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Publication# How single neuron properties shape chaotic dynamics and signal transmission in random neural networks

Résumé

While most models of randomly connected neural networks assume single-neuron models with simple dynamics, neurons in the brain exhibit complex intrinsic dynamics over multiple timescales. We analyze how the dynamical properties of single neurons and recurrent connections interact to shape the effective dynamics in large randomly connected networks. A novel dynamical mean-field theory for strongly connected networks of multi-dimensional rate neurons shows that the power spectrum of the network activity in the chaotic phase emerges from a nonlinear sharpening of the frequency response function of single neurons. For the case of two-dimensional rate neurons with strong adaptation, we find that the network exhibits a state of resonant chaos, characterized by robust, narrow-band stochastic oscillations. The coherence of stochastic oscillations is maximal at the onset of chaos and their correlation time scales with the adaptation timescale of single units. Surprisingly, the resonance frequency can be predicted from the properties of isolated neurons, even in the presence of heterogeneity in the adaptation parameters. In the presence of these internally-generated chaotic fluctuations, the transmission of weak, low-frequency signals is strongly enhanced by adaptation, whereas signal transmission is not influenced by adaptation in the non-chaotic regime. Our theoretical framework can be applied to other mechanisms at the level of single neurons, such as synaptic filtering, refractoriness or spike synchronization. These results advance our understanding of the interaction between the dynamics of single units and recurrent connectivity, which is a fundamental step toward the description of biologically realistic neural networks. Author summary Biological neural networks are formed by a large number of neurons whose interactions can be extremely complex. Such systems have been successfully studied using random network models, in which the interactions among neurons are assumed to be random. However, the dynamics of single units are usually described using over-simplified models, which might not capture several salient features of real neurons. Here, we show how accounting for richer single-neuron dynamics results in shaping the network dynamics and determines which signals are better transmitted. We focus on adaptation, an important mechanism present in biological neurons that consists in the decrease of their firing rate in response to a sustained stimulus. Our mean-field approach reveals that the presence of adaptation shifts the network into a previously unreported dynamical regime, that we term resonant chaos, in which chaotic activity has a strong oscillatory component. Moreover, we show that this regime is advantageous for the transmission of low-frequency signals. Our work bridges the microscopic dynamics (single neurons) to the macroscopic dynamics (network), and shows how the global signal-transmission properties of the network can be controlled by acting on the single-neuron dynamics. These results paves the way for further developments that include more complex neural mechanisms, and considerably advance our understanding of realistic neural networks.

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Modèles du neurone biologique

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Réseau de neurones récurrents

Un réseau de neurones récurrents (RNN pour recurrent neural network en anglais) est un réseau de neurones artificiels présentant des connexions récurrentes. Un réseau de neurones récurrents est const

Adaptation (biologie)

En biologie, l'adaptation peut se définir d’une manière générale comme l’ajustement fonctionnel de l’être vivant au milieu, et, en particulier, comme l’appropriation de l’organe à sa fonction.
L’

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Humans and some other animals are able to perform tasks that require coordination of movements across multiple temporal scales, ranging from hundreds of milliseconds to several seconds. The fast timescale at which neurons naturally operate, on the order of tens of milliseconds, is well-suited to support motor control of rapid movements. In contrast, to coordinate movements on the order of seconds, a neural network should produce reliable dynamics on a similarly âslowâ timescale. Neurons and synapses exhibit biophysical mechanisms whose timescales range from tens of milliseconds to hours, which suggests a possible role of these mechanisms in producing slow reliable dynamics. However, how such mechanisms influence network dynamics is not yet understood. An alternative approach to achieve slow dynamics in a neural network consists in modifying its connectivity structure. Still, the limitations of this approach and in particular to what degree the weights require fine-tuning, remain unclear. Understanding how both the single neuron mechanisms and the connectivity structure might influence the network dynamics
to produce slow timescales is the main goal of this thesis.
We first consider the possibility of obtaining slow dynamics in binary networks by tuning their connectivity. It is known that binary networks can produce sequential dynamics. However, if the sequences consist of random patterns, the typical length of the longest sequence that can be produced grows linearly with the number of units. Here, we show that we can overcome this limitation by carefully designing the sequence structure. More precisely, we obtain a constructive proof that allows to obtain sequences whose length scales exponentially with the number of units. To achieve this however, one needs to exponentially fine-tune the connectivity matrix.
Next, we focus on the interaction between single neuron mechanisms and recurrent dynamics. Particular attention is dedicated to adaptation, which is known to have a broad range of timescales and is therefore particularly interesting for the subject of this thesis. We study the dynamics of a random network with adaptation using mean-field techniques, and we show that the network can enter a state of resonant chaos. Interestingly, the resonance frequency of this state is independent of the connectivity strength and depends only on the properties of the single neuron model. The approach used to study networks with adaptation can also be applied when considering linear rate units with an arbitrary number of auxiliary variables. Based on a qualitative analysis of the mean-field theory for a random network whose neurons are described by a D -dimensional rate model, we conclude that the statistics of the chaotic dynamics are strongly influenced by the single neuron model under investigation.
Using a reservoir computing approach, we show preliminary evidence that slow adaptation can be beneficial when performing tasks that require slow timescales. The positive impact of adaptation on the network performance is particularly strong in the presence of noise. Finally, we propose a network architecture in which the slowing-down effect due to adaptation is combined with a hierarchical structure, with the purpose of efficiently generate sequences that require multiple, hierarchically organized timescales.

