triangular motif count (relative ...

Visually Cued Action Timing in the Primary Visual Cortex

Most behaviors are generated in three steps: sensing the external world, processing that information to instruct decision-making, and producing a motor action. Sensory areas, especially primary sensory cortices, have long been held to be involved only in the first step of this sequence. Here, we develop a visually cued interval timing task that requires rats to decide when to perform an action following a brief visual stimulus. Using single-unit recordings and optogenetics in this task, we show that activity generated by the primary visual cortex (V1) embodies the target interval and may instruct the decision to time the action on a trial-by-trial basis. A spiking neuronal model of local recurrent connections in V1 produces neural responses that predict and drive the timing of future actions, rationalizing our observations. Our data demonstrate that the primary visual cortex may contribute to the instruction of visually cued timed actions.

Local changes in neocortical circuit dynamics coincide with the spread of seizures to thalamus in a model of epilepsy.

During the generalization of epileptic seizures, pathological activity in one brain area recruits distant brain structures into joint synchronous discharges. However, it remains unknown whether specific changes in local circuit activity are related to the aberrant recruitment of anatomically distant structures into epileptiform discharges. Further, it is not known whether aberrant areas recruit or entrain healthy ones into pathological activity. Here we study the dynamics of local circuit activity during the spread of epileptiform discharges in the zero-magnesium in vitro model of epilepsy. We employ high-speed multi-photon imaging in combination with dual whole-cell recordings in acute thalamocortical (TC) slices of the juvenile mouse to characterize the generalization of epileptic activity between neocortex and thalamus. We find that, although both structures are exposed to zero-magnesium, the initial onset of focal epileptiform discharge occurs in cortex. This suggests that local recurrent connectivity that is particularly prevalent in cortex is important for the initiation of seizure activity. Subsequent recruitment of thalamus into joint, generalized discharges is coincident with an increase in the coherence of local cortical circuit activity that itself does not depend on thalamus. Finally, the intensity of population discharges is positively correlated between both brain areas. This suggests that during and after seizure generalization not only the timing but also the amplitude of epileptiform discharges in thalamus is entrained by cortex. Together these results suggest a central role of neocortical activity for the onset and the structure of pathological recruitment of thalamus into joint synchronous epileptiform discharges.

The Correlation Structure of Local Neuronal Networks Intrinsically Results from Recurrent Dynamics

Correlated neuronal activity is a natural consequence of network connectivity and shared inputs to pairs of neurons, but the task-dependent modulation of correlations in relation to behavior also hints at a functional role. Correlations influence the gain of postsynaptic neurons, the amount of information encoded in the population activity and decoded by readout neurons, and synaptic plasticity. Further, it affects the power and spatial reach of extracellular signals like the local-field potential. A theory of correlated neuronal activity accounting for recurrent connectivity as well as fluctuating external sources is currently lacking. In particular, it is unclear how the recently found mechanism of active decorrelation by negative feedback on the population level affects the network response to externally applied correlated stimuli. Here, we present such an extension of the theory of correlations in stochastic binary networks. We show that (1) for homogeneous external input, the structure of correlations is mainly determined by the local recurrent connectivity, (2) homogeneous external inputs provide an additive, unspecific contribution to the correlations, (3) inhibitory feedback effectively decorrelates neuronal activity, even if neurons receive identical external inputs, and (4) identical synaptic input statistics to excitatory and to inhibitory cells increases intrinsically generated fluctuations and pairwise correlations. We further demonstrate how the accuracy of mean-field predictions can be improved by self-consistently including correlations. As a byproduct, we show that the cancellation of correlations between the summed inputs to pairs of neurons does not originate from the fast tracking of external input, but from the suppression of fluctuations on the population level by the local network. This suppression is a necessary constraint, but not sufficient to determine the structure of correlations; specifically, the structure observed at finite network size differs from the prediction based on perfect tracking, even though perfect tracking implies suppression of population fluctuations.

Recurrence and external sources differentially shape network correlations

The presence of correlated neuronal activity as such is not surprising, but rather a natural consequence of network connectivity and dynamics, in particular direct synaptic connections and shared local and non-local presynaptic sources [1]. The intriguing feature, however, is the modulation of correlations in relation to behavior [2]. These task-dependent changes may indicate that correlated spike timing is used for the storage, transmission, and processing of information. Moreover, correlated synaptic activation strongly influences the power and the spatial reach of the local field potential [3], a commonly recorded signal in experimental neuroscience. A theoretical understanding of correlations requires the representation of (1) the recurrent connectivity and (2) external and internal sources of temporally varying or fluctuating signals. Such a theory is currently lacking. In particular it is still unclear how the recently found mechanism of active decorrelation [4], explained by negative feedback on the population level [5], affects the network response to externally applied stimuli. We here extend the theory of correlations in binary networks [6] to external correlated input. We show that (1) for homogeneous external input, the structure of correlations [7] is mainly determined by the local recurrent connectivity, (2) common external inputs provide an additive, homogeneous contribution to the correlation, (3) inhibitory feedback effectively decorrelates neuronal activity, even if neurons receive identical external inputs, and (4) connectivity with approximately identical synapses to excitatory and inhibitory cells increases internally generated fluctuations and pairwise correlations. We further present a new method which self-consistently includes correlations into the established mean-field description to increase the accuracy of the theoretical predictions. As a byproduct of our derivation we show that the cancellation of correlations between the summed inputs to pairs of neurons, in contrast to previous reports [4], does not uniquely determine the structure of correlations, but rather provides only a constraint, which is equivalent to the suppression of fluctuations on the population level [5]. We hope that our work provides a first stepping stone in the endeavor to understand the transformation of impinging correlated external activity into correlated activity between the neurons of the local network.