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Topological and dynamical complexity of random neural networks
Gilles Wainrib1, Jonathan Touboul2
1LAGA, Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), 99 avenue J.B. Clément, F-93430 Villetaneuse, France.
Physical Review Letters
|August 29, 2014
Summary
Researchers uncovered the hidden mechanisms driving chaos in random neural networks. They found a link between topological complexity and the maximal Lyapunov exponent, revealing how systems transition to chaotic behavior.
Area of Science:
- Complex systems
- Computational neuroscience
- Statistical physics
Background:
- Random neural networks exhibit a phase transition to chaos with increasing disorder.
- The microscopic origins of this transition remain largely unknown.
- Understanding this transition is crucial, drawing parallels to spin glass systems.
Purpose of the Study:
- To investigate the explosion of complexity near the phase transition in random neural networks.
- To identify the microscopic mechanisms underlying the transition to chaos.
- To explore the relationship between topological and dynamical complexity.
Main Methods:
- Analysis of the mean number of equilibria as a function of system dimension.
- Computation of topological complexity near the critical point.
- Comparison of topological complexity with the maximal Lyapunov exponent.
Main Results:
- A sharp transition in the mean number of equilibria from one to an exponentially large number.
- Topological complexity near criticality was computed.
- Topological complexity was shown to precisely match the maximal Lyapunov exponent.
Conclusions:
- A microscopic mechanism for chaos in random neural networks was revealed.
- A deep link between topological and dynamical complexity was established.
- This finding suggests new avenues for understanding complex dynamical systems.
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