Robustness to Edge Removal

Train the GNN on incomplete connectomes where 2%, 5%, 10%, and 20% of edges have been removed. Evaluate whether the model can still recover synaptic weights, biophysical parameters, and neuron-type identity despite missing connections.

Robustness to Edge Removal

In a real experimental setting, the connectome may contain false negatives: true synaptic connections that are missed during reconstruction. To test robustness to such incomplete adjacency matrices, we randomly removed a fraction of edges from the true connectome (434,112 edges) before training the GNN. The model must recover the circuit parameters using only the remaining connections.

We tested four levels of edge removal:

Config	Removed edges	Remaining edges	Fraction removed
flyvis_noise_005_removed_pc_02	8,682	425,430	2%
flyvis_noise_005_removed_pc_05	21,706	412,406	5%
flyvis_noise_005_removed_pc_10	43,411	390,701	10%
flyvis_noise_005_removed_pc_20	86,822	347,290	20%

Noise Level

Recall that the simulated dynamics include an intrinsic noise term \(\sigma\,\xi_i(t)\) where \(\xi_i(t) \sim \mathcal{N}(0,1)\) (Notebook 00). All edge-removal experiments presented here use a fixed noise level of \(\sigma = 0.05\) (low noise). To change the noise level, edit the noise_model_level field in the respective config files:

• config/fly/flyvis_noise_005_removed_pc_02.yaml
• config/fly/flyvis_noise_005_removed_pc_05.yaml
• config/fly/flyvis_noise_005_removed_pc_10.yaml
• config/fly/flyvis_noise_005_removed_pc_20.yaml

Results

Each config extends the base flyvis_noise_005 setup with a different fraction of edges randomly removed from the adjacency matrix. Edges are removed uniformly at random per column (consistent across pre-synaptic neurons). The GNN architecture and training hyperparameters are otherwise identical across conditions.

The GNN tolerates significant edge removal: even with 20% of connections missing, it recovers the remaining synaptic weights and biophysical parameters with high fidelity. This suggests the model exploits redundancy in the network dynamics to compensate for incomplete connectivity information.

Metric	2%	5%	10%	20%
\(W\) corrected \(R^2\)	0.8721	0.8413	0.8042	0.8367
\(W\) corrected slope	0.9778	0.9752	0.9865	0.9674
\(\tau\) \(R^2\)	0.9674	0.9799	0.9316	0.9787
\(V^{\text{rest}}\) \(R^2\)	0.3289	0.1936	0.0079	0.1248
Clustering accuracy	—	—	—	—

Loss Curves

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

Testing

We evaluate each trained model on held-out stimuli and compute rollout predictions.

for config_name, table_label, label in datasets:
    config = configs[config_name]
    gnn_log_dir = log_path(config.config_file)
    print(f"\n--- Testing {label} ---")
    data_test(
        config=config,
        visualize=True,
        style="color name continuous_slice",
        verbose=False,
        best_model='best',
        run=0,
        step=10,
        n_rollout_frames=250,
        device=device,
    )

Rollout Traces

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

GNN Analysis: Learned Representations

We run the same analysis as Notebook 04 on each edge-removal model to assess whether circuit recovery is preserved despite the incomplete adjacency matrix.

for config_name, table_label, label in datasets:
    config = configs[config_name]
    print(f"\n--- Generating analysis plots for {label} ---")
    data_plot(
        config=config,
        config_file=config.config_file,
        epoch_list=['best'],
        style='color',
        extended='plots',
        device=device,
    )

Corrected Weights (\(W\))

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

\(f_\theta\) (MLP\(_0\)): Neuron Update Function

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

Time Constants (\(\tau\))

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

Resting Potentials (\(V^{\text{rest}}\))

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

\(g_\phi\) (MLP\(_1\)): Edge Message Function

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

Neural Embeddings

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

UMAP Projections

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

Spectral Analysis

2% edges removed (8,682 removed / 425,430 remaining)

5% edges removed (21,706 removed / 412,406 remaining)

10% edges removed (43,411 removed / 390,701 remaining)

20% edges removed (86,822 removed / 347,290 remaining)

Rollout Metrics

Metric	2%	5%	10%	20%
RMSE	0.1028 +/- 0.0537	0.1057 +/- 0.0556	0.0986 +/- 0.0506	0.0932 +/- 0.0524
Pearson r	0.761 +/- 0.247	0.756 +/- 0.250	0.748 +/- 0.256	0.728 +/- 0.269

References

[1] J. K. Lappalainen et al., “Connectome-constrained networks predict neural activity across the fly visual system,” Nature, 2024. doi:10.1038/s41586-024-07939-3

[2] C. Allier, L. Heinrich, M. Schneider, S. Saalfeld, “Graph neural networks uncover structure and functions underlying the activity of simulated neural assemblies,” arXiv:2602.13325, 2026. doi:10.48550/arXiv.2602.13325