Supplementary Figure 12: many types - 32 neuron types

This script reproduces the panels of paper’s Supplementary Figure 12. Test with 32 different neuron types (update functions).

Simulation parameters:

• N_neurons: 1000
• N_types: 32 parameterized by \(s_i\)={1,2,3,4,5,6,7,8} and \(\tau_i\)={0.25,0.5,0.75,1.0}
• N_frames: 100,000
• Connectivity: 100% (dense)
• Connectivity weights: random, Lorentz distribution
• Noise: none
• External inputs: none

The simulation follows Equation 2 from the paper:

\[\frac{dx_i}{dt} = -\frac{x_i}{\tau_i} + s_i \cdot \tanh(x_i) + g_i \cdot \sum_j W_{ij} \cdot \psi(x_j)\]

Classification accuracy expected: 0.99

Configuration and Setup

print()
print("=" * 80)
print("Supplementary Figure 12: 1000 neurons, 32 types, dense connectivity")
print("=" * 80)

device = []
best_model = ''
config_file_ = 'signal_fig_supp_12'

print()
config_root = "./config"
config_file, pre_folder = add_pre_folder(config_file_)

# load config
config = NeuralGraphConfig.from_yaml(f"{config_root}/{config_file}.yaml")
config.config_file = config_file
config.dataset = config_file

if device == []:
    device = set_device(config.training.device)

log_dir = f'./log/{config_file}'
graphs_dir = f'./graphs_data/{config_file}'

Step 1: Generate Data

Generate synthetic neural activity data using the PDE_N2 model with 32 neuron types. This tests the GNN’s ability to learn many distinct update functions.

Outputs:

• Sample time series
• True connectivity matrix \(W_{ij}\)

# STEP 1: GENERATE
print()
print("-" * 80)
print("STEP 1: GENERATE - Simulating neural activity (32 neuron types)")
print("-" * 80)

# Check if data already exists
data_file = f'{graphs_dir}/x_list_0.npy'
if os.path.exists(data_file):
    print(f"data already exists at {graphs_dir}/")
    print("skipping simulation, regenerating figures...")
    data_generate(
        config,
        device=device,
        visualize=False,
        run_vizualized=0,
        style="color",
        alpha=1,
        erase=False,
        bSave=True,
        step=2,
        regenerate_plots_only=True,
    )
else:
    print(f"simulating {config.simulation.n_neurons} neurons, {config.simulation.n_neuron_types} types")
    print(f"generating {config.simulation.n_frames} time frames")
    print(f"output: {graphs_dir}/")
    print()
    data_generate(
        config,
        device=device,
        visualize=False,
        run_vizualized=0,
        style="color",
        alpha=1,
        erase=False,
        bSave=True,
        step=2,
    )

Sample time series taken from the activity data (32 neuron types).

True connectivity \(W_{ij}\). The inset shows 20×20 weights.

Step 2: Train GNN

Train the GNN to learn connectivity \(W\), latent embeddings \(\mathbf{a}_i\), and functions \(\phi^*, \psi^*\). The GNN must learn to distinguish 32 different update functions.

The GNN optimizes the update rule (Equation 3 from the paper):

\[\hat{\dot{x}}_i = \phi^*(\mathbf{a}_i, x_i) + \sum_j W_{ij} \psi^*(x_j)\]

# STEP 2: TRAIN
print()
print("-" * 80)
print("STEP 2: TRAIN - Training GNN to learn 32 neuron types")
print("-" * 80)

# Check if trained model already exists (any .pt file in models folder)
import glob
model_files = glob.glob(f'{log_dir}/models/*.pt')
if model_files:
    print(f"trained model already exists at {log_dir}/models/")
    print("skipping training (delete models folder to retrain)")
else:
    print(f"training for {config.training.n_epochs} epochs, {config.training.n_runs} run(s)")
    print(f"learning: connectivity W, latent vectors a_i for 32 types, functions phi* and psi*")
    print(f"models: {log_dir}/models/")
    print(f"training plots: {log_dir}/tmp_training")
    print(f"tensorboard: tensorboard --logdir {log_dir}/")
    print()
    data_train(
        config=config,
        erase=False,
        best_model=best_model,
        style='color',
        device=device
    )

Step 3: GNN Evaluation

Figures matching Supplementary Figure 12 from the paper.

Figure panels:

• Learned connectivity matrix
• Comparison of learned vs true connectivity
• Learned latent vectors \(\mathbf{a}_i\) (32 clusters expected)
• Learned update functions \(\phi^*(\mathbf{a}_i, x)\) (32 distinct functions)
• Learned transfer function \(\psi^*(x)\)

# STEP 3: GNN EVALUATION
print()
print("-" * 80)
print("STEP 3: GNN EVALUATION - Generating Supplementary Figure 12 panels")
print("-" * 80)
print(f"learned connectivity matrix")
print(f"W learned vs true (R^2, slope)")
print(f"latent vectors a_i (32 clusters)")
print(f"update functions phi*(a_i, x) - 32 distinct functions")
print(f"transfer function psi*(x)")
print(f"output: {log_dir}/results/")
print()
folder_name = './log/' + pre_folder + '/tmp_results/'
os.makedirs(folder_name, exist_ok=True)
data_plot(config=config, config_file=config_file, epoch_list=['best'], style='color', extended='plots', device=device, apply_weight_correction=True, plot_eigen_analysis=False)

Supplementary Figure 12: GNN Evaluation Results

Learned connectivity.

Comparison of learned and true connectivity (given \(g_i\)=10).

Learned latent vectors \(a_i\) of all neurons. 32 clusters expected (one per neuron type).

Learned update functions \(\phi^*(a_i, x)\). The plot shows 1000 overlaid curves representing 32 distinct update functions. Colors indicate true neuron types. True functions are overlaid in light gray.

Learned transfer function \(\psi^*(x)\), normalized to a maximum value of 1. True function is overlaid in light gray.