Does the Cerebral Cortex Exploit High-Dimensional, Non-linear Dynamics for Information Processing?

Sequential activity of CA1 hippocampal cells constitutes a temporal memory map for associative learning in mice

Sequential neural dynamics encoded by time cells play a crucial role in hippocampal function. However, the role of hippocampal sequential neural dynamics in associative learning is an open question. We used two-photon Ca2+ imaging of dorsal CA1 (dCA1) neurons in the stratum pyramidale (SP) in head-fixed mice performing a go-no go associative learning task to investigate how odor valence is temporally encoded in this area of the brain. We found that SP cells responded differentially to the rewarded or unrewarded odor. The stimuli were decoded accurately from the activity of the neuronal ensemble, and accuracy increased substantially as the animal learned to differentiate the stimuli. Decoding the stimulus from individual SP cells responding differentially revealed that decision-making took place at discrete times after stimulus presentation. Lick prediction decoded from the ensemble activity of cells in dCA1 correlated linearly with lick behavior. Our findings indicate that sequential activity of SP cells in dCA1 constitutes a temporal memory map used for decision-making in associative learning. VIDEO ABSTRACT.

Dynamic fading memory and expectancy effects in the monkey primary visual cortex

In order to investigate the involvement of the primary visual cortex (V1) in working memory (WM), parallel, multisite recordings of multi-unit activity were obtained from monkey V1 while the animals performed a delayed match-to-sample (DMS) task. During the delay period, V1 population firing rate vectors maintained a lingering trace of the sample stimulus that could be reactivated by intervening impulse stimuli that enhanced neuronal firing. This fading trace of the sample did not require active engagement of the monkeys in the DMS task and likely reflects the intrinsic dynamics of recurrent cortical networks in lower visual areas. This renders an active, attention-dependent involvement of V1 in the maintenance of WM contents unlikely. By contrast, population responses to the test stimulus depended on the probabilistic contingencies between sample and test stimuli. Responses to tests that matched expectations were reduced which agrees with concepts of predictive coding.

Joint encoding of stimulus and decision in monkey primary visual cortex

We investigated whether neurons in monkey primary visual cortex (V1) exhibit mixed selectivity for sensory input and behavioral choice. Parallel multisite spiking activity was recorded from area V1 of awake monkeys performing a delayed match-to-sample task. The monkeys had to make a forced choice decision of whether the test stimulus matched the preceding sample stimulus. The population responses evoked by the test stimulus contained information about both the identity of the stimulus and with some delay but before the onset of the motor response the forthcoming choice. The results of subspace identification analysis indicate that stimulus-specific and decision-related information coexists in separate subspaces of the high-dimensional population activity, and latency considerations suggest that the decision-related information is conveyed by top-down projections.

Contribution of membrane-associated oscillators to biological timing at different timescales

Environmental rhythms such as the daily light-dark cycle selected for endogenous clocks. These clocks predict regular environmental changes and provide the basis for well-timed adaptive homeostasis in physiology and behavior of organisms. Endogenous clocks are oscillators that are based on positive feedforward and negative feedback loops. They generate stable rhythms even under constant conditions. Since even weak interactions between oscillators allow for autonomous synchronization, coupling/synchronization of oscillators provides the basis of self-organized physiological timing. Amongst the most thoroughly researched clocks are the endogenous circadian clock neurons in mammals and insects. They comprise nuclear clockworks of transcriptional/translational feedback loops (TTFL) that generate ∼24 h rhythms in clock gene expression entrained to the environmental day-night cycle. It is generally assumed that this TTFL clockwork drives all circadian oscillations within and between clock cells, being the basis of any circadian rhythm in physiology and behavior of organisms. Instead of the current gene-based hierarchical clock model we provide here a systems view of timing. We suggest that a coupled system of autonomous TTFL and posttranslational feedback loop (PTFL) oscillators/clocks that run at multiple timescales governs adaptive, dynamic homeostasis of physiology and behavior. We focus on mammalian and insect neurons as endogenous oscillators at multiple timescales. We suggest that neuronal plasma membrane-associated signalosomes constitute specific autonomous PTFL clocks that generate localized but interlinked oscillations of membrane potential and intracellular messengers with specific endogenous frequencies. In each clock neuron multiscale interactions of TTFL and PTFL oscillators/clocks form a temporally structured oscillatory network with a common complex frequency-band comprising superimposed multiscale oscillations. Coupling between oscillator/clock neurons provides the next level of complexity of an oscillatory network. This systemic dynamic network of molecular and cellular oscillators/clocks is suggested to form the basis of any physiological homeostasis that cycles through dynamic homeostatic setpoints with a characteristic frequency-band as hallmark. We propose that mechanisms of homeostatic plasticity maintain the stability of these dynamic setpoints, whereas Hebbian plasticity enables switching between setpoints via coupling factors, like biogenic amines and/or neuropeptides. They reprogram the network to a new common frequency, a new dynamic setpoint. Our novel hypothesis is up for experimental challenge.