Michele Giugliano, Eleni Vasilaki

Recent experimental data from the rodent cerebral cortex and olfactory bulb indicate that specific connectivity motifs are correlated with short-term dynamics of excitatory synaptic transmission. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form predominantly unidirectional pairwise connections. The cause of these structural differences in excitatory synaptic microcircuits is unknown. We show that these connectivity motifs emerge in networks of model neurons, from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). While the impact of STDP on SD was shown in simultaneous neuronal pair recordings in vitro, the mutual interactions between STDP and SD in large networks are still the subject of intense research. Our approach combines an SD phenomenological model with an STDP model that faithfully captures long-term plasticity dependence on both spike times and frequency. As a proof of concept, we first simulate and analyze recurrent networks of spiking neurons with random initial connection efficacies and where synapses are either all short-term facilitating or all depressing. For identical external inputs to the network, and as a direct consequence of internally generated activity, we find that networks with depressing synapses evolve unidirectional connectivity motifs, while networks with facilitating synapses evolve reciprocal connectivity motifs. We then show that the same results hold for heterogeneous networks, including both facilitating and depressing synapses. This does not contradict a recent theory that proposes that motifs are shaped by external inputs, but rather complements it by examining the role of both the external inputs and the internally generated network activity. Our study highlights the conditions under which SD-STDP might explain the correlation between facilitation and reciprocal connectivity motifs, as well as between depression and unidirectional motifs.

Our brain has the capacity to analyze a visual scene in a split second, to learn how to play an instrument, and to remember events, faces and concepts. Neurons underlie all of these diverse functions. Neurons, cells within the brain that generate and transmit electrical activity, communicate with each other through chemical synapses. These synaptic connections dynamically change with experience, a process referred to as synaptic plasticity, which is thought to be at the core of the brain's ability to learn and process the world in sophisticated ways. Our understanding of the rules of synaptic plasticity remains quite limited. To enable efficient computations among neurons or to serve as a trace of memory, synapses must create stable connectivity patterns between neurons. However there remains an insufficient theoretical explanation as to how stable connectivity patterns can form in the presence of synaptic plasticity. Since the dynamics of recurrently connected neurons depend upon their connections, which themselves change in response to the network dynamics, synaptic plasticity and network dynamics have to be treated as a compound system. Due to the nonlinear nature of the system this can be analytically challenging. Utilizing network simulations that model the interplay between the network connectivity and synaptic plasticity can provide valuable insights. However, many existing network models that implement biologically relevant forms of plasticity become unstable. This suggests that current models do not accurately describe the biological networks, which have no difficulty functioning without succumbing to exploding network activity. The instability in these network simulations could originate from the fact that theoretical studies have, almost exclusively, focused on Hebbian plasticity at excitatory synapses. Hebbian plasticity causes connected neurons that are active together to increase the connection strength between them. Biological networks, however, display a large variety of different forms of synaptic plasticity and homeostatic mechanisms, beyond Hebbian plasticity. Furthermore, inhibitory cells can undergo synaptic plasticity as well. These diverse forms of plasticity are active at the same time, and our understanding of the computational role of most of these synaptic dynamics remains elusive. This raises the important question as to whether forms of plasticity that have not been previously considered could -in combination with Hebbian plasticity- lead to stable network dynamics. Here we illustrate that by combining multiple forms of plasticity with distinct roles, a recurrently connected spiking network model self-organizes to distinguish and extract multiple overlapping external stimuli. Moreover we show that the acquired network structures remain stable over hours while plasticity is active. This long-term stability allows the network to function as an associative memory and to correctly classify distorted or partially cued stimuli. During intervals in which no stimulus is shown the network dynamically remembers the last stimulus as selective delay activity. Taken together this work suggest that multiple forms of plasticity and homeostasis on different timescales have to work together to create stable connectivity patterns in neuronal networks which enable them to perform relevant computation.