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Adaptive self-organization in a realistic neural network model
Christian Meisel, Thilo Gross
TL;DR
Few generative mechanisms explain how neural networks might maintain criticality as they adapt. This paper tests adaptive self-organization driven by spike-time-dependent plasticity in a realistic neural model. The network evolves to a critical state marked by power laws in synaptic conductance and synchronization.
Problem
Few generative mechanisms explain how neural networks can maintain criticality while their structure changes.
Source: §I · p. 1Method
The paper models integrate-and-fire neural activity coupled to slower, spike-time-dependent plasticity that updates network topology.
Source: §I · p. 2, §II · p. 2Results
The networks robustly evolve to critical states with power-law distributions of synaptic conductances and the synchronization order parameter Csyn.
Source: §IV · p. 5Takeaways & Limitations
The results support adaptive-network dynamics as a mechanism that can robustly self-organize realistic neural-network models to critical states.
Source: §IV · p. 5
Abstract
from arXiv · showhide
Information processing in complex systems is often found to be maximally efficient close to critical states associated with phase transitions. It is therefore conceivable that also neural information processing operates close to criticality. This is further supported by the observation of power-law distributions, which are a hallmark of phase transitions. An important open question is how neural networks could remain close to a critical point while undergoing a continual change in the course of development, adaptation, learning, and more. An influential contribution was made by Bornholdt and Rohlf, introducing a generic mechanism of robust self-organized criticality in adaptive networks. Here, we address the question whether this mechanism is relevant for real neural networks. We show in a realistic model that spike-time-dependent synaptic plasticity can self-organize neural networks robustly toward criticality. Our model reproduces several empirical observations and makes testable predictions on the distribution of synaptic strength, relating them to the critical state of the network. These results suggest that the interplay between dynamics and topology may be essential for neural information processing.
I. INTRODUCTION
Neural criticality has empirical support, but few generative mechanisms explain how networks maintain it. This work tests whether adaptive self-organization driven by spike-time-dependent plasticity can robustly bring a realistic neural model to a critical state.
I. INTRODUCTION
- Neural criticality is supported by power-law patterns in neuronal avalanches, EEG spectra, and human fMRI and MEG synchronization measures.Earlier work links criticality to information transfer, storage, and sensitivity to external stimuli.Source: §I · p. 1
- Despite empirical evidence for neural criticality, few generative mechanisms explain it, and a robust mechanism should restore criticality after perturbation.Adaptive networks combine changing topology with dynamics in network nodes.Source: §I · p. 1
- Neural activity and network topology evolve on separate timescales: activity is faster, while topology changes according to time-averaged activity.Topology changes include developing connections and synaptic plasticity.Source: §I · p. 1
- Adaptive networks can use local topological update rules to drive the network toward criticality by exploiting information about global topology in node dynamics.Prior work showed that adaptive networks can exhibit robust self-organized criticality based on simple local rules [16–18].Source: §I · p. 1
- Spike-time-dependent plasticity robustly brings the realistic neural-network model to a critical state different from those reached by activity-dependent plasticity.The proposed mechanism couples neural dynamics with topological adaptation.Source: §I · p. 2
II. DESCRIPTION OF THE MODEL
The model combines integrate-and-fire neuronal activity with slower STDP-driven changes to network topology. It simulates activity to an attractor before applying topology updates, while using simplified network scale and stronger-than-realistic synapses to keep simulations feasible.