SpikeShip: A method for fast, unsupervised discovery of high-dimensional neural spiking patterns

Neural coding and memory formation depend on temporal spiking sequences that span high-dimensional neural ensembles. The unsupervised discovery and characterization of these spiking sequences requires a suitable dissimilarity measure to spiking patterns, which can then be used for clustering and decoding. Here, we present a new dissimilarity measure based on optimal transport theory called SpikeShip, which compares multi-neuron spiking patterns based on all the relative spike-timing relationships among neurons. SpikeShip computes the optimal transport cost to make all the relative spike-timing relationships (across neurons) identical between two spiking patterns. We show that this transport cost can be decomposed into a temporal rigid translation term, which captures global latency shifts, and a vector of neuron-specific transport flows, which reflect inter-neuronal spike timing differences. SpikeShip can be effectively computed for high-dimensional neuronal ensembles, has a low (linear) computational cost that has the same order as the spike count, and is sensitive to higher-order correlations. Furthermore, SpikeShip is binless, can handle any form of spike time distributions, is not affected by firing rate fluctuations, can detect patterns with a low signal-to-noise ratio, and can be effectively combined with a sliding window approach. We compare the advantages and differences between SpikeShip and other measures like SPIKE and Victor-Purpura distance. We applied SpikeShip to large-scale Neuropixel recordings during spontaneous activity and visual encoding. We show that high-dimensional spiking sequences detected via SpikeShip reliably distinguish between different natural images and different behavioral states. These spiking sequences carried complementary information to conventional firing rate codes. SpikeShip opens new avenues for studying neural coding and memory consolidation by rapid and unsupervised detection of temporal spiking patterns in high-dimensional neural ensembles.

Robust encoding of natural stimuli by neuronal response sequences in monkey visual cortex

Parallel multisite recordings in the visual cortex of trained monkeys revealed that the responses of spatially distributed neurons to natural scenes are ordered in sequences. The rank order of these sequences is stimulus-specific and maintained even if the absolute timing of the responses is modified by manipulating stimulus parameters. The stimulus specificity of these sequences was highest when they were evoked by natural stimuli and deteriorated for stimulus versions in which certain statistical regularities were removed. This suggests that the response sequences result from a matching operation between sensory evidence and priors stored in the cortical network. Decoders trained on sequence order performed as well as decoders trained on rate vectors but the former could decode stimulus identity from considerably shorter response intervals than the latter. A simulated recurrent network reproduced similarly structured stimulus-specific response sequences, particularly once it was familiarized with the stimuli through non-supervised Hebbian learning. We propose that recurrent processing transforms signals from stationary visual scenes into sequential responses whose rank order is the result of a Bayesian matching operation. If this temporal code were used by the visual system it would allow for ultrafast processing of visual scenes.

