Balanced cortical microcircuitry for spatial working memory based on corrective feedback control

An oscillatory mechanism for multi-level storage in short-term memory

Oscillatory activity is commonly observed during the maintenance of information in short-term memory, but its role remains unclear. Non-oscillatory models of short-term memory storage are able to encode stimulus identity through their spatial patterns of activity, but are typically limited to either an all-or-none representation of stimulus amplitude or exhibit a biologically implausible exact-tuning condition. Here we demonstrate a simple mechanism by which oscillatory input enables a circuit to generate persistent or sequential activity that encodes information not only in the spatial pattern of activity, but also in the amplitude of activity. This is accomplished through a phase-locking phenomenon that permits many different amplitudes of persistent activity to be stored without requiring exact tuning of model parameters. Altogether, this work proposes a class of models for the storage of information in working memory, a potential role for brain oscillations, and a dynamical mechanism for maintaining multi-stable neural representations.

New insights into binocular rivalry from the reconstruction of evolving percepts using model network dynamics

When the two eyes are presented with highly distinct stimuli, the resulting visual percept generally switches every few seconds between the two monocular images in an irregular fashion, giving rise to a phenomenon known as binocular rivalry. While a host of theoretical studies have explored potential mechanisms for binocular rivalry in the context of evoked model dynamics in response to simple stimuli, here we investigate binocular rivalry directly through complex stimulus reconstructions based on the activity of a two-layer neuronal network model with competing downstream pools driven by disparate monocular stimuli composed of image pixels. To estimate the dynamic percept, we derive a linear input-output mapping rooted in the non-linear network dynamics and iteratively apply compressive sensing techniques for signal recovery. Utilizing a dominance metric, we are able to identify when percept alternations occur and use data collected during each dominance period to generate a sequence of percept reconstructions. We show that despite the approximate nature of the input-output mapping and the significant reduction in neurons downstream relative to stimulus pixels, the dominant monocular image is well-encoded in the network dynamics and improvements are garnered when realistic spatial receptive field structure is incorporated into the feedforward connectivity. Our model demonstrates gamma-distributed dominance durations and well obeys Levelt's four laws for how dominance durations change with stimulus strength, agreeing with key recurring experimental observations often used to benchmark rivalry models. In light of evidence that individuals with autism exhibit relatively slow percept switching in binocular rivalry, we corroborate the ubiquitous hypothesis that autism manifests from reduced inhibition in the brain by systematically probing our model alternation rate across choices of inhibition strength. We exhibit sufficient conditions for producing binocular rivalry in the context of natural scene stimuli, opening a clearer window into the dynamic brain computations that vary with the generated percept and a potential path toward further understanding neurological disorders.

Evaluating the extent to which homeostatic plasticity learns to compute prediction errors in unstructured neuronal networks

The brain is believed to operate in part by making predictions about sensory stimuli and encoding deviations from these predictions in the activity of "prediction error neurons." This principle defines the widely influential theory of predictive coding. The precise circuitry and plasticity mechanisms through which animals learn to compute and update their predictions are unknown. Homeostatic inhibitory synaptic plasticity is a promising mechanism for training neuronal networks to perform predictive coding. Homeostatic plasticity causes neurons to maintain a steady, baseline firing rate in response to inputs that closely match the inputs on which a network was trained, but firing rates can deviate away from this baseline in response to stimuli that are mismatched from training. We combine computer simulations and mathematical analysis systematically to test the extent to which randomly connected, unstructured networks compute prediction errors after training with homeostatic inhibitory synaptic plasticity. We find that homeostatic plasticity alone is sufficient for computing prediction errors for trivial time-constant stimuli, but not for more realistic time-varying stimuli. We use a mean-field theory of plastic networks to explain our findings and characterize the assumptions under which they apply.

Unsupervised learning for robust working memory

Working memory is a core component of critical cognitive functions such as planning and decision-making. Persistent activity that lasts long after the stimulus offset has been considered a neural substrate for working memory. Attractor dynamics based on network interactions can successfully reproduce such persistent activity. However, it requires a fine-tuning of network connectivity, in particular, to form continuous attractors which were suggested for encoding continuous signals in working memory. Here, we investigate whether a specific form of synaptic plasticity rules can mitigate such tuning problems in two representative working memory models, namely, rate-coded and location-coded persistent activity. We consider two prominent types of plasticity rules, differential plasticity correcting the rapid activity changes and homeostatic plasticity regularizing the long-term average of activity, both of which have been proposed to fine-tune the weights in an unsupervised manner. Consistent with the findings of previous works, differential plasticity alone was enough to recover a graded-level persistent activity after perturbations in the connectivity. For the location-coded memory, differential plasticity could also recover persistent activity. However, its pattern can be irregular for different stimulus locations under slow learning speed or large perturbation in the connectivity. On the other hand, homeostatic plasticity shows a robust recovery of smooth spatial patterns under particular types of synaptic perturbations, such as perturbations in incoming synapses onto the entire or local populations. However, homeostatic plasticity was not effective against perturbations in outgoing synapses from local populations. Instead, combining it with differential plasticity recovers location-coded persistent activity for a broader range of perturbations, suggesting compensation between two plasticity rules.

