Approximately Equivariant Graph Networks

This repo contains codes for paper "Approximately Equivariant Graph Networks" (https://arxiv.org/abs/2308.10436)

Dependencies

• Python 3.7+
• Pytorch 1.10+

Experiments

0. Simulations

• Fig 1.: Symmetry model selection example for $f: \mathbb R^3 \to \mathbb R$, where $f$ can be non-invariant, $S_2$-invaraint, or $S_3$-invariant. See project_subgroup.ipynb

1. Image Inpainting

See folder ./image_inpainting

• Figure 2 (left): Bias-Variance tradeoff via graph coarsening
  • To reproduce the results, see notebook graph_coarsen_runs.ipynb
  • The linear model baselines are implemented in notebook graph_coarsen_runs_linear.ipynb
• Figure 2 (right): Ablation of coarsened graph symmetry
  • To reproduce the results, see notebook FASHION+hflip_inpainting_reflection.ipynb

2. Traffic Forecasting:

See folder ./DCRNN_Pytorch The model architecture and data are adapated from: https://github.com/chnsh/DCRNN_PyTorch

(a) Download the following data folders and store them to ./DCRNN_Pytorch/data

• METR-LA-T3 : G drive link here to download and store the traffic graph signals, with using (T-3, T-2, T-1) graph signals to predict (T, T+1, T+2) graