Oscillatory recurrent gated neural integrator circuits (ORGaNICs), a unifying theoretical framework for neural dynamics

Unconditional stability of a recurrent neural circuit implementing divisive normalization

Stability in recurrent neural models poses a significant challenge, particularly in developing biologically plausible neurodynamical models that can be seamlessly trained. Traditional cortical circuit models are notoriously difficult to train due to expansive nonlinearities in the dynamical system, leading to an optimization problem with nonlinear stability constraints that are difficult to impose. Conversely, recurrent neural networks (RNNs) excel in tasks involving sequential data but lack biological plausibility and interpretability. In this work, we address these challenges by linking dynamic divisive normalization (DN) to the stability of "oscillatory recurrent gated neural integrator circuits" (ORGaNICs), a biologically plausible recurrent cortical circuit model that dynamically achieves DN and that has been shown to simulate a wide range of neurophysiological phenomena. By using the indirect method of Lyapunov, we prove the remarkable property of unconditional local stability for an arbitrary-dimensional ORGaNICs circuit when the recurrent weight matrix is the identity. We thus connect ORGaNICs to a system of coupled damped harmonic oscillators, which enables us to derive the circuit's energy function, providing a normative principle of what the circuit, and individual neurons, aim to accomplish. Further, for a generic recurrent weight matrix, we prove the stability of the 2D model and demonstrate empirically that stability holds in higher dimensions. Finally, we show that ORGaNICs can be trained by backpropagation through time without gradient clipping/scaling, thanks to its intrinsic stability property and adaptive time constants, which address the problems of exploding, vanishing, and oscillating gradients. By evaluating the model's performance on RNN benchmarks, we find that ORGaNICs outperform alternative neurodynamical models on static image classification tasks and perform comparably to LSTMs on sequential tasks.

Cellular psychology: relating cognition to context-sensitive pyramidal cells

'Cellular psychology' is a new field of inquiry that studies dendritic mechanisms for adapting mental events to the current context, thus increasing their coherence, flexibility, effectiveness, and comprehensibility. Apical dendrites of neocortical pyramidal cells have a crucial role in cognition - those dendrites receive input from diverse sources, including feedback, and can amplify the cell's feedforward transmission if relevant in that context. Specialized subsets of inhibitory interneurons regulate this cooperative context-sensitive processing by increasing or decreasing amplification. Apical input has different effects on cellular output depending on whether we are awake, deeply asleep, or dreaming. Furthermore, wakeful thought and imagery may depend on apical input. High-resolution neuroimaging in humans supports and complements evidence on these cellular mechanisms from other mammals.

Neuronal heterogeneity of normalization strength in a circuit model

The size of a neuron's receptive field increases along the visual hierarchy. Neurons in higher-order visual areas integrate information through a canonical computation called normalization, where neurons respond sublinearly to multiple stimuli in the receptive field. Neurons in the visual cortex exhibit highly heterogeneous degrees of normalization. Recent population recordings from visual cortex find that the interactions between neurons, measured by spike count correlations, depend on their normalization strengths. However, the circuit mechanism underlying the heterogeneity of normalization is unclear. In this work, we study normalization in a spiking neuron network model of visual cortex. The model produces a range of neuronal heterogeneity of normalization strength and the heterogeneity is highly correlated with the inhibitory current each neuron receives. Our model reproduces the dependence of spike count correlations on normalization as observed in experimental data, which is explained by the covariance with the inhibitory current. We find that neurons with stronger normalization are more sensitive to contrast differences in images and encode information more efficiently. In addition, networks with more heterogeneity in normalization encode more information about visual stimuli. Together, our model provides a mechanistic explanation of heterogeneous normalization strengths in the visual cortex, and sheds new light on the computational benefits of neuronal heterogeneity.

Can human brain connectivity explain verbal working memory?