A Circuit Model for Working Memory Based on Hybrid Positive and Negative-Derivative Feedback Mechanism

Working memory (WM) plays an important role in cognitive activity. The WM system is used to temporarily store information in learning and decision-making. WM always functions in many aspects of daily life, such as the short-term memory of words, cell phone verification codes, and cell phone numbers. In young adults, studies have shown that a central memory store is limited to three to five meaningful items. Little is known about how WM functions at the microscopic neural level, but appropriate neural network computational models can help us gain a better understanding of it. In this study, we attempt to design a microscopic neural network model to explain the internal mechanism of WM. The performance of existing positive feedback models depends on the parameters of a synapse. We use a negative-derivative feedback mechanism to counteract the drift in persistent activity, making the hybrid positive and negative-derivative feedback (HPNF) model more robust to common disturbances. To fulfill the mechanism of WM at the neural circuit level, we construct two main neural networks based on the HPNF model: a memory-storage sub-network (the memory-storage sub-network is composed of several sets of neurons, so we call it "SET network", or "SET" for short) with positive feedback and negative-derivative feedback and a storage distribution network (SDN) designed by combining SET for memory item storage and memory updating. The SET network is a neural information self-sustaining mechanism, which is robust to common disturbances; the SDN constructs a storage distribution network at the neural circuit level; the experimental results show that our network can fulfill the storage, association, updating, and forgetting of information at the level of neural circuits, and it can work in different individuals with little change in parameters.

A differential Hebbian framework for biologically-plausible motor control

In this paper we explore a neural control architecture that is both biologically plausible, and capable of fully autonomous learning. It consists of feedback controllers that learn to achieve a desired state by selecting the errors that should drive them. This selection happens through a family of differential Hebbian learning rules that, through interaction with the environment, can learn to control systems where the error responds monotonically to the control signal. We next show that in a more general case, neural reinforcement learning can be coupled with a feedback controller to reduce errors that arise non-monotonically from the control signal. The use of feedback control can reduce the complexity of the reinforcement learning problem, because only a desired value must be learned, with the controller handling the details of how it is reached. This makes the function to be learned simpler, potentially allowing learning of more complex actions. We use simple examples to illustrate our approach, and discuss how it could be extended to hierarchical architectures.

Functional Implications of Dale's Law in Balanced Neuronal Network Dynamics and Decision Making

The notion that a neuron transmits the same set of neurotransmitters at all of its post-synaptic connections, typically known as Dale's law, is well supported throughout the majority of the brain and is assumed in almost all theoretical studies investigating the mechanisms for computation in neuronal networks. Dale's law has numerous functional implications in fundamental sensory processing and decision-making tasks, and it plays a key role in the current understanding of the structure-function relationship in the brain. However, since exceptions to Dale's law have been discovered for certain neurons and because other biological systems with complex network structure incorporate individual units that send both positive and negative feedback signals, we investigate the functional implications of network model dynamics that violate Dale's law by allowing each neuron to send out both excitatory and inhibitory signals to its neighbors. We show how balanced network dynamics, in which large excitatory and inhibitory inputs are dynamically adjusted such that input fluctuations produce irregular firing events, are theoretically preserved for a single population of neurons violating Dale's law. We further leverage this single-population network model in the context of two competing pools of neurons to demonstrate that effective decision-making dynamics are also produced, agreeing with experimental observations from honeybee dynamics in selecting a food source and artificial neural networks trained in optimal selection. Through direct comparison with the classical two-population balanced neuronal network, we argue that the one-population network demonstrates more robust balanced activity for systems with less computational units, such as honeybee colonies, whereas the two-population network exhibits a more rapid response to temporal variations in network inputs, as required by the brain. We expect this study will shed light on the role of neurons violating Dale's law found in experiment as well as shared design principles across biological systems that perform complex computations.

Trial-to-Trial Variability of Spiking Delay Activity in Prefrontal Cortex Constrains Burst-Coding Models of Working Memory

A hallmark neuronal correlate of working memory (WM) is stimulus-selective spiking activity of neurons in PFC during mnemonic delays. These observations have motivated an influential computational modeling framework in which WM is supported by persistent activity. Recently, this framework has been challenged by arguments that observed persistent activity may be an artifact of trial-averaging, which potentially masks high variability of delay activity at the single-trial level. In an alternative scenario, WM delay activity could be encoded in bursts of selective neuronal firing which occur intermittently across trials. However, this alternative proposal has not been tested on single-neuron spike-train data. Here, we developed a framework for addressing this issue by characterizing the trial-to-trial variability of neuronal spiking quantified by Fano factor (FF). By building a doubly stochastic Poisson spiking model, we first demonstrated that the burst-coding proposal implies a significant increase in FF positively correlated with firing rate, and thus loss of stability across trials during the delay. Simulation of spiking cortical circuit WM models further confirmed that FF is a sensitive measure that can well dissociate distinct WM mechanisms. We then tested these predictions on datasets of single-neuron recordings from macaque PFC during three WM tasks. In sharp contrast to the burst-coding model predictions, we only found a small fraction of neurons showing increased WM-dependent burstiness, and stability across trials during delay was strengthened in empirical data. Therefore, reduced trial-to-trial variability during delay provides strong constraints on the contribution of single-neuron intermittent bursting to WM maintenance.SIGNIFICANCE STATEMENT There are diverging classes of theoretical models explaining how information is maintained in working memory by cortical circuits. In an influential model class, neurons exhibit persistent elevated memorandum-selective firing, whereas a recently developed class of burst-coding models suggests that persistent activity is an artifact of trial-averaging, and spiking is sparse in each single trial, subserved by brief intermittent bursts. However, this alternative picture has not been characterized or tested on empirical spike-train data. Here we combine mathematical analysis, computational model simulation, and experimental data analysis to test empirically these two classes of models and show that the trial-to-trial variability of empirical spike trains is not consistent with burst coding. These findings provide constraints for theoretical models of working memory.

