Distributed and dynamical communication: a mechanism for flexible cortico-cortical interactions and its functional roles in visual attention.

Perceptual and cognitive processing relies on flexible communication among cortical areas; however, the underlying neural mechanism remains unclear. Here we report a mechanism based on the realistic spatiotemporal dynamics of propagating wave patterns in neural population activity. Using a biophysically plausible, multiarea spiking neural circuit model, we demonstrate that these wave patterns, characterized by their rich and complex dynamics, can account for a wide variety of empirically observed neural processes. The coordinated interactions of these wave patterns give rise to distributed and dynamic communication (DDC) that enables flexible and rapid routing of neural activity across cortical areas. We elucidate how DDC unifies the previously proposed oscillation synchronization-based and subspace-based views of interareal communication, offering experimentally testable predictions that we validate through the analysis of Allen Institute Neuropixels data. Furthermore, we demonstrate that DDC can be effectively modulated during attention tasks through the interplay of neuromodulators and cortical feedback loops. This modulation process explains many neural effects of attention, underscoring the fundamental functional role of DDC in cognition.

Self-Organization of Nonlinearly Coupled Neural Fluctuations Into Synergistic Population Codes.

Neural activity in the brain exhibits correlated fluctuations that may strongly influence the properties of neural population coding. However, how such correlated neural fluctuations may arise from the intrinsic neural circuit dynamics and subsequently affect the computational properties of neural population activity remains poorly understood. The main difficulty lies in resolving the nonlinear coupling between correlated fluctuations with the overall dynamics of the system. In this study, we investigate the emergence of synergistic neural population codes from the intrinsic dynamics of correlated neural fluctuations in a neural circuit model capturing realistic nonlinear noise coupling of spiking neurons. We show that a rich repertoire of spatial correlation patterns naturally emerges in a bump attractor network and further reveals the dynamical regime under which the interplay between differential and noise correlations leads to synergistic codes. Moreover, we find that negative correlations may induce stable bound states between two bumps, a phenomenon previously unobserved in firing rate models. These noise-induced effects of bump attractors lead to a number of computational advantages including enhanced working memory capacity and efficient spatiotemporal multiplexing and can account for a range of cognitive and behavioral phenomena related to working memory. This study offers a dynamical approach to investigating realistic correlated neural fluctuations and insights to their roles in cortical computations.

Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing.

The large-scale activity of the human brain exhibits rich and complex patterns, but the spatiotemporal dynamics of these patterns and their functional roles in cognition remain unclear. Here by characterizing moment-by-moment fluctuations of human cortical functional magnetic resonance imaging signals, we show that spiral-like, rotational wave patterns (brain spirals) are widespread during both resting and cognitive task states. These brain spirals propagate across the cortex while rotating around their phase singularity centres, giving rise to spatiotemporal activity dynamics with non-stationary features. The properties of these brain spirals, such as their rotational directions and locations, are task relevant and can be used to classify different cognitive tasks. We also demonstrate that multiple, interacting brain spirals are involved in coordinating the correlated activations and de-activations of distributed functional regions; this mechanism enables flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing. Our findings suggest that brain spirals organize complex spatiotemporal dynamics of the human brain and have functional correlates to cognitive processing.

Complexity of cortical wave patterns of the wake mouse cortex.

Rich spatiotemporal dynamics of cortical activity, including complex and diverse wave patterns, have been identified during unconscious and conscious brain states. Yet, how these activity patterns emerge across different levels of wakefulness remain unclear. Here we study the evolution of wave patterns utilizing data from high spatiotemporal resolution optical voltage imaging of mice transitioning from barbiturate-induced anesthesia to wakefulness (N = 5) and awake mice (N = 4). We find that, as the brain transitions into wakefulness, there is a reduction in hemisphere-scale voltage waves, and an increase in local wave events and complexity. A neural mass model recapitulates the essential cellular-level features and shows how the dynamical competition between global and local spatiotemporal patterns and long-range connections can explain the experimental observations. These mechanisms possibly endow the awake cortex with enhanced integrative processing capabilities.