The fractal brain: scale-invariance in structure and dynamics

The past 40 years have witnessed extensive research on fractal structure and scale-free dynamics in the brain. Although considerable progress has been made, a comprehensive picture has yet to emerge, and needs further linking to a mechanistic account of brain function. Here, we review these concepts, connecting observations across different levels of organization, from both a structural and functional perspective. We argue that, paradoxically, the level of cortical circuits is the least understood from a structural point of view and perhaps the best studied from a dynamical one. We further link observations about scale-freeness and fractality with evidence that the environment provides constraints that may explain the usefulness of fractal structure and scale-free dynamics in the brain. Moreover, we discuss evidence that behavior exhibits scale-free properties, likely emerging from similarly organized brain dynamics, enabling an organism to thrive in an environment that shares the same organizational principles. Finally, we review the sparse evidence for and try to speculate on the functional consequences of fractality and scale-freeness for brain computation. These properties may endow the brain with computational capabilities that transcend current models of neural computation and could hold the key to unraveling how the brain constructs percepts and generates behavior.

A hybrid biological neural network model for solving problems in cognitive planning

A variety of behaviors, like spatial navigation or bodily motion, can be formulated as graph traversal problems through cognitive maps. We present a neural network model which can solve such tasks and is compatible with a broad range of empirical findings about the mammalian neocortex and hippocampus. The neurons and synaptic connections in the model represent structures that can result from self-organization into a cognitive map via Hebbian learning, i.e. into a graph in which each neuron represents a point of some abstract task-relevant manifold and the recurrent connections encode a distance metric on the manifold. Graph traversal problems are solved by wave-like activation patterns which travel through the recurrent network and guide a localized peak of activity onto a path from some starting position to a target state.

Kv2.1 Potassium Channels Regulate Repetitive Burst Firing in Extratelencephalic Neocortical Pyramidal Neurons

Coincidence detection and cortical rhythmicity are both greatly influenced by neurons' propensity to fire bursts of action potentials. In the neocortex, repetitive burst firing can also initiate abnormal neocortical rhythmicity (including epilepsy). Bursts are generated by inward currents that underlie a fast afterdepolarization (fADP) but less is known about outward currents that regulate bursting. We tested whether Kv2 channels regulate the fADP and burst firing in labeled layer 5 PNs from motor cortex of the Thy1-h mouse. Kv2 block with guangxitoxin-1E (GTx) converted single spike responses evoked by dendritic stimulation into multispike bursts riding on an enhanced fADP. Immunohistochemistry revealed that Thy1-h PNs expressed Kv2.1 (not Kv2.2) channels perisomatically (not in the dendrites). In somatic macropatches, GTx-sensitive current was the largest component of outward current with biophysical properties well-suited for regulating bursting. GTx drove ~40% of Thy1 PNs stimulated with noisy somatic current steps to repetitive burst firing and shifted the maximal frequency-dependent gain. A network model showed that reduction of Kv2-like conductance in a small subset of neurons resulted in repetitive bursting and entrainment of the circuit to seizure-like rhythmic activity. Kv2 channels play a dominant role in regulating onset bursts and preventing repetitive bursting in Thy1 PNs.

Recurrent dynamics in the cerebral cortex: Integration of sensory evidence with stored knowledge

Current concepts of sensory processing in the cerebral cortex emphasize serial extraction and recombination of features in hierarchically structured feed-forward networks in order to capture the relations among the components of perceptual objects. These concepts are implemented in convolutional deep learning networks and have been validated by the astounding similarities between the functional properties of artificial systems and their natural counterparts. However, cortical architectures also display an abundance of recurrent coupling within and between the layers of the processing hierarchy. This massive recurrence gives rise to highly complex dynamics whose putative function is poorly understood. Here a concept is proposed that assigns specific functions to the dynamics of cortical networks and combines, in a unifying approach, the respective advantages of recurrent and feed-forward processing. It is proposed that the priors about regularities of the world are stored in the weight distributions of feed-forward and recurrent connections and that the high-dimensional, dynamic space provided by recurrent interactions is exploited for computations. These comprise the ultrafast matching of sensory evidence with the priors covertly represented in the correlation structure of spontaneous activity and the context-dependent grouping of feature constellations characterizing natural objects. The concept posits that information is encoded not only in the discharge frequency of neurons but also in the precise timing relations among the discharges. Results of experiments designed to test the predictions derived from this concept support the hypothesis that cerebral cortex exploits the high-dimensional recurrent dynamics for computations serving predictive coding.