The ability of humans to store spoken words in verbal working memory and build extensive vocabularies is believed to stem from evolutionary changes in cortical connectivity across primate species. However, the underlying neurobiological mechanisms remain unclear. Why can humans acquire vast vocabularies, while non-human primates cannot? This study addresses this question using brain-constrained neural networks that realize between-species differences in cortical connectivity. It investigates how these structural differences support the formation of neural representations for spoken words and the emergence of verbal working memory, crucial for human vocabulary building. We develop comparative models of frontotemporal and occipital cortices, reflecting human and non-human primate neuroanatomy. Using meanfield and spiking neural networks, we simulate auditory word recognition and examine verbal working memory function. The "human models", characterized by denser inter-area connectivity in core language areas, produced larger cell assemblies than the "monkey models", with specific topographies reflecting semantic properties of the represented words. Crucially, longer-lasting reverberant neural activity was observed in human versus monkey architectures, compatible with robust verbal working memory, a necessary condition for vocabulary building. Our findings offer insights into the structural basis of human-specific symbol learning and verbal working memory, shedding light on humans' unique capacity for large vocabulary acquisition.

Dysfunctions of cellular context-sensitivity in neurodevelopmental learning disabilities

Pyramidal neurons have a pivotal role in the cognitive capabilities of neocortex. Though they have been predominantly modeled as integrate-and-fire point processors, many of them have another point of input integration in their apical dendrites that is central to mechanisms endowing them with the sensitivity to context that underlies basic cognitive capabilities. Here we review evidence implicating impairments of those mechanisms in three major neurodevelopmental disabilities, fragile X, Down syndrome, and fetal alcohol spectrum disorders. Multiple dysfunctions of the mechanisms by which pyramidal cells are sensitive to context are found to be implicated in all three syndromes. Further deciphering of these cellular mechanisms would lead to the understanding of and therapies for learning disabilities beyond any that are currently available.

Cellular mechanisms of cooperative context-sensitive predictive inference

We argue that prediction success maximization is a basic objective of cognition and cortex, that it is compatible with but distinct from prediction error minimization, that neither objective requires subtractive coding, that there is clear neurobiological evidence for the amplification of predicted signals, and that we are unconvinced by evidence proposed in support of subtractive coding. We outline recent discoveries showing that pyramidal cells on which our cognitive capabilities depend usually transmit information about input to their basal dendrites and amplify that transmission when input to their distal apical dendrites provides a context that agrees with the feedforward basal input in that both are depolarizing, i.e., both are excitatory rather than inhibitory. Though these intracellular discoveries require a level of technical expertise that is beyond the current abilities of most neuroscience labs, they are not controversial and acclaimed as groundbreaking. We note that this cellular cooperative context-sensitivity greatly enhances the cognitive capabilities of the mammalian neocortex, and that much remains to be discovered concerning its evolution, development, and pathology.

Modeling the diverse effects of divisive normalization on noise correlations

Divisive normalization, a prominent descriptive model of neural activity, is employed by theories of neural coding across many different brain areas. Yet, the relationship between normalization and the statistics of neural responses beyond single neurons remains largely unexplored. Here we focus on noise correlations, a widely studied pairwise statistic, because its stimulus and state dependence plays a central role in neural coding. Existing models of covariability typically ignore normalization despite empirical evidence suggesting it affects correlation structure in neural populations. We therefore propose a pairwise stochastic divisive normalization model that accounts for the effects of normalization and other factors on covariability. We first show that normalization modulates noise correlations in qualitatively different ways depending on whether normalization is shared between neurons, and we discuss how to infer when normalization signals are shared. We then apply our model to calcium imaging data from mouse primary visual cortex (V1), and find that it accurately fits the data, often outperforming a popular alternative model of correlations. Our analysis indicates that normalization signals are often shared between V1 neurons in this dataset. Our model will enable quantifying the relation between normalization and covariability in a broad range of neural systems, which could provide new constraints on circuit mechanisms of normalization and their role in information transmission and representation.