Uncertainty is maintained and used in working memory

What are the contents of working memory? In both behavioral and neural computational models, a working memory representation is typically described by a single number, namely, a point estimate of a stimulus. Here, we asked if people also maintain the uncertainty associated with a memory and if people use this uncertainty in subsequent decisions. We collected data in a two-condition orientation change detection task; while both conditions measured whether people used memory uncertainty, only one required maintaining it. For each condition, we compared an optimal Bayesian observer model, in which the observer uses an accurate representation of uncertainty in their decision, to one in which the observer does not. We find that this “Use Uncertainty” model fits better for all participants in both conditions. In the first condition, this result suggests that people use uncertainty optimally in a working memory task when that uncertainty information is available at the time of decision, confirming earlier results. Critically, the results of the second condition suggest that this uncertainty information was maintained in working memory. We test model variants and find that our conclusions do not depend on our assumptions about the observer's encoding process, inference process, or decision rule. Our results provide evidence that people have uncertainty that reflects their memory precision on an item-specific level, maintain this information over a working memory delay, and use it implicitly in a way consistent with an optimal observer. These results challenge existing computational models of working memory to update their frameworks to represent uncertainty.

Increased repulsion of working memory representations in schizophrenia

Computational neuroscience models propose that working memory (WM) involves recurrent excitatory feedback loops that maintain firing over time along with lateral inhibition that prevents the spreading of activity to other feature values. In behavioral paradigms, this lateral inhibition appears to cause a repulsion of WM representations away from each other and from other strong sources of input. Recent computational models of schizophrenia have proposed that reduction in the strength of inhibition relative to strength of excitation may underlie impaired cognition, and this leads to the prediction that repulsion effects should be reduced in people with schizophrenia spectrum disorders (PSZ) relative to healthy control subjects (HCS). We tested this hypothesis in 2 experiments measuring WM repulsion effects. In Experiment 1, 45 PSZ and 32 HCS remembered the location of a single object relative to a centrally presented visual landmark and reported this location after a short delay. The reported location was repelled away from the landmark in both groups, but this repulsion effect was increased rather than decreased in PSZ relative to HCS. In Experiment 2, 41 PSZ and 34 HCS remembered 2 sequentially presented orientations and reported each orientation after a short delay. The reported orientations were biased away from each other in both groups, and this repulsion effect was again more pronounced in PSZ than in HCS. Contrary to the widespread hypothesis of reduced inhibition in schizophrenia, we provide robust evidence from 2 experiments showing that the behavioral performance of PSZ exhibited an exaggeration rather than a reduction of competitive inhibition. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Poisson balanced spiking networks

An important problem in computational neuroscience is to understand how networks of spiking neurons can carry out various computations underlying behavior. Balanced spiking networks (BSNs) provide a powerful framework for implementing arbitrary linear dynamical systems in networks of integrate-and-fire neurons. However, the classic BSN model requires near-instantaneous transmission of spikes between neurons, which is biologically implausible. Introducing realistic synaptic delays leads to an pathological regime known as "ping-ponging", in which different populations spike maximally in alternating time bins, causing network output to overshoot the target solution. Here we document this phenomenon and provide a novel solution: we show that a network can have realistic synaptic delays while maintaining accuracy and stability if neurons are endowed with conditionally Poisson firing. Formally, we propose two alternate formulations of Poisson balanced spiking networks: (1) a "local" framework, which replaces the hard integrate-and-fire spiking rule within each neuron by a "soft" threshold function, such that firing probability grows as a smooth nonlinear function of membrane potential; and (2) a "population" framework, which reformulates the BSN objective function in terms of expected spike counts over the entire population. We show that both approaches offer improved robustness, allowing for accurate implementation of network dynamics with realistic synaptic delays between neurons. Both Poisson frameworks preserve the coding accuracy and robustness to neuron loss of the original model and, moreover, produce positive correlations between similarly tuned neurons, a feature of real neural populations that is not found in the deterministic BSN. This work unifies balanced spiking networks with Poisson generalized linear models and suggests several promising avenues for future research.

Excitation-Inhibition Balanced Neural Networks for Fast Signal Detection

Excitation-inhibition (E-I) balanced neural networks are a classic model for modeling neural activities and functions in the cortex. The present study investigates the potential application of E-I balanced neural networks for fast signal detection in brain-inspired computation. We first theoretically analyze the response property of an E-I balanced network, and find that the asynchronous firing state of the network generates an optimal noise structure enabling the network to track input changes rapidly. We then extend the homogeneous connectivity of an E-I balanced neural network to include local neuronal connections, so that the network can still achieve fast response and meanwhile maintain spatial information in the face of spatially heterogeneous signal. Finally, we carry out simulations to demonstrate that our model works well.

Understanding the computation of time using neural network models

Perceiving, maintaining, and using time intervals in working memory are crucial for animals to anticipate or act correctly at the right time in the ever-changing world. Here, we systematically study the underlying neural mechanisms by training recurrent neural networks to perform temporal tasks or complex tasks in combination with spatial information processing and decision making. We found that neural networks perceive time through state evolution along stereotypical trajectories and produce time intervals by scaling evolution speed. Temporal and nontemporal information is jointly coded in a way that facilitates decoding generalizability. We also provided potential sources for the temporal signals observed in nontiming tasks. Our study revealed the computational principles of a number of experimental phenomena and provided several predictions.

To maximize future rewards in this ever-changing world, animals must be able to discover the temporal structure of stimuli and then anticipate or act correctly at the right time. How do animals perceive, maintain, and use time intervals ranging from hundreds of milliseconds to multiseconds in working memory? How is temporal information processed concurrently with spatial information and decision making? Why are there strong neuronal temporal signals in tasks in which temporal information is not required? A systematic understanding of the underlying neural mechanisms is still lacking. Here, we addressed these problems using supervised training of recurrent neural network models. We revealed that neural networks perceive elapsed time through state evolution along stereotypical trajectory, maintain time intervals in working memory in the monotonic increase or decrease of the firing rates of interval-tuned neurons, and compare or produce time intervals by scaling state evolution speed. Temporal and nontemporal information is coded in subspaces orthogonal with each other, and the state trajectories with time at different nontemporal information are quasiparallel and isomorphic. Such coding geometry facilitates the decoding generalizability of temporal and nontemporal information across each other. The network structure exhibits multiple feedforward sequences that mutually excite or inhibit depending on whether their preferences of nontemporal information are similar or not. We identified four factors that facilitate strong temporal signals in nontiming tasks, including the anticipation of coming events. Our work discloses fundamental computational principles of temporal processing, and it is supported by and gives predictions to a number of experimental phenomena.

Velocity coupling of grid cell modules enables stable embedding of a low dimensional variable in a high dimensional neural attractor

Grid cells in the medial entorhinal cortex (MEC) encode position using a distributed representation across multiple neural populations (modules), each possessing a distinct spatial scale. The modular structure of the representation confers the grid cell neural code with large capacity. Yet, the modularity poses significant challenges for the neural circuitry that maintains the representation, and updates it based on self motion. Small incompatible drifts in different modules, driven by noise, can rapidly lead to large, abrupt shifts in the represented position, resulting in catastrophic readout errors. Here, we propose a theoretical model of coupled modules. The coupling suppresses incompatible drifts, allowing for a stable embedding of a two-dimensional variable (position) in a higher dimensional neural attractor, while preserving the large capacity. We propose that coupling of this type may be implemented by recurrent synaptic connectivity within the MEC with a relatively simple and biologically plausible structure.

Stability of working memory in continuous attractor networks under the control of short-term plasticity

Continuous attractor models of working-memory store continuous-valued information in continuous state-spaces, but are sensitive to noise processes that degrade memory retention. Short-term synaptic plasticity of recurrent synapses has previously been shown to affect continuous attractor systems: short-term facilitation can stabilize memory retention, while short-term depression possibly increases continuous attractor volatility. Here, we present a comprehensive description of the combined effect of both short-term facilitation and depression on noise-induced memory degradation in one-dimensional continuous attractor models. Our theoretical description, applicable to rate models as well as spiking networks close to a stationary state, accurately describes the slow dynamics of stored memory positions as a combination of two processes: (i) diffusion due to variability caused by spikes; and (ii) drift due to random connectivity and neuronal heterogeneity. We find that facilitation decreases both diffusion and directed drifts, while short-term depression tends to increase both. Using mutual information, we evaluate the combined impact of short-term facilitation and depression on the ability of networks to retain stable working memory. Finally, our theory predicts the sensitivity of continuous working memory to distractor inputs and provides conditions for stability of memory.

The ability to transiently memorize positions in the visual field is crucial for behavior. Models and experiments have shown that such memories can be maintained in networks of cortical neurons with a continuum of possible activity states, that reflects the continuum of positions in the environment. However, the accuracy of positions stored in such networks will degrade over time due to the noisiness of neuronal signaling and imperfections of the biological substrate. Previous work in simplified models has shown that synaptic short-term plasticity could stabilize this degradation by dynamically up- or down-regulating the strength of synaptic connections, thereby “pinning down” memorized positions. Here, we present a general theory that accurately predicts the extent of this “pinning down” by short-term plasticity in a broad class of biologically plausible network models, thereby untangling the interplay of varying biological sources of noise with short-term plasticity. Importantly, our work provides a novel theoretical link from the microscopic substrate of working memory—neurons and synaptic connections—to observable behavioral correlates, for example the susceptibility to distracting stimuli.