Extended Anderson Criticality in Heavy-Tailed Neural Networks.

We investigate the emergence of complex dynamics in networks with heavy-tailed connectivity by developing a non-Hermitian random matrix theory. We uncover the existence of an extended critical regime of spatially multifractal fluctuations between the quiescent and active phases. This multifractal critical phase combines features of localization and delocalization and differs from the edge of chaos in classical networks by the appearance of universal hallmarks of Anderson criticality over an extended region in phase space. We show that the rich nonlinear response properties of the extended critical regime can account for a variety of neural dynamics such as the diversity of timescales, providing a computational advantage for persistent classification in a reservoir setting.

Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits.

A range of perceptual and cognitive processes have been characterized from the perspective of probabilistic representations and inference. To understand the neural circuit mechanism underlying these probabilistic computations, we develop a theory based on complex spatiotemporal dynamics of neural population activity. We first implement and explore this theory in a biophysically realistic, spiking neural circuit. Population activity patterns emerging from the circuit capture realistic variability or fluctuations of neural dynamics both in time and in space. These activity patterns implement a type of probabilistic computations that we name fractional neural sampling (FNS). We further develop a mathematical model to reveal the algorithmic nature of FNS and its computational advantages for representing multimodal distributions, a major challenge faced by existing theories. We demonstrate that FNS provides a unified account of a diversity of experimental observations of neural spatiotemporal dynamics and perceptual processes such as visual perception inference, and that FNS makes experimentally testable predictions.

A spatiotemporal mechanism of visual attention: Superdiffusive motion and theta oscillations of neural population activity patterns.

Recent evidence has demonstrated that during visual spatial attention sampling, neural activity and behavioral performance exhibit large fluctuations. To understand the origin of these fluctuations and their functional role, here, we introduce a mechanism based on the dynamical activity pattern (attention spotlight) emerging from neural circuit models in the transition regime between different dynamical states. This attention activity pattern with rich spatiotemporal dynamics flexibly samples from different stimulus locations, explaining many key aspects of temporal fluctuations such as variable theta oscillations of visual spatial attention. Moreover, the mechanism expands our understanding of how visual attention exploits spatially complex fluctuations characterized by superdiffusive motion in space and makes experimentally testable predictions. We further illustrate that attention sampling based on such spatiotemporal fluctuations provides profound functional advantages such as adaptive switching between exploitation and exploration activities and is particularly efficient at sampling natural scenes with multiple salient objects.

Anomalous diffusion dynamics of learning in deep neural networks.

Learning in deep neural networks (DNNs) is implemented through minimizing a highly non-convex loss function, typically by a stochastic gradient descent (SGD) method. This learning process can effectively find generalizable solutions at flat minima. In this study, we present a novel account of how such effective deep learning emerges through the interactions of the SGD and the geometrical structure of the loss landscape. We find that the SGD exhibits rich, complex dynamics when navigating through the loss landscape; initially, the SGD exhibits superdiffusion, which attenuates gradually and changes to subdiffusion at long times when approaching a solution. Such learning dynamics happen ubiquitously in different DNN types such as ResNet, VGG-like networks and Vision Transformers; similar results emerge for various batch size and learning rate settings. The superdiffusion process during the initial learning phase indicates that the motion of SGD along the loss landscape possesses intermittent, big jumps; this non-equilibrium property enables the SGD to effectively explore the loss landscape. By adapting methods developed for studying energy landscapes in complex physical systems, we find that such superdiffusive learning processes are due to the interactions of the SGD and the fractal-like regions of the loss landscape. We further develop a phenomenological model to demonstrate the mechanistic role of the fractal-like loss landscape in enabling the SGD to effectively find flat minima. Our results reveal the effectiveness of SGD in deep learning from a novel perspective and have implications for designing efficient deep neural networks.