A manifold neural population code for space in hippocampal coactivity dynamics independent of place fields

Hippocampus place cell discharge is temporally unreliable across seconds and days, and place fields are multimodal, suggesting an "ensemble cofiring" spatial coding hypothesis with manifold dynamics that does not require reliable spatial tuning, in contrast to hypotheses based on place field (spatial tuning) stability. We imaged mouse CA1 (cornu ammonis 1) ensembles in two environments across three weeks to evaluate these coding hypotheses. While place fields "remap," being more distinct between than within environments, coactivity relationships generally change less. Decoding location and environment from 1-s ensemble location-specific activity is effective and improves with experience. Decoding environment from cell-pair coactivity relationships is also effective and improves with experience, even after removing place tuning. Discriminating environments from 1-s ensemble coactivity relies crucially on the cells with the most anti-coactive cell-pair relationships because activity is internally organized on a low-dimensional manifold of non-linear coactivity relationships that intermittently reregisters to environments according to the anti-cofiring subpopulation activity.

Waves traveling over a map of visual space can ignite short-term predictions of sensory input

Recent analyses have found waves of neural activity traveling across entire visual cortical areas in awake animals. These traveling waves modulate the excitability of local networks and perceptual sensitivity. The general computational role of these spatiotemporal patterns in the visual system, however, remains unclear. Here, we hypothesize that traveling waves endow the visual system with the capacity to predict complex and naturalistic inputs. We present a network model whose connections can be rapidly and efficiently trained to predict individual natural movies. After training, a few input frames from a movie trigger complex wave patterns that drive accurate predictions many frames into the future solely from the network's connections. When the recurrent connections that drive waves are randomly shuffled, both traveling waves and the ability to predict are eliminated. These results suggest traveling waves may play an essential computational role in the visual system by embedding continuous spatiotemporal structures over spatial maps.

Different eigenvalue distributions encode the same temporal tasks in recurrent neural networks

Different brain areas, such as the cortex and, more specifically, the prefrontal cortex, show great recurrence in their connections, even in early sensory areas. Several approaches and methods based on trained networks have been proposed to model and describe these regions. It is essential to understand the dynamics behind the models because they are used to build different hypotheses about the functioning of brain areas and to explain experimental results. The main contribution here is the description of the dynamics through the classification and interpretation carried out with a set of numerical simulations. This study sheds light on the multiplicity of solutions obtained for the same tasks and shows the link between the spectra of linearized trained networks and the dynamics of the counterparts. The patterns in the distribution of the eigenvalues of the recurrent weight matrix were studied and properly related to the dynamics in each task.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09802-5.

Coordinated multiplexing of information about separate objects in visual cortex

Sensory receptive fields are large enough that they can contain more than one perceptible stimulus. How, then, can the brain encode information about each of the stimuli that may be present at a given moment? We recently showed that when more than one stimulus is present, single neurons can fluctuate between coding one vs. the other(s) across some time period, suggesting a form of neural multiplexing of different stimuli (Caruso et al., 2018). Here, we investigate (a) whether such coding fluctuations occur in early visual cortical areas; (b) how coding fluctuations are coordinated across the neural population; and (c) how coordinated coding fluctuations depend on the parsing of stimuli into separate vs. fused objects. We found coding fluctuations do occur in macaque V1 but only when the two stimuli form separate objects. Such separate objects evoked a novel pattern of V1 spike count ('noise') correlations involving distinct distributions of positive and negative values. This bimodal correlation pattern was most pronounced among pairs of neurons showing the strongest evidence for coding fluctuations or multiplexing. Whether a given pair of neurons exhibited positive or negative correlations depended on whether the two neurons both responded better to the same object or had different object preferences. Distinct distributions of spike count correlations based on stimulus preferences were also seen in V4 for separate objects but not when two stimuli fused to form one object. These findings suggest multiple objects evoke different response dynamics than those evoked by single stimuli, lending support to the multiplexing hypothesis and suggesting a means by which information about multiple objects can be preserved despite the apparent coarseness of sensory coding.

