Self-organization in Balanced State Networks by STDP and Homeostatic Plasticity

Effenberger, Felix; Jost, Jürgen; Levina, Anna

doi:10.1371/journal.pcbi.1004420

Cited by 54 publications

(68 citation statements)

References 89 publications

(208 reference statements)

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“…389 A neuron with a high firing rate therefore has a higher probability of making its 390 outgoing weights larger, exploiting STDP to achieve a stronger influence on the network. 391 With the above, we replicate findings by Effenberger and colleagues ('driver 392 neurons', [19]), and extend them to inhibitory neurons. Moreover, the impact of a 393 neuron on the rest of the network should be a function of both its firing rate and its 394 outgoing weights (see Methods).…”

supporting

confidence: 82%

Neural oligarchy: how synaptic plasticity breeds neurons with extreme influence

Kleberg

Triesch

2018

Preprint

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Synapses between cortical neurons are subject to constant modifications through synaptic plasticity mechanisms, which are believed to underlie learning and memory formation. The strengths of excitatory and inhibitory synapses in the cortex follow a right-skewed long-tailed distribution. Similarly, the firing rates of excitatory and inhibitory neurons also follow a right-skewed long-tailed distribution. How these distributions come about and how they maintain their shape over time is currently not well understood. Here we propose a spiking neural network model that explains the origin of these distributions as a consequence of the interaction of spike-timing dependent plasticity (STDP) of excitatory and inhibitory synapses and a multiplicative form of synaptic normalisation. Specifically, we show that the combination of additive STDP and multiplicative normalisation leads to lognormal-like distributions of excitatory and inhibitory synaptic efficacies as observed experimentally. The shape of these distributions remains stable even if spontaneous fluctuations of synaptic efficacies are added. In the same network, lognormal-like distributions of the firing rates of excitatory and inhibitory neurons result from small variability in the spiking thresholds of individual neurons. Interestingly, we find that variation in firing rates is strongly coupled to variation in synaptic efficacies: neurons with the highest firing rates develop very strong connections onto other neurons. Finally, we define an impact measure for individual neurons and demonstrate the existence of a small group of neurons with an exceptionally strong impact on the network, that arise as a result of synaptic plasticity. In summary, synaptic plasticity and small variability in neuronal parameters underlie a neural oligarchy in recurrent neural networks. Author summaryOur brain's neural networks are composed of billions of neurons that exchange signals via trillions of synapses. Are these neurons created equal, or do they contribute in similar ways to the network dynamics? Or do some neurons wield much more power than others? Recent experiments have shown that some neurons are much more active than the average neuron and that some synaptic connections are much stronger than the average synaptic connection. However, it is still unclear how these properties come about in the brain. Here we present a neural network model that explains these findings as a result of the interaction of synaptic plasticity mechanisms that modify synapses' efficacies. The model reproduces recent findings on the statistics of neuronal firing rates PLOS

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confidence: 82%

Neural oligarchy: how synaptic plasticity breeds neurons with extreme influence

Kleberg

Triesch

2018

Preprint

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“…23 Moreover, the discovered skeleton of neurons with strong bi-directional links may help 24 to optimize information storage [15]. 25 In a recent paper [16], we have investigated the relation between connectivity and 26 system dynamics in small motifs of probabilistic neurons with binary outputs, assuming 27 discrete, ternary connection strengths. We found that the balance between excitatory 28 and inhibitory connections has a strong effect on the transition probabilities between 29 successive motif states, whereas the total density of non-zero connections is less 30 important.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, fine tuning of the balance 187 parameter can bring the system to the edge of the chaotic regime, where the outputs of 188 the neurons produce complex wave forms, and where the system may depend sensibly, 189 but still regularly, on external inputs. We speculate that this regime is most suitable for 190 purposes of neural information processing [20][21][22][23][24], and that biological brains may 191 therefore control the parameterb in a homeostatic way [1,25,26].…”