A Primer on Hyperdimensional Computing for iEEG Seizure Detection

A central challenge in today's care of epilepsy patients is that the disease dynamics are severely under-sampled in the currently typical setting with appointment-based clinical and electroencephalographic examinations. Implantable devices to monitor electrical brain signals and to detect epileptic seizures may significantly improve this situation and may inform personalized treatment on an unprecedented scale. These implantable devices should be optimized for energy efficiency and compact design. Energy efficiency will ease their maintenance by reducing the time of recharging, or by increasing the lifetime of their batteries. Biological nervous systems use an extremely small amount of energy for information processing. In recent years, a number of methods, often collectively referred to as brain-inspired computing, have also been developed to improve computation in non-biological hardware. Here, we give an overview of one of these methods, which has in particular been inspired by the very size of brains' circuits and termed hyperdimensional computing. Using a tutorial style, we set out to explain the key concepts of hyperdimensional computing including very high-dimensional binary vectors, the operations used to combine and manipulate these vectors, and the crucial characteristics of the mathematical space they inhabit. We then demonstrate step-by-step how hyperdimensional computing can be used to detect epileptic seizures from intracranial electroencephalogram (EEG) recordings with high energy efficiency, high specificity, and high sensitivity. We conclude by describing potential future clinical applications of hyperdimensional computing for the analysis of EEG and non-EEG digital biomarkers.

Relation between gamma oscillations and neuronal plasticity in the visual cortex

Learning is thought to be mediated by activity-dependent modification of neuronal interactions. To avoid maladaptive modifications of synaptic transmission by spurious activity, synaptic plasticity has to be gated. In the case of supervised learning, these gating functions are accomplished by reinforcement through value-assigning systems. Here we show that the dynamic state of local circuits correlates with the occurrence of activity-dependent long-term changes in neuronal response properties. We find that repeated visual stimuli induce long-term changes of orientation preference of neuronal populations in visual cortex if stimuli induce synchronized population responses oscillating at ɣ-frequencies. This suggests that neuronal plasticity is controlled by a hierarchy of gating systems and assigns critical gating functions to resonance properties of local circuits.

Use-dependent long-term changes of neuronal response properties must be gated to prevent irrelevant activity from inducing inappropriate modifications. Here we test the hypothesis that local network dynamics contribute to such gating. As synaptic modifications depend on temporal contiguity between presynaptic and postsynaptic activity, we examined the effect of synchronized gamma (ɣ) oscillations on stimulation-dependent modifications of orientation selectivity in adult cat visual cortex. Changes of orientation maps were induced by pairing visual stimulation with electrical activation of the mesencephalic reticular formation. Changes in orientation selectivity were assessed with optical recording of intrinsic signals and multiunit recordings. When conditioning stimuli were associated with strong ɣ-oscillations, orientation domains matching the orientation of the conditioning grating stimulus became more responsive and expanded, because neurons with preferences differing by less than 30° from the orientation of the conditioning grating shifted their orientation preference toward the conditioned orientation. When conditioning stimuli induced no or only weak ɣ-oscillations, responsiveness of neurons driven by the conditioning stimulus decreased. These differential effects depended on the power of oscillations in the low ɣ-band (20 Hz to 48 Hz) and not on differences in discharge rate of cortical neurons, because there was no correlation between the discharge rates during conditioning and the occurrence of changes in orientation preference. Thus, occurrence and polarity of use-dependent long-term changes of cortical response properties appear to depend on the occurrence of ɣ-oscillations during induction and hence on the degree of temporal coherence of the change-inducing network activity.

