scholarly journals How neural circuits achieve and use stable dynamics

2019 ◽  
Author(s):  
Leo Kozachkov ◽  
Mikael Lundqvist ◽  
Jean-Jacques Slotine ◽  
Earl K. Miller
Keyword(s):  
Neural Networks ◽  
Synaptic Plasticity ◽  
Recurrent Neural Networks ◽  
Neural Circuits ◽  
Stable State ◽  
Distributed Networks ◽  
Time Varying ◽  
Multiple Sources ◽  
Hebbian Plasticity ◽  
The Brain

1AbstractThe brain consists of many interconnected networks with time-varying activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable state for its computations to make sense. We approached this from a control-theory perspective by applying contraction analysis to recurrent neural networks. This allowed us to find mechanisms for achieving stability in multiple connected networks with biologically realistic dynamics, including synaptic plasticity and time-varying inputs. These mechanisms included anti-Hebbian plasticity, synaptic sparsity and excitatory-inhibitory balance. We leveraged these findings to construct networks that could perform functionally relevant computations in the presence of noise and disturbance. Our work provides a blueprint for how to construct stable plastic and distributed networks.

scholarly journals Achieving stable dynamics in neural circuits

2020 ◽  
Author(s):  
Leo Kozachkov ◽  
Mikael Lundqvist ◽  
Jean-Jacques Slotine ◽  
Earl K. Miller
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Neural Circuits ◽  
Time Varying ◽  
Biological Complexity ◽  
Multiple Sources ◽  
Hebbian Plasticity ◽  
Autonomous Activity ◽  
The Brain ◽  
Shed Light

1AbstractThe brain consists of many interconnected networks with time-varying, partially autonomous activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable, reproducible state (or sequence of states) for its computations to make sense. We approached this problem from a control-theory perspective by applying contraction analysis to recurrent neural networks. This allowed us to find mechanisms for achieving stability in multiple connected networks with biologically realistic dynamics, including synaptic plasticity and time-varying inputs. These mechanisms included inhibitory Hebbian plasticity, excitatory anti-Hebbian plasticity, synaptic sparsity and excitatory-inhibitory balance. Our findings shed light on how stable computations might be achieved despite biological complexity.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

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