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confidence: 99%

Weight statistics controls dynamics in recurrent neural networks

Krauß

Schuster

Dietrich

et al. 2018

Preprint

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Recurrent neural networks are complex non-linear systems, capable of ongoing activity in the absence of driving inputs. The dynamical properties of these systems, in particular their long-time attractor states, are determined on the microscopic level by the connection strengths w ij between the individual neurons. However, little is known to which extent network dynamics is tunable on a more coarse-grained level by the statistical features of the weight matrix. In this work, we investigate the dynamical impact of three statistical parameters: density (the fraction of non-zero connections), balance (the ratio of excitatory to inhibitory connections), and symmetry (the fraction of neuron pairs with w ij = w ji ). By computing a 'phase diagram' of network dynamics, we find that balance is the essential control parameter: Its gradual increase from negative to positive values drives the system from oscillatory behavior into a chaotic regime, and eventually into stationary fix points. Only directly at the border of the chaotic regime do the neural networks display rich but regular dynamics, thus enabling actual information processing. These results suggest that the brain, too, is fine-tuned to the 'edge of chaos' by assuring a proper balance between excitatory and inhibitory neural connections. Author summaryComputations in the brain need to be both reproducible and sensitive to changing input from the environment. It has been shown that recurrent neural networks can meet these simultaneous requirements only in a particular dynamical regime, called the edge of chaos in non-linear systems theory. Here, we demonstrate that recurrent neural networks can be easily tuned to this critical regime of optimal information processing by assuring a proper ratio of excitatory and inhibitory connections between the neurons. This result is in line with several micro-anatomical studies of the cortex, which frequently confirm that the excitatory-inhibitory balance is strictly conserved in the cortex. Furthermore, it turns out that neural dynamics is largely independent from the total density of connections, a feature that explains how the brain remains functional during periods of growth or decay. Finally, we find that the existence of too many symmetric connections is detrimental for the above mentioned critical dynamical regime, but maybe in turn useful for pattern completion tasks.

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“…Modularity, the presence of clusters of elements that are more densely connected witch each other than with 17 the rest of the network, is a ubiquitous topological feature of complex networks and, in particular, structural 18 brain networks at various scales of organization [1]. 19 Modularity was among the first topological features of complex networks to be associated with a systematic 20 impact on dynamical network processes. Random walks are trapped in modules [2], the synchronization of 21 coupled oscillators over time maps out the modular organization of a graph [3] and co-activation patterns of 22 excitable dynamics tend to reflect the graph's modular organization [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…Given the well accepted role of synaptic plasticity in brain 39 development and activity-dependent adaptation [19], other perspectives focus on changes driven by such local 40 plasticity mechanisms in physiologically more realistic models. A considerable proportion of this work aims at 41 explaining empirically observed distributions of physiological parameters at the cellular scale, such as synaptic 42 weights [20], and only a few studies have paid attention to topological aspects, such as the proportion of local 43 motifs [21]. Some of the mentioned modeling studies showed an emergence of modular network structure and 44 attempted to provide an underlying mechanism based on the reinforcement of paths between highly correlated 45 nodes [22].…”

Section: Introductionmentioning

confidence: 99%

Topological Reinforcement as a Principle of Modularity Emergence in Brain Networks

Damicelli

Hilgetag

Hütt

et al. 2018

Preprint

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1Modularity is a ubiquitous topological feature of structural brain networks at various scales. While a variety of 2 potential mechanisms have been proposed, the fundamental principles by which modularity emerges in neural 3 networks remain elusive. We tackle this question with a plasticity model of neural networks derived from a 4 purely topological perspective. Our topological reinforcement model acts enhancing the topological overlap 5 between nodes, iteratively connecting a randomly selected node to a non-neighbor with the highest topological 6 overlap, while pruning another network link at random. This rule reliably evolves synthetic random networks 7 toward a modular architecture. Such final modular structure reflects initial 'proto-modules', thus allowing 8 to predict the modules of the evolved graph. Subsequently, we show that this topological selection principle 9 might be biologically implemented as a Hebbian rule. Concretely, we explore a simple model of excitable 10 dynamics, where the plasticity rule acts based on the functional connectivity between nodes represented by 11 co-activations. Results produced by the activity-based model are consistent with the ones from the purely 12 topological rule, showing a consistent final network configuration. Our findings suggest that the selective 13 reinforcement of topological overlap may be a fundamental mechanism by which brain networks evolve toward 14 modular structure. 15

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Self-organization in Balanced State Networks by STDP and Homeostatic Plasticity

Cited by 54 publications

References 89 publications

Neural oligarchy: how synaptic plasticity breeds neurons with extreme influence

Neural oligarchy: how synaptic plasticity breeds neurons with extreme influence

Weight statistics controls dynamics in recurrent neural networks

Topological Reinforcement as a Principle of Modularity Emergence in Brain Networks

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