Unsupervised identification of states from voltage recordings of neural networks

BACKGROUND

Modern techniques for multi-neuronal recording produce large amounts of data. There is no automatic procedure for the identification of states in recurrent voltage patterns.

NEW METHOD

We propose NetSAP (Network States And Pathways), a data-driven analysis method that is able to recognize multi-neuron voltage patterns (states). To capture the subtle differences between snapshots in voltage recordings, NetSAP infers the underlying functional neural network in a time-resolved manner with a sliding window approach. Then NetSAP identifies states from a reordering of the time series of inferred networks according to a user-defined metric. The procedure for unsupervised identification of states was developed originally for the analysis of molecular dynamics simulations of proteins.

RESULTS

We tested NetSAP on neural network simulations of GABAergic inhibitory interneurons. Most simulation parameters are chosen to reproduce literature observations, and we keep noise terms as control parameters to regulate the coherence of the simulated signals. NetSAP is able to identify multiple states even in the case of high internal noise and low signal coherence. We provide evidence that NetSAP is robust for networks with up to about 50% of the neurons spiking randomly. NetSAP is scalable and its code is open source.

COMPARISON WITH EXISTING METHODS

NetSAP outperforms common analysis techniques, such as PCA and k-means clustering, on a simulated recording of voltage traces of 50 neurons.

CONCLUSIONS

NetSAP analysis is an efficient tool to identify voltage patterns from neuronal recordings.

The Rat Medial Prefrontal Cortex Exhibits Flexible Neural Activity States during the Performance of an Odor Span Task

Medial prefrontal cortex (mPFC) activity is fundamental for working memory (WM), attention, and behavioral inhibition; however, a comprehensive understanding of the neural computations underlying these processes is still forthcoming. Toward this goal, neural recordings were obtained from the mPFC of awake, behaving rats performing an odor span task of WM capacity. Neural populations were observed to encode distinct task epochs and the transitions between epochs were accompanied by abrupt shifts in neural activity patterns. Putative pyramidal neuron activity increased earlier in the delay for sessions where rats achieved higher spans. Furthermore, increased putative interneuron activity was only observed at the termination of the delay thus indicating that local processing in inhibitory networks was a unique feature to initiate foraging. During foraging, changes in neural activity patterns associated with the approach to a novel odor, but not familiar odors, were robust. Collectively, these data suggest that distinct mPFC activity states underlie the delay, foraging, and reward epochs of the odor span task. Transitions between these states likely enables adaptive behavior in dynamic environments that place strong demands on the substrates of working memory.

A roadmap towards a functional paradigm for learning & memory in plants

In plants, the acquisition, processing and storage of empirical information can result in the modification of their behavior according to the nature of the stimulus, and yet this area of research remained relatively understudied until recently. As the body of evidence supporting the inclusion of plants among the higher organisms demonstrating the adaptations to accomplish these tasks keeps increasing, the resistance by traditional botanists and agricultural scientists, who were at first cautious in allowing the application of animal models onto plant physiology and development, subsides. However, the debate retains much of its heat, a good part of it originating from the controversial use of nervous system terms to describe plant processes. By focusing on the latest findings on the cellular and molecular mechanisms underlying the well established processes of Learning and Memory, recognizing what has been accomplished and what remains to be explored, and without seeking to bootstrap neuronal characteristics where none are to be found, a roadmap guiding towards a comprehensive paradigm for Learning and Memory in plants begins to emerge. Meanwhile the applications of the new field of Plant Gnosophysiology look as promising as ever.

Computational models of motivated frontal function

Computational models of frontal function have made important contributions to understanding how the frontal lobes support a wide range of important functions, in their interactions with other brain areas including, critically, the basal ganglia (BG). We focus here on the specific case of how different frontal areas support goal-directed, motivated decision-making, by representing three essential types of information: possible plans of action (in more dorsal and lateral frontal areas), affectively significant outcomes of those action plans (in ventral, medial frontal areas including the orbital frontal cortex), and the overall utility of a given plan compared to other possible courses of action (in anterior cingulate cortex). Computational models of goal-directed action selection at multiple different levels of analysis provide insight into the nature of learning and processing in these areas and the relative contributions of the frontal cortex versus the BG. The most common neurologic disorders implicate these areas, and understanding their precise function and modes of dysfunction can contribute to the new field of computational psychiatry, within the broader field of computational neuroscience.

Circuit Models of Low-Dimensional Shared Variability in Cortical Networks

Trial-to-trial variability is a reflection of the circuitry and cellular physiology that make up a neuronal network. A pervasive yet puzzling feature of cortical circuits is that despite their complex wiring, population-wide shared spiking variability is low dimensional. Previous model cortical networks cannot explain this global variability, and rather assume it is from external sources. We show that if the spatial and temporal scales of inhibitory coupling match known physiology, networks of model spiking neurons internally generate low-dimensional shared variability that captures population activity recorded in vivo. Shifting spatial attention into the receptive field of visual neurons has been shown to differentially modulate shared variability within and between brain areas. A top-down modulation of inhibitory neurons in our network provides a parsimonious mechanism for this attentional modulation. Our work provides a critical link between observed cortical circuit structure and realistic shared neuronal variability and its modulation.

