Conformal Isometry of Lie Group Representation in Recurrent Network of Grid Cells

This repo contains the official implementation for the paper Conformal Isometry of Lie Group Representation in Recurrent Network of Grid Cells (NeurReps Workshop 2022).

Authors: Dehong Xu, Ruiqi Gao, Wen-Hao Zhang, Xue-Xin Wei, Ying Nian Wu

Hexagon grid firing patterns emerge in our learned $v(x)$ from a 10-step RNN model:

Learned hexagon grid patterns of $v(x)$, which is the hidden state vector in the LSTM transformation model:

The learned model can perform accurate long distance path integration:

Requirements

Requires python >= 3.5. To install dependencies:

pip install -r requirements.txt

Usage

• To train the nonlinear attractor model, run:

python main.py --config=configs/rnn_isometry.py

• To train the LSTM, run:

python main.py --config=configs/lstm_isometry.py

Reference

@article{xu2022conformal,
  title={Conformal Isometry of Lie Group Representation in Recurrent Network of Grid Cells},
  author={Xu, Dehong and Gao, Ruiqi and Zhang, Wen-Hao and Wei, Xue-Xin and Wu, Ying Nian},
  journal={arXiv preprint arXiv:2210.02684},
  year={2022}
}