Lévy walk dynamics explain gamma burst patterns in primate cerebral cortex.

Lévy walks describe patterns of intermittent motion with variable step sizes. In complex biological systems, Lévy walks (non-Brownian, superdiffusive random walks) are associated with behaviors such as search patterns of animals foraging for food. Here we show that Lévy walks also describe patterns of oscillatory activity in primate cerebral cortex. We used a combination of empirical observation and modeling to investigate high-frequency (gamma band) local field potential activity in visual motion-processing cortical area MT of marmoset monkeys. We found that gamma activity is organized as localized burst patterns that propagate across the cortical surface with Lévy walk dynamics. Lévy walks are fundamentally different from either global synchronization, or regular propagating waves, because they include large steps that enable activity patterns to move rapidly over cortical modules. The presence of Lévy walk dynamics therefore represents a previously undiscovered mode of brain activity, and implies a novel way for the cortex to compute. We apply a biophysically realistic circuit model to explain that the Lévy walk dynamics arise from critical-state transitions between asynchronous and localized propagating wave states, and that these dynamics yield optimal spatial sampling of the cortical sheet. We hypothesise that Lévy walk dynamics could help the cortex to efficiently process variable inputs, and to find links in patterns of activity among sparsely spiking populations of neurons.

Cortex-Wide Dynamics of Intrinsic Electrical Activities: Propagating Waves and Their Interactions.

Cortical circuits generate patterned activities that reflect intrinsic brain dynamics that lay the foundation for any, including stimuli-evoked, cognition and behavior. However, the spatiotemporal organization properties and principles of this intrinsic activity have only been partially elucidated because of previous poor resolution of experimental data and limited analysis methods. Here we investigated continuous wave patterns in the 0.5-4 Hz (delta band) frequency range on data from high-spatiotemporal resolution optical voltage imaging of the upper cortical layers in anesthetized mice. Waves of population activities propagate in heterogeneous directions to coordinate neuronal activities between different brain regions. The complex wave patterns show characteristics of both stereotypy and variety. The location and type of wave patterns determine the dynamical evolution when different waves interact with each other. Local wave patterns of source, sink, or saddle emerge at preferred spatial locations. Specifically, "source" patterns are predominantly found in cortical regions with low multimodal hierarchy such as the primary somatosensory cortex. Our findings reveal principles that govern the spatiotemporal dynamics of spontaneous cortical activities and associate them with the structural architecture across the cortex.SIGNIFICANCE STATEMENT Intrinsic brain activities, as opposed to external stimulus-evoked responses, have increasingly gained attention, but it remains unclear how these intrinsic activities are spatiotemporally organized at the cortex-wide scale. By taking advantage of the high spatiotemporal resolution of optical voltage imaging, we identified five wave pattern types, and revealed the organization properties of different wave patterns and the dynamical mechanisms when they interact with each other. Moreover, we found a relationship between the emergence probability of local wave patterns and the multimodal structure hierarchy across cortical areas. Our findings reveal the principles of spatiotemporal wave dynamics of spontaneous activities and associate them with the underlying hierarchical architecture across the cortex.

Fractal spike dynamics and neuronal coupling in the primate visual system.