II. DESCRIPTION OF THE MODEL
- The model uses leaky integrate-and-fire neurons in an 80% excitatory, 20% inhibitory network, with spikes triggering threshold reset and delayed transmission.Between inputs, membrane potential returns exponentially to rest; after threshold crossing, neurons reset for a refractory period.Source: §II · p. 2
- The simulation runs on a quasi-static topology until neurons average 100 spikes or activity stops, then applies the topology update after the attractor is reached.Further simulation on the attractor adds no information, and the exact duration is immaterial if it is sufficiently long.Source: §II · p. 2
- STDP tracks elapsed time since each neuron's last spike and spike count, while pairwise variables encode spike order and give stronger updates to closer-spaced spikes.The pairwise variable increases for the sequence i, j and decreases for j, i.Source: §II · p. 2
- One update variant creates or deletes synapses according to normalized pairwise STDP correlation, while another increases or decreases synaptic weights within zero-to-one bounds.The connection-formation threshold is θ_STDP = 0.4, and new synapses use g_c = 0.15.Source: §II · p. 2
- The model omits detailed brain-area organization and realistic neuron and synapse counts; feasible connectivity requires unrealistically strong synapses.Activity self-organizes, so lowering synapse counts raises self-organized conductance levels, while fixing conductance low raises synapse counts.Source: §II · pp. 2–3
III. RESULTS
STDP drives networks toward a characteristic connectivity near the synchrony transition, with power-law behavior in spike-time correlations and synaptic weights. The evolved connectivity scales with network size and synaptic conductance, while empirical weight data resemble the model distribution but do not establish whole-brain criticality.
III. RESULTS
- Different initial connectivities converge to a characteristic Kev, robust to initial conditions and tested numerical-constant variation.The representative N = 500 simulation spans 20,000 iterations, corresponding to at least 6,000 seconds.Source: §III · p. 3, Figure 1 · p. 3
- K∞ = 2.58, a = 266.1, and β = 1.382 fit the system-size scaling; b = 0.1633, γ = 1.565, and c = −0.3916 fit its conductance dependence.The conductance-dependent scaling was evaluated across different synaptic conductances.Source: §III · p. 3, Figure 2 · p. 3
- At gc = 0.000375, the extrapolated K∞ ≈ 40000 is a rough estimate in the order of magnitude of observed cortical connectivity.The estimate uses about 20 excitatory inputs to reach spike threshold and is explicitly described as a rough extrapolation.Source: §III · p. 3
- The STDP-driven connectivity change pushes networks toward the synchrony transition, although long-range topology correlations can shift the threshold from the static-network value.The threshold KSTDP approximately corresponds to the self-organized connectivity K∞, but an exact match is not expected.Source: §III · p. 4
- At the self-organized state, Csyn follows a power law over one decade, with the figure indicating exponent −2 despite strong numerical cutoffs.The authors treat this scaling as additional evidence for dynamical criticality.Source: §III · p. 4, Figure 4 · p. 5
- Synaptic weights follow a power law with exponent −1.5, and the critical state contains many zero weights, whose fraction depends strongly on synapse count.The same distribution was also observed with different and/or asymmetric strengthening and weakening rates.Source: §III · p. 4, Figure 4 · p. 5
- Combined experimental weight datasets resemble the model distribution, but the authors caution that this does not establish whole-brain self-organized criticality.For several individual brain-area datasets, tests could not exclude a power law whose best-fit exponent closely matches −1.5.Source: §III · pp. 4–5, Figure 4 · p. 5
IV. DISCUSSION
The realistic model robustly evolves toward a critical state with power laws in synaptic conductances and the synchronization order parameter. The discussion distinguishes this STDP-driven synchronization transition from the order-disorder transition associated with activity-dependent plasticity, while noting that the evolved topology was not studied in detail.
IV. DISCUSSION
- The realistic neural-network model robustly evolves to a state with power laws in synaptic conductances and the synchronization order parameter Csyn.The authors interpret these observations as strong evidence for self-organized criticality.Source: §IV · p. 5
- The authors argue that the adaptive mechanism based on dynamics and topology could robustly organize realistic neural models and may also drive criticality in other models.Source: §IV · p. 5
- STDP drives the network to a critical state marking synchronous activity's onset, unlike activity-dependent plasticity, which produces an order-disorder transition.The order-disorder transition depends mainly on average connectivity, while synchronization is more sensitive to larger topological motifs.Source: §IV · p. 5
- The evolved topology was not studied in detail; sustained activity in small networks suggests non-random structures that may support synfire-chain-like propagation.Source: §IV · p. 5
- Because the model couples integrate-and-fire neurons with STDP and yields results in good agreement with empirical observations, the authors argue self-organization may occur in nature unless disrupted.They also state that the mechanism's local nature may confer robustness to noise and that finite-size effects are unlikely to matter in human cortical networks.Source: §IV · pp. 5–6