Competing inhibition-stabilized networks in sensory and memory processing

In simplified models of neocortical circuits, inhibition is either modeled in a feedforward manner or through mutual inhibitory interactions that provide for competition between neuronal populations. By contrast, recent work has suggested a critical role for recurrent inhibition as a negative feedback element that stabilizes otherwise unstable recurrent excitation. Here, we show how models based upon a motif of recurrently connected "E-I" pairs of excitatory and inhibitory units can be used to describe experimental observations in sensory and memory networks. In a sensory network model of binocular rivalry, a model based on competing E-I motifs captures psychophysical observations about how incongruous images presented to the two eyes compete. In a model of cortical working memory, an architecturally similar model with modified synaptic time constants can mathematically accumulate signals into a working memory buffer in a manner that is robust to the abrupt removal of cells. These results suggest the inhibition-stabilized E-I motif as a fundamental building block for models of a wide array of neocortical dynamics.

Synaptic efficacy shapes resource limitations in working memory

Working memory (WM) is limited in its temporal length and capacity. Classic conceptions of WM capacity assume the system possesses a finite number of slots, but recent evidence suggests WM may be a continuous resource. Resource models typically assume there is no hard upper bound on the number of items that can be stored, but WM fidelity decreases with the number of items. We analyze a neural field model of multi-item WM that associates each item with the location of a bump in a finite spatial domain, considering items that span a one-dimensional continuous feature space. Our analysis relates the neural architecture of the network to accumulated errors and capacity limitations arising during the delay period of a multi-item WM task. Networks with stronger synapses support wider bumps that interact more, whereas networks with weaker synapses support narrower bumps that are more susceptible to noise perturbations. There is an optimal synaptic strength that both limits bump interaction events and the effects of noise perturbations. This optimum shifts to weaker synapses as the number of items stored in the network is increased. Our model not only provides a circuit-based explanation for WM capacity, but also speaks to how capacity relates to the arrangement of stored items in a feature space.

Imbalanced amplification: A mechanism of amplification and suppression from local imbalance of excitation and inhibition in cortical circuits

Understanding the relationship between external stimuli and the spiking activity of cortical populations is a central problem in neuroscience. Dense recurrent connectivity in local cortical circuits can lead to counterintuitive response properties, raising the question of whether there are simple arithmetical rules for relating circuits’ connectivity structure to their response properties. One such arithmetic is provided by the mean field theory of balanced networks, which is derived in a limit where excitatory and inhibitory synaptic currents precisely balance on average. However, balanced network theory is not applicable to some biologically relevant connectivity structures. We show that cortical circuits with such structure are susceptible to an amplification mechanism arising when excitatory-inhibitory balance is broken at the level of local subpopulations, but maintained at a global level. This amplification, which can be quantified by a linear correction to the classical mean field theory of balanced networks, explains several response properties observed in cortical recordings and provides fundamental insights into the relationship between connectivity structure and neural responses in cortical circuits.

Understanding how the brain represents and processes stimuli requires a quantitative understanding of how signals propagate through networks of neurons. Developing such an understanding is made difficult by the dense interconnectivity of neurons, especially in the cerebral cortex. One approach to quantifying neural processing in the cortex is derived from observations that excitatory (positive) and inhibitory (negative) interactions between neurons tend to balance each other in many brain areas. This balance is achieved under a class of computational models called “balanced networks.” However, previous approaches to the mathematical analysis of balanced network models is not possible under some biologically relevant connectivity structures. We show that, under these structures, balance between excitation and inhibition is necessarily broken and the resulting imbalance causes some stimulus features to be amplified. This “imbalanced amplification” of stimuli can explain several observations from recordings in mouse somatosensory and visual cortical circuits and provides fundamental insights into the relationship between connectivity structure and neural responses in cortical circuits.

Fluid network dynamics in the prefrontal cortex during multiple strategy switching

Coordinated shifts of neuronal activity in the prefrontal cortex are associated with strategy adaptations in behavioural tasks, when animals switch from following one rule to another. However, network dynamics related to multiple-rule changes are scarcely known. We show how firing rates of individual neurons in the prelimbic and cingulate cortex correlate with the performance of rats trained to change their navigation multiple times according to allocentric and egocentric strategies. The concerted population activity exhibits a stable firing during the performance of one rule but shifted to another neuronal firing state when a new rule is learnt. Interestingly, when the same rule is presented a second time within the same session, neuronal firing does not revert back to the original neuronal firing state, but a new activity-state is formed. Our data indicate that neuronal firing of prefrontal cortical neurons represents changes in strategy and task-performance rather than specific strategies or rules.

Population activity of neurons in the prefrontal cortex has been shown to represent cognitive strategy and rules. Here the authors report that when the same rule is repeated on multiple occasions in the task, it is accompanied each time by a new prefrontal firing rate state.