KEY POINTS: We measured fractal (self-similar) fluctuations in ongoing spiking activity in subcortical (lateral geniculate nucleus, LGN) and cortical (area MT) visual areas in anaesthetised marmosets. Cells in the evolutionary ancient koniocellular LGN pathway and in area MT show high-amplitude fractal fluctuations, whereas evolutionarily newer parvocellular and magnocellular LGN cells do not. Spiking activity in koniocellular cells and MT cells shows substantial correlation to the local population activity, whereas activity in parvocellular and magnocellular cells is less correlated with local activity. We develop a model consisting of a fractal process and a global rate modulation which can reproduce and explain the fundamental relationship between fractal fluctuations and population coupling in LGN and MT. The model provides a unified account of apparently disparate aspects of neural spiking activity and can improve our understanding of information processing in evolutionary ancient and modern visual pathways. ABSTRACT: The brain represents and processes information through patterns of spiking activity, which is influenced by local and widescale brain circuits as well as intrinsic neural dynamics. Whether these influences have independent or linked effects on spiking activity is, however, not known. Here we measured spiking activity in two visual centres, the lateral geniculate nucleus (LGN) and cortical area MT, in marmoset monkeys. By combining the Fano-factor time curve, power spectral analysis and rescaled range analysis, we reveal inherent fractal fluctuations of spiking activity in LGN and MT. We found that the evolutionary ancient koniocellular (K) pathway in LGN and area MT exhibits strong fractal fluctuations at short (<1 s) time scales. Parvocellular (P) and magnocellular (M) LGN cells show weaker fractal fluctuations at longer (multi-second) time scales. In both LGN and MT, the amplitude and time scale of fractal fluctuations can explain short and long time scale spiking dynamics. We further show differential neuronal coupling of LGN and MT cells to local population spiking activity. The population coupling is intrinsically linked to fractal fluctuations: neurons showing stronger fluctuations are more strongly correlated to the local population activity. To understand this relationship, we modelled spiking activity using a fractal inhomogeneous Poisson process with dynamic rate, which is the product of an intrinsic stochastic fractal rate and a global modulatory gain. Our model explains the intrinsic links between neuronal spike rate and population coupling in LGN and MT, and establishes a unified account of dynamic spiking properties in afferent visual pathways.

Computing by modulating spontaneous cortical activity patterns as a mechanism of active visual processing.

Cortical populations produce complex spatiotemporal activity spontaneously without sensory inputs. However, the fundamental computational roles of such spontaneous activity remain unclear. Here, we propose a new neural computation mechanism for understanding how spontaneous activity is actively involved in cortical processing: Computing by Modulating Spontaneous Activity (CMSA). Using biophysically plausible circuit models, we demonstrate that spontaneous activity patterns with dynamical properties, as found in empirical observations, are modulated or redistributed by external stimuli to give rise to neural responses. We find that this CMSA mechanism of generating neural responses provides profound computational advantages, such as actively speeding up cortical processing. We further reveal that the CMSA mechanism provides a unifying explanation for many experimental findings at both the single-neuron and circuit levels, and that CMSA in response to natural stimuli such as face images is the underlying neurophysiological mechanism of perceptual "bubbles" as found in psychophysical studies.

Complex Dynamics of Propagating Waves in a Two-Dimensional Neural Field.

Propagating waves with complex dynamics have been widely observed in neural population activity. To understand their formation mechanisms, we investigate a type of two-dimensional neural field model by systematically varying its recurrent excitatory and inhibitory inputs. We show that the neural field model exhibits a rich repertoire of dynamical activity states when the relevant strength of excitation and inhibition is increased, ranging from localized rotating and traveling waves to global waves. Particularly, near the transition between stable states of rotating and traveling waves, the model exhibits a bistable state; that is, both the rotating and the traveling waves can exist, and the inclusion of noise can induce spontaneous transitions between them. Furthermore, we demonstrate that when there are multiple propagating waves, they exhibit rich collective propagation dynamics with variable propagating speeds and trajectories. We use techniques from time series analysis such detrended fluctuation analysis to characterize the effect of the strength of excitation and inhibition on these collective dynamics, which range from purely random motion to motion with long-range spatiotemporal correlations. These results provide insights into the possible contribution of excitation and inhibition toward a range of previously observed spatiotemporal wave phenomena.

Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits.