Neural Algorithms and Circuits for Motor Planning

The brain plans and executes volitional movements. The underlying patterns of neural population activity have been explored in the context of movements of the eyes, limbs, tongue, and head in nonhuman primates and rodents. How do networks of neurons produce the slow neural dynamics that prepare specific movements and the fast dynamics that ultimately initiate these movements? Recent work exploits rapid and calibrated perturbations of neural activity to test specific dynamical systems models that are capable of producing the observed neural activity. These joint experimental and computational studies show that cortical dynamics during motor planning reflect fixed points of neural activity (attractors). Subcortical control signals reshape and move attractors over multiple timescales, causing commitment to specific actions and rapid transitions to movement execution. Experiments in rodents are beginning to reveal how these algorithms are implemented at the level of brain-wide neural circuits.

Neural circuit mechanisms of hierarchical sequence learning tested on large-scale recording data

The brain performs various cognitive functions by learning the spatiotemporal salient features of the environment. This learning requires unsupervised segmentation of hierarchically organized spike sequences, but the underlying neural mechanism is only poorly understood. Here, we show that a recurrent gated network of neurons with dendrites can efficiently solve difficult segmentation tasks. In this model, multiplicative recurrent connections learn a context-dependent gating of dendro-somatic information transfers to minimize error in the prediction of somatic responses by the dendrites. Consequently, these connections filter the redundant input features represented by the dendrites but unnecessary in the given context. The model was tested on both synthetic and real neural data. In particular, the model was successful for segmenting multiple cell assemblies repeating in large-scale calcium imaging data containing thousands of cortical neurons. Our results suggest that recurrent gating of dendro-somatic signal transfers is crucial for cortical learning of context-dependent segmentation tasks.

Implicit-explicit gradient of nondual awareness or consciousness as such

Consciousness is multi-dimensional but is most often portrayed with a two-dimensional (2D) map that has global levels or states on one axis and phenomenal contents on the other. On this map, awareness is conflated either with general alertness or with phenomenal content. This contributes to ongoing difficulties in the scientific understanding of consciousness. Previously, I have proposed that consciousness as such or nondual awareness-a basic non-conceptual, non-propositional awareness in itself free of subject-object fragmentation-is a unique kind that cannot be adequately specified by this 2D map of states and contents. Here, I propose an implicit-explicit gradient of nondual awareness to be added as the z-axis to the existing 2D map of consciousness. This gradient informs about the degree to which nondual awareness is manifest in any experience, independent of the specifics of global state or local content. Alternatively, within the multi-dimensional state space model of consciousness, nondual awareness can be specified by several vectors, each representing one of its properties. In the first part, I outline nondual awareness or consciousness as such in terms of its phenomenal description, its function and its neural correlates. In the second part, I explore the implicit-explicit gradient of nondual awareness and how including it as an additional axis clarifies certain features of everyday dualistic experiences and is especially relevant for understanding the unitary and nondual experiences accessed via different contemplative methods, mind-altering substances or spontaneously.

Gated Recurrent Units Viewed Through the Lens of Continuous Time Dynamical Systems

Gated recurrent units (GRUs) are specialized memory elements for building recurrent neural networks. Despite their incredible success on various tasks, including extracting dynamics underlying neural data, little is understood about the specific dynamics representable in a GRU network. As a result, it is both difficult to know a priori how successful a GRU network will perform on a given task, and also their capacity to mimic the underlying behavior of their biological counterparts. Using a continuous time analysis, we gain intuition on the inner workings of GRU networks. We restrict our presentation to low dimensions, allowing for a comprehensive visualization. We found a surprisingly rich repertoire of dynamical features that includes stable limit cycles (nonlinear oscillations), multi-stable dynamics with various topologies, and homoclinic bifurcations. At the same time we were unable to train GRU networks to produce continuous attractors, which are hypothesized to exist in biological neural networks. We contextualize the usefulness of different kinds of observed dynamics and support our claims experimentally.