Short-term depression and transient memory in sensory cortex

Persistent neuronal activity is usually studied in the context of short-term memory localized in central cortical areas. Recent studies show that early sensory areas also can have persistent representations of stimuli which emerge quickly (over tens of milliseconds) and decay slowly (over seconds). Traditional positive feedback models cannot explain sensory persistence for at least two reasons: (i) They show attractor dynamics, with transient perturbations resulting in a quasi-permanent change of system state, whereas sensory systems return to the original state after a transient. (ii) As we show, those positive feedback models which decay to baseline lose their persistence when their recurrent connections are subject to short-term depression, a common property of excitatory connections in early sensory areas. Dual time constant network behavior has also been implemented by nonlinear afferents producing a large transient input followed by much smaller steady state input. We show that such networks require unphysiologically large onset transients to produce the rise and decay observed in sensory areas. Our study explores how memory and persistence can be implemented in another model class, derivative feedback networks. We show that these networks can operate with two vastly different time courses, changing their state quickly when new information is coming in but retaining it for a long time, and that these capabilities are robust to short-term depression. Specifically, derivative feedback networks with short-term depression that acts differentially on positive and negative feedback projections are capable of dynamically changing their time constant, thus allowing fast onset and slow decay of responses without requiring unrealistically large input transients.

Slow diffusive dynamics in a chaotic balanced neural network

It has been proposed that neural noise in the cortex arises from chaotic dynamics in the balanced state: in this model of cortical dynamics, the excitatory and inhibitory inputs to each neuron approximately cancel, and activity is driven by fluctuations of the synaptic inputs around their mean. It remains unclear whether neural networks in the balanced state can perform tasks that are highly sensitive to noise, such as storage of continuous parameters in working memory, while also accounting for the irregular behavior of single neurons. Here we show that continuous parameter working memory can be maintained in the balanced state, in a neural circuit with a simple network architecture. We show analytically that in the limit of an infinite network, the dynamics generated by this architecture are characterized by a continuous set of steady balanced states, allowing for the indefinite storage of a continuous parameter. In finite networks, we show that the chaotic noise drives diffusive motion along the approximate attractor, which gradually degrades the stored memory. We analyze the dynamics and show that the slow diffusive motion induces slowly decaying temporal cross correlations in the activity, which differ substantially from those previously described in the balanced state. We calculate the diffusivity, and show that it is inversely proportional to the system size. For large enough (but realistic) neural population sizes, and with suitable tuning of the network connections, the proposed balanced network can sustain continuous parameter values in memory over time scales larger by several orders of magnitude than the single neuron time scale.

This work studies the effects of chaotic dynamics, a prominent feature of the balanced state model, on storage of continuous parameters in working memory. We propose a simple model of a balanced network with mutual inhibition, and show that it possesses a continuum of steady states, a commonly proposed mechanism for maintenance of continuous parameter working memory in the brain. We use analytical methods, combined with large scale numerical simulations, to analyze the diffusive dynamics and correlation patterns generated by the chaotic nature of the system. We obtain new conclusions and predictions on irregular activity resulting from the combination of continuous attractor dynamics with the balanced state. These include a prediction of measurable, slowly decaying spike correlations, and a quantification of how persistence depends on the neural population size.

The spatial structure of correlated neuronal variability

Shared neural variability is ubiquitous in cortical populations. While this variability is presumed to arise from overlapping synaptic input, its precise relationship to local circuit architecture remains unclear. We combine computational models and in vivo recordings to study the relationship between the spatial structure of connectivity and correlated variability in neural circuits. Extending the theory of networks with balanced excitation and inhibition, we find that spatially localized lateral projections promote weakly correlated spiking, but broader lateral projections produce a distinctive spatial correlation structure: nearby neuron pairs are positively correlated, pairs at intermediate distances are negatively correlated and distant pairs are weakly correlated. This non-monotonic dependence of correlation on distance is revealed in a new analysis of recordings from superficial layers of macaque primary visual cortex. Our findings show that incorporating distance-dependent connectivity improves the extent to which balanced network theory can explain correlated neural variability.

Efficient codes and balanced networks

Recent years have seen a growing interest in inhibitory interneurons and their circuits. A striking property of cortical inhibition is how tightly it balances excitation. Inhibitory currents not only match excitatory currents on average, but track them on a millisecond time scale, whether they are caused by external stimuli or spontaneous fluctuations. We review, together with experimental evidence, recent theoretical approaches that investigate the advantages of such tight balance for coding and computation. These studies suggest a possible revision of the dominant view that neurons represent information with firing rates corrupted by Poisson noise. Instead, tight excitatory/inhibitory balance may be a signature of a highly cooperative code, orders of magnitude more precise than a Poisson rate code. Moreover, tight balance may provide a template that allows cortical neurons to construct high-dimensional population codes and learn complex functions of their inputs.

