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Ring Attractor Network

Introduction

This repository holds the Neuromatch Academy 2020 project work of Stefano, Nikitas, Pranjal and Angela for a ring attractor network under the guidance of our pod TA, Peter Vincent and mentorship of Mehrdad Jazayeri.

Scientific Question

How to construct a biologically plausible, dynamic ring attractor network of firing neurons?

Background

The ring attractor with bump like neural activity has been hypothesised to work as a biologically plausible model for memory. It can be used to model the dynamics of head direction, encoded by E-PG neurons of Ellipsoid Body of Drosophilla melanogoster and other cyclic parameters like colours.

Methods

Modelling of LIF neurons with a connectivity matrix of 4-4 topology to construct a desirable ring attractor. Subsequently, fix points are added to the network along with normal white noise to make it more biologically plausible. Several iterations of simulation were run with altering parameters to find optimal parameters that allow the network to sustain its activity and behave in an explainable way.

Conclusions

In conclusion, it was found that for a working model of a ring attractor, fixed points at various positions in the ring network are needed to prevent drifting caused by noise. The dynamics of the network are determined by a variety of parameters such as the balance between inhibitory and excitatory neurons, number of fixed points and the strength of the noise.

Code

Please reference the Github Wiki of this repository for more information on the dirty details of our code.

What we have done

  • Built an IAF model with conductance based synapses
  • Connected 128 neurons with 2-4 connectivity rule in a ring
  • Found out the parameters to have a stable bump after an input
  • Implemented gaussian noise to every voltage update of every neuron
  • Manipulated simulation parameters so that bumps don't get ignited by noise
  • Implemented fixed points as groups of 3 adjacent neurons with stronger excitatory and inhibitory weights
  • Implemented an equation to uodate weights as a function of number of fixed ponts
  • Implemented an error metric based on the mean of the median neuron that fired in every timestep for the last 100 timesteps
  • Performed many simulations with different fixed points to find the one with least error
  • Repeated simulations with different levels of noise
  • Moved codebase to Julia to gain simulation speed and code maintainability
  • Performed many simulations with different weights to find parameters for bump stability
  • Performed many simulations with different weights to find parameters for fixed point stability

Yet to do

  • Implement learning rules

Resources

Theoretical Neuroscience, Peter Dayan and L. F. Abbot
Critical Limits in a Bump Attractor Network of Spiking Neurons, Alberto Arturo Vergani and Christian Robert Huyck

Wandering Bumps in Stochastic Neural Fields, Zachary P. Kilpatrick and Bard Ermentrout

Local/Global Analysis of the Stationary Solutions of some Neural Field Equations, Romain Veltz and Olivier Faugeras