Experimental studies have begun revealing essential properties of the structural connectivity and the spatiotemporal activity dynamics of cortical circuits. To integrate these properties from anatomy and physiology, and to elucidate the links between them, we develop a novel cortical circuit model that captures a range of realistic features of synaptic connectivity. We show that the model accounts for the emergence of higher-order connectivity structures, including highly connected hub neurons that form an interconnected rich-club. The circuit model exhibits a rich repertoire of dynamical activity states, ranging from asynchronous to localized and global propagating wave states. We find that around the transition between asynchronous and localized propagating wave states, our model quantitatively reproduces a variety of major empirical findings regarding neural spatiotemporal dynamics, which otherwise remain disjointed in existing studies. These dynamics include diverse coupling (correlation) between spiking activity of individual neurons and the population, dynamical wave patterns with variable speeds and precise temporal structures of neural spikes. We further illustrate how these neural dynamics are related to the connectivity properties by analysing structural contributions to variable spiking dynamics and by showing that the rich-club structure is related to the diverse population coupling. These findings establish an integrated account of structural connectivity and activity dynamics of local cortical circuits, and provide new insights into understanding their working mechanisms.

Detection and analysis of spatiotemporal patterns in brain activity.

There is growing evidence that population-level brain activity is often organized into propagating waves that are structured in both space and time. Such spatiotemporal patterns have been linked to brain function and observed across multiple recording methodologies and scales. The ability to detect and analyze these patterns is thus essential for understanding the working mechanisms of neural circuits. Here we present a mathematical and computational framework for the identification and analysis of multiple classes of wave patterns in neural population-level recordings. By drawing a conceptual link between spatiotemporal patterns found in the brain and coherent structures such as vortices found in turbulent flows, we introduce velocity vector fields to characterize neural population activity. These vector fields are calculated for both phase and amplitude of oscillatory neural signals by adapting optical flow estimation methods from the field of computer vision. Based on these velocity vector fields, we then introduce order parameters and critical point analysis to detect and characterize a diverse range of propagating wave patterns, including planar waves, sources, sinks, spiral waves, and saddle patterns. We also introduce a novel vector field decomposition method that extracts the dominant spatiotemporal structures in a recording. This enables neural data to be represented by the activity of a small number of independent spatiotemporal modes, providing an alternative to existing dimensionality reduction techniques which separate space and time components. We demonstrate the capabilities of the framework and toolbox with simulated data, local field potentials from marmoset visual cortex and optical voltage recordings from whole mouse cortex, and we show that pattern dynamics are non-random and are modulated by the presence of visual stimuli. These methods are implemented in a MATLAB toolbox, which is freely available under an open-source licensing agreement.

Functional mechanisms underlie the emergence of a diverse range of plasticity phenomena.

Diverse plasticity mechanisms are orchestrated to shape the spatiotemporal dynamics underlying brain functions. However, why these plasticity rules emerge and how their dynamics interact with neural activity to give rise to complex neural circuit dynamics remains largely unknown. Here we show that both Hebbian and homeostatic plasticity rules emerge from a functional perspective of neuronal dynamics whereby each neuron learns to encode its own activity in the population activity, so that the activity of the presynaptic neuron can be decoded from the activity of its postsynaptic neurons. We explain how a range of experimentally observed plasticity phenomena with widely separated time scales emerge from learning this encoding function, including STDP and its frequency dependence, and metaplasticity. We show that when implemented in neural circuits, these plasticity rules naturally give rise to essential neural response properties, including variable neural dynamics with balanced excitation and inhibition, and approximately log-normal distributions of synaptic strengths, while simultaneously encoding a complex real-world visual stimulus. These findings establish a novel function-based account of diverse plasticity mechanisms, providing a unifying framework relating plasticity, dynamics and neural computation.

Maintenance of postsynaptic neuronal excitability by a positive feedback loop of postsynaptic BDNF expression.

