Neural connectivities are critical in computational modeling but hard to measure in experiments. Can we infer the neural connectivities given the neural activity data? The problem can be modeled as a system identification process, thus, estimating parameters based on the input-response pairs.
The key barrier is that for the recorded neural responses, their relationships with the external inputs are usually obscure. In this work, we propose to use input-separated recurrent neural networks (RNNs) to solve the problem. We illustrate the effectiveness of our method by identifying a ring attractor network, which is the theoretical model of the drosophila head-direction (HD) system.
To install dependancies
pip install -r requirements.txt
To simulate a ring attractor model and collect the firing rates data, run
python cann.py
and data will be stored in the folder data. You could turn visualize=True to visualize the continuous attractor activity.
To train a RNN model fitting the simulated data, run the script
sh train.sh
you may want to register for the W & B service to log the training process.
To visualize the neural system identification results, check the jupyter notebook in test.ipynb.
- Tuning curves.
- Connectivity matrix.
Experiments show that:
- Input-separated RNN successfully identifies the structure of the connectivity matrix.
- Without input separation, the RNN identifies a mixture of compass and shifter neurons, thus fails to genuinely reconstruct the network.
- Shifter neurons automatically emerge within the input/hidden neurons, even only the compass neurons are observed during training.
In all, our results imply two constraints are effective in neural system identification---a neural activity constraint determining the response-response connectivity (attractors in working memory) and a neural dynamics constraint determining the input-response connectivity (transformations between the attractor states).
Future directions include identifying neural systems with higher-order input-response relations, mutual inference between input and response neurons, and application to actual physiology data, especially examining the 2D continuous attractor model of the grid cell system.