Graded, Dynamically Routable Information Processing with Synfire-Gated Synfire Chains

Coherent neural spiking and local field potentials are believed to be signatures of the binding and transfer of information in the brain. Coherent activity has now been measured experimentally in many regions of mammalian cortex. Recently experimental evidence has been presented suggesting that neural information is encoded and transferred in packets, i.e., in stereotypical, correlated spiking patterns of neural activity. Due to their relevance to coherent spiking, synfire chains are one of the main theoretical constructs that have been appealed to in order to describe coherent spiking and information transfer phenomena. However, for some time, it has been known that synchronous activity in feedforward networks asymptotically either approaches an attractor with fixed waveform and amplitude, or fails to propagate. This has limited the classical synfire chain’s ability to explain graded neuronal responses. Recently, we have shown that pulse-gated synfire chains are capable of propagating graded information coded in mean population current or firing rate amplitudes. In particular, we showed that it is possible to use one synfire chain to provide gating pulses and a second, pulse-gated synfire chain to propagate graded information. We called these circuits synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded information can rapidly cascade through a neural circuit, and show a correspondence between this type of transfer and a mean-field model in which gating pulses overlap in time. We show that SGSCs are robust in the presence of variability in population size, pulse timing and synaptic strength. Finally, we demonstrate the computational capabilities of SGSC-based information coding by implementing a self-contained, spike-based, modular neural circuit that is triggered by streaming input, processes the input, then makes a decision based on the processed information and shuts itself down.

Cognitive tasks are associated with the dynamic excitation of neural assemblies. When we consider how quickly and flexibly such collectives may be formed and incorporated in a task, a persistent question has been: how can the brain rapidly evoke and involve different neural assemblies in a computation, when synaptic coupling changes only slowly? Here, we demonstrate mechanisms whereby information may be rapidly and selectively routed through a neural circuit, and sub-circuits may be turned on and off. The resulting information processing framework achieves the goal that has been pursued, but until now largely not attained, of achieving faithful, flexible information transfer across many synapses and dynamic excitation of neural assemblies with fixed connectivities.

Calcium regulation of HCN channels supports persistent activity in a multiscale model of neocortex

Neuronal persistent activity has been primarily assessed in terms of electrical mechanisms, without attention to the complex array of molecular events that also control cell excitability. We developed a multiscale neocortical model proceeding from the molecular to the network level to assess the contributions of calcium (Ca(2+)) regulation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels in providing additional and complementary support of continuing activation in the network. The network contained 776 compartmental neurons arranged in the cortical layers, connected using synapses containing AMPA/NMDA/GABAA/GABAB receptors. Metabotropic glutamate receptors (mGluR) produced inositol triphosphate (IP3) which caused the release of Ca(2+) from endoplasmic reticulum (ER) stores, with reuptake by sarco/ER Ca(2+)-ATP-ase pumps (SERCA), and influence on HCN channels. Stimulus-induced depolarization led to Ca(2+) influx via NMDA and voltage-gated Ca(2+) channels (VGCCs). After a delay, mGluR activation led to ER Ca(2+) release via IP3 receptors. These factors increased HCN channel conductance and produced firing lasting for ∼1min. The model displayed inter-scale synergies among synaptic weights, excitation/inhibition balance, firing rates, membrane depolarization, Ca(2+) levels, regulation of HCN channels, and induction of persistent activity. The interaction between inhibition and Ca(2+) at the HCN channel nexus determined a limited range of inhibition strengths for which intracellular Ca(2+) could prepare population-specific persistent activity. Interactions between metabotropic and ionotropic inputs to the neuron demonstrated how multiple pathways could contribute in a complementary manner to persistent activity. Such redundancy and complementarity via multiple pathways is a critical feature of biological systems. Mediation of activation at different time scales, and through different pathways, would be expected to protect against disruption, in this case providing stability for persistent activity.

Constructing Precisely Computing Networks with Biophysical Spiking Neurons

While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates. In equivalent spiking implementations, firing is assumed to be random such that averaging across populations of neurons recovers the rate-based approach. Recently, however, Denéve and colleagues have suggested that the spiking behavior of neurons may be fundamental to how neuronal networks compute, with precise spike timing determined by each neuron's contribution to producing the desired output (Boerlin and Denéve, 2011; Boerlin et al., 2013). By postulating that each neuron fires to reduce the error in the network's output, it was demonstrated that linear computations can be performed by networks of integrate-and-fire neurons that communicate through instantaneous synapses. This left open, however, the possibility that realistic networks, with conductance-based neurons with subthreshold nonlinearity and the slower timescales of biophysical synapses, may not fit into this framework. Here, we show how the spike-based approach can be extended to biophysically plausible networks. We then show that our network reproduces a number of key features of cortical networks including irregular and Poisson-like spike times and a tight balance between excitation and inhibition. Lastly, we discuss how the behavior of our model scales with network size or with the number of neurons "recorded" from a larger computing network. These results significantly increase the biological plausibility of the spike-based approach to network computation.

SIGNIFICANCE STATEMENT

We derive a network of neurons with standard spike-generating currents and synapses with realistic timescales that computes based upon the principle that the precise timing of each spike is important for the computation. We then show that our network reproduces a number of key features of cortical networks including irregular, Poisson-like spike times, and a tight balance between excitation and inhibition. These results significantly increase the biological plausibility of the spike-based approach to network computation, and uncover how several components of biological networks may work together to efficiently carry out computation.