Discrete Attractor Dynamics in the Frontal Cortex

Reproducing Neuron Dynamics with Highly Structured and Trained Chaotic Random RNN Models

This project was developed for the course "Physical Models for Living Systems", University of Padova. It explores how persistent neural activity, firing that continues after a stimulus is removed, can be reproduced through both biophysically structured models and trained chaotic recurrent neural networks (RNNs).

Persistent activity is crucial for short-term memory and motor planning. In their study, Inagaki et al. (2019) demonstrated that such activity in the anterior lateral motor cortex (ALM) of mice arises from network dynamics, not intrinsic cellular properties. Their results were modeled using structured discrete attractor networks.

This project asks:
What happens if we instead train a chaotic random RNN to reproduce the same dynamics observed during a delayed paired-association task?

Inagaki et al. Experimental Background

Original experimental data were download from FigShare.

• Task: Delayed-response left/right licking task
• Epochs: Sample → Delay → Go cue
• Data: Neural recordings from ALM using silicon probes
• Key feature: Persistent activity observed during the delay epoch

Project Goals

This project is divided into two main parts:

1. Reproducing Inagaki et al. (2019)

• Analyze extracellular recordings from the ALM replicating key analyses:
  • Coding Direction (CD) projection
  • Neural variability over time
  • Photoinhibition response
• Simulate the three-population structured attractor model (Excitatory Left, Excitatory Right, Inhibitory)
• Show that fixed parameters in the structured model can reproduce persistent activity and discrete attractor states

2. Training a Chaotic Random RNN via FORCE Learning

Following the method of Rajan et al. (2016), we:

• Implement a chaotic RNN where all synapses are trainable using the FORCE algorithm
• Design task-aligned external input:
  • Identical signals for both left/right trials during pre-sample and delay
  • Divergent signals only during sample and after-cue epochs
• Train on trial-averaged activity from 87 neurons (largest available dataset)
• Also train a variant with explicit suppression of non-selective activity
• Evaluate performance using:
  • CD projection
  • Selectivity measures
  • Robustness tests (e.g., noise perturbation, photoinhibition)
• Analyze network structure:
  • Synaptic weight distributions
  • PCA and eigenvalue spectrum of connectivity matrices

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Main Findings

• Structured attractor models successfully replicate persistent activity and discrete state transitions under photoinhibition
• Random RNNs trained with FORCE can memorize left/right trial inputs during the delay period
• Noise perturbations during the delay can cause right-trial trajectories to collapse into left-trial dynamics