Increase in Mutual Information During Interaction with the Environment Contributes to Perception

Perception and motor interaction with physical surroundings can be analyzed by the changes in probability laws governing two possible outcomes of neuronal activity, namely the presence or absence of spikes (binary states). Perception and motor interaction with the physical environment are partly accounted for by a reduction in entropy within the probability distributions of binary states of neurons in distributed neural circuits, given the knowledge about the characteristics of stimuli in physical surroundings. This reduction in the total entropy of multiple pairs of circuits in networks, by an amount equal to the increase of mutual information, occurs as sensory information is processed successively from lower to higher cortical areas or between different areas at the same hierarchical level, but belonging to different networks. The increase in mutual information is partly accounted for by temporal coupling as well as synaptic connections as proposed by Bahmer and Gupta (Front. Neurosci. 2018). We propose that robust increases in mutual information, measuring the association between the characteristics of sensory inputs' and neural circuits' connectivity patterns, are partly responsible for perception and successful motor interactions with physical surroundings. The increase in mutual information, given the knowledge about environmental sensory stimuli and the type of motor response produced, is responsible for the coupling between action and perception. In addition, the processing of sensory inputs within neural circuits, with no prior knowledge of the occurrence of a sensory stimulus, increases Shannon information. Consequently, the increase in surprise serves to increase the evidence of the sensory model of physical surroundings.

The multidimensional brain

Brain activity takes place in three spatial-plus time dimensions. This rather obvious claim has been recently questioned by papers that, taking into account the big data outburst and novel available computational tools, are starting to unveil a more intricate state of affairs. Indeed, various brain activities and their correlated mental functions can be assessed in terms of trajectories embedded in phase spaces of dimensions higher than the canonical ones. In this review, I show how further dimensions may not just represent a convenient methodological tool that allows a better mathematical treatment of otherwise elusive cortical activities, but may also reflect genuine functional or anatomical relationships among real nervous functions. I then describe how to extract hidden multidimensional information from real or artificial neurodata series, and make clear how our mind dilutes, rather than concentrates as currently believed, inputs coming from the environment. Finally, I argue that the principle "the higher the dimension, the greater the information" may explain the occurrence of mental activities and elucidate the mechanisms of human diseases associated with dimensionality reduction.

High-dimensional dynamics in a single-transistor oscillator containing Feynman-Sierpiński resonators: Effect of fractal depth and irregularity

Fractal structures pervade nature and are receiving increasing engineering attention towards the realization of broadband resonators and antennas. We show that fractal resonators can support the emergence of high-dimensional chaotic dynamics even in the context of an elementary, single-transistor oscillator circuit. Sierpiński gaskets of variable depth are constructed using discrete capacitors and inductors, whose values are scaled according to a simple sequence. It is found that in regular fractals of this kind, each iteration effectively adds a conjugate pole/zero pair, yielding gradually more complex and broader frequency responses, which can also be implemented as much smaller Foster equivalent networks. The resonators are instanced in the circuit as one-port devices, replacing the inductors found in the initial version of the oscillator. By means of a highly simplified numerical model, it is shown that increasing the fractal depth elevates the dimension of the chaotic dynamics, leading to high-order hyperchaos. This result is overall confirmed by SPICE simulations and experiments, which however also reveal that the non-ideal behavior of physical components hinders obtaining high-dimensional dynamics. The issue could be practically mitigated by building the Foster equivalent networks rather than the verbatim fractals. Furthermore, it is shown that considerably more complex resonances, and consequently richer dynamics, can be obtained by rendering the fractal resonators irregular through reshuffling the inductors, or even by inserting a limited number of focal imperfections. The present results draw attention to the potential usefulness of fractal resonators for generating high-dimensional chaotic dynamics, and underline the importance of irregularities and component non-idealities.