Experiments have demonstrated that in mice, the PVT strongly projects to the CeL and participates in the formation of fear memories by synaptic potentiation in the amygdala. Herein, we propose a mathematical model based on a positive feedback loop of BDNF expression and signaling to investigate PVT manipulation of synaptic potentiation. The model is validated by comparisons with experimental observations. We find that a high postsynaptic firing frequency after stimulation is induced by presynaptic Ca2+ when the rates of BDNF secretion from PVT and LA neurons to the CeL are above a threshold value. Moreover, the positive feedback of postsynaptic BDNF production is important for the maintenance of the high excitability of the SOM+ CeL neuron after stimulation. The model brings insight into the underlying mechanisms of PVT modulation of synaptic potentiation at LA-CeL synapses and provides a framework of understanding other similar processes associated with synaptic plasticity.

Critical Dynamics of Natural Time-Varying Images.

A deep understanding of the dynamical properties of natural time-varying images is essential for interpreting how they are efficiently processed in the brain. Here we examine natural time-varying images from the perspective of their spatiotemporal patterns and find evidence of dynamical thermodynamic criticality. We further demonstrate that these spatiotemporal patterns ubiquitously organize as localized, propagating patterns. By studying these propagating patterns and their spreading dynamics over time, we demonstrate that the critical dynamics of natural time-varying images belong to the universality class of directed percolation. These critical dynamics have important implications for understanding neural processing of time-varying stimuli.

Dynamical patterns underlying response properties of cortical circuits.

Recent experimental studies show cortical circuit responses to external stimuli display varied dynamical properties. These include stimulus strength-dependent population response patterns, a shift from synchronous to asynchronous states and a decline in neural variability. To elucidate the mechanisms underlying these response properties and explore how they are mechanistically related, we develop a neural circuit model that incorporates two essential features widely observed in the cerebral cortex. The first feature is a balance between excitatory and inhibitory inputs to individual neurons; the second feature is distance-dependent connectivity. We show that applying a weak external stimulus to the model evokes a wave pattern propagating along lateral connections, but a strong external stimulus triggers a localized pattern; these stimulus strength-dependent population response patterns are quantitatively comparable with those measured in experimental studies. We identify network mechanisms underlying this population response, and demonstrate that the dynamics of population-level response patterns can explain a range of prominent features in neural responses, including changes to the dynamics of neurons' membrane potentials and synaptic inputs that characterize the shift of cortical states, and the stimulus-evoked decline in neuron response variability. Our study provides a unified population activity pattern-based view of diverse cortical response properties, thus shedding new insights into cortical processing.

Visual Motion Discrimination by Propagating Patterns in Primate Cerebral Cortex.

Visual stimuli can evoke waves of neural activity that propagate across the surface of visual cortical areas. The relevance of these waves for visual processing is unknown. Here, we measured the phase and amplitude of local field potentials (LFPs) in electrode array recordings from the motion-processing medial temporal (MT) area of anesthetized male marmosets. Animals viewed grating or dot-field stimuli drifting in different directions. We found that, on individual trials, the direction of LFP wave propagation is sensitive to the direction of stimulus motion. Propagating LFP patterns are also detectable in trial-averaged activity, but the trial-averaged patterns exhibit different dynamics and behaviors from those in single trials and are similar across motion directions. We show that this difference arises because stimulus-sensitive propagating patterns are present in the phase of single-trial oscillations, whereas the trial-averaged signal is dominated by additive amplitude effects. Our results demonstrate that propagating LFP patterns can represent sensory inputs at timescales relevant to visually guided behaviors and raise the possibility that propagating activity patterns serve neural information processing in area MT and other cortical areas.SIGNIFICANCE STATEMENT Propagating wave patterns are widely observed in the cortex, but their functional relevance remains unknown. We show here that visual stimuli generate propagating wave patterns in local field potentials (LFPs) in a movement-sensitive area of the primate cortex and that the propagation direction of these patterns is sensitive to stimulus motion direction. We also show that averaging LFP signals across multiple stimulus presentations (trial averaging) yields propagating patterns that capture different dynamic properties of the LFP response and show negligible direction sensitivity. Our results demonstrate that sensory stimuli can modulate propagating wave patterns reliably in the cortex. The relevant dynamics are normally masked by trial averaging, which is a conventional step in LFP signal processing.