Superimposed gratings induce diverse response patterns of gamma oscillations in primary visual cortex

Stimulus-dependence of gamma oscillations (GAMMA, 30-90 Hz) has not been fully understood, but it is important for revealing neural mechanisms and functions of GAMMA. Here, we recorded spiking activity (MUA) and the local field potential (LFP), driven by a variety of plaids (generated by two superimposed gratings orthogonal to each other and with different contrast combinations), in the primary visual cortex of anesthetized cats. We found two distinct narrow-band GAMMAs in the LFPs and a variety of response patterns to plaids. Similar to MUA, most response patterns showed that the second grating suppressed GAMMAs driven by the first one. However, there is only a weak site-by-site correlation between cross-orientation interactions in GAMMAs and those in MUAs. We developed a normalization model that could unify the response patterns of both GAMMAs and MUAs. Interestingly, compared with MUAs, the GAMMAs demonstrated a wider range of model parameters and more diverse response patterns to plaids. Further analysis revealed that normalization parameters for high GAMMA, but not those for low GAMMA, were significantly correlated with the discrepancy of spatial frequency between stimulus and sites' preferences. Consistent with these findings, normalization parameters and diversity of high GAMMA exhibited a clear transition trend and region difference between area 17 to 18. Our results show that GAMMAs are also regulated in the form of normalization, but that the neural mechanisms for these normalizations might differ from those of spiking activity. Normalizations in different brain signals could be due to interactions of excitation and inhibitions at multiple stages in the visual system.

A recurrent circuit implements normalization, simulating the dynamics of V1 activity

The normalization model has been applied to explain neural activity in diverse neural systems including primary visual cortex (V1). The model's defining characteristic is that the response of each neuron is divided by a factor that includes a weighted sum of activity of a pool of neurons. Despite the success of the normalization model, there are three unresolved issues. 1) Experimental evidence supports the hypothesis that normalization in V1 operates via recurrent amplification, i.e., amplifying weak inputs more than strong inputs. It is unknown how normalization arises from recurrent amplification. 2) Experiments have demonstrated that normalization is weighted such that each weight specifies how one neuron contributes to another's normalization pool. It is unknown how weighted normalization arises from a recurrent circuit. 3) Neural activity in V1 exhibits complex dynamics, including gamma oscillations, linked to normalization. It is unknown how these dynamics emerge from normalization. Here, a family of recurrent circuit models is reported, each of which comprises coupled neural integrators to implement normalization via recurrent amplification with arbitrary normalization weights, some of which can recapitulate key experimental observations of the dynamics of neural activity in V1.

Transformation of speech sequences in human sensorimotor circuits

After we listen to a series of words, we can silently replay them in our mind. Does this mental replay involve a reactivation of our original perceptual dynamics? We recorded electrocorticographic (ECoG) activity across the lateral cerebral cortex as people heard and then mentally rehearsed spoken sentences. For each region, we tested whether silent rehearsal of sentences involved reactivation of sentence-specific representations established during perception or transformation to a distinct representation. In sensorimotor and premotor cortex, we observed reliable and temporally precise responses to speech; these patterns transformed to distinct sentence-specific representations during mental rehearsal. In contrast, we observed less reliable and less temporally precise responses in prefrontal and temporoparietal cortex; these higher-order representations, which were sensitive to sentence semantics, were shared across perception and rehearsal of the same sentence. The mental rehearsal of natural speech involves the transformation of stimulus-locked speech representations in sensorimotor and premotor cortex, combined with diffuse reactivation of higher-order semantic representations.

Oscillatory recurrent gated neural integrator circuits (ORGaNICs), a unifying theoretical framework for neural dynamics

Working memory is an example of a cognitive and neural process that is not static but evolves dynamically with changing sensory inputs; another example is motor preparation and execution. We introduce a theoretical framework for neural dynamics, based on oscillatory recurrent gated neural integrator circuits (ORGaNICs), and apply it to simulate key phenomena of working memory and motor control. The model circuits simulate neural activity with complex dynamics, including sequential activity and traveling waves of activity, that manipulate (as well as maintain) information during working memory. The same circuits convert spatial patterns of premotor activity to temporal profiles of motor control activity and manipulate (e.g., time warp) the dynamics. Derivative-like recurrent connectivity, in particular, serves to manipulate and update internal models, an essential feature of working memory and motor execution. In addition, these circuits incorporate recurrent normalization, to ensure stability over time and robustness with respect to perturbations of synaptic weights.