Connecting occipital alpha band peak frequency, visual temporal resolution, and occipital GABA levels in healthy participants and hepatic encephalopathy patients

Recent studies have proposed a connection between the individual alpha band peak frequency and the temporal resolution of visual perception in healthy human participants. This connection rests on animal studies describing oscillations in the alpha band as a mode of phasic thalamocortical information transfer for low-level visual stimuli, which critically relies on GABAergic interneurons. Here, we investigated the interplay of these parameters by measuring occipital alpha band peak frequency by means of magnetoencephalography, visual temporal resolution by means of behavioral testing, and occipital GABA levels by means of magnetic resonance spectroscopy. Importantly, we investigated a sample of healthy participants and patients with varying grades of hepatic encephalopathy, which are known to exhibit decreases in the investigated parameters, thus providing an increased parameter space. We found that occipital alpha band peak frequency and visual temporal resolution were positively correlated, i.e., higher occipital alpha band peak frequencies were on average related to a higher temporal resolution. Likewise, occipital alpha band peak frequency correlated positively with occipital GABA levels. However, correlations were significant only when both healthy participants and patients were included in the analysis, thereby indicating a connection of the measures on group level (instead of the individual level). These findings provide new insights into neurophysiological and neurochemical underpinnings of visual perception.

Unsupervised clustering of temporal patterns in high-dimensional neuronal ensembles using a novel dissimilarity measure

Temporally ordered multi-neuron patterns likely encode information in the brain. We introduce an unsupervised method, SPOTDisClust (Spike Pattern Optimal Transport Dissimilarity Clustering), for their detection from high-dimensional neural ensembles. SPOTDisClust measures similarity between two ensemble spike patterns by determining the minimum transport cost of transforming their corresponding normalized cross-correlation matrices into each other (SPOTDis). Then, it performs density-based clustering based on the resulting inter-pattern dissimilarity matrix. SPOTDisClust does not require binning and can detect complex patterns (beyond sequential activation) even when high levels of out-of-pattern "noise" spiking are present. Our method handles efficiently the additional information from increasingly large neuronal ensembles and can detect a number of patterns that far exceeds the number of recorded neurons. In an application to neural ensemble data from macaque monkey V1 cortex, SPOTDisClust can identify different moving stimulus directions on the sole basis of temporal spiking patterns.

Neuronal oscillations: unavoidable and useful?

Neuronal systems have a high propensity to engage in oscillatory activity because both the properties of individual neurons and canonical circuit motifs favour rhythmic activity. In addition, coupled oscillators can engage in a large variety of dynamical regimes, ranging from synchronization with different phase offsets to chaotic behaviour. Which regime prevails depends on differences between preferred oscillation frequencies, coupling strength and coupling delays. The ability of delay coupled oscillator networks to generate a rich repertoire of temporally structured activation sequences is exploited by central pattern generator networks for the control of movements. However, it is less clear whether temporal patterning of neuronal discharges also plays a role in cognitive processes. Here, it will be argued that the temporal patterning of neuronal discharges emerging from delay coupled oscillator networks plays a pivotal role in all instances in which selective relations have to be established between the responses of distributed assemblies of neurons. Examples are the dynamic formation of functional networks, the selective routing of activity in densely interconnected networks, the attention-dependent selection of sensory signals, the fast and context-dependent binding of responses for further joint processing in pattern recognition and the formation of associations by learning. Special consideration is given to arguments that challenge a functional role of oscillations and synchrony in cognition because of the volatile nature of these phenomena and recent evidence will be reviewed suggesting that this volatility is functionally advantageous.

Revisiting the Quantum Brain Hypothesis: Toward Quantum (Neuro)biology?

The nervous system is a non-linear dynamical complex system with many feedback loops. A conventional wisdom is that in the brain the quantum fluctuations are self-averaging and thus functionally negligible. However, this intuition might be misleading in the case of non-linear complex systems. Because of an extreme sensitivity to initial conditions, in complex systems the microscopic fluctuations may be amplified and thereby affect the system's behavior. In this way quantum dynamics might influence neuronal computations. Accumulating evidence in non-neuronal systems indicates that biological evolution is able to exploit quantum stochasticity. The recent rise of quantum biology as an emerging field at the border between quantum physics and the life sciences suggests that quantum events could play a non-trivial role also in neuronal cells. Direct experimental evidence for this is still missing but future research should address the possibility that quantum events contribute to an extremely high complexity, variability and computational power of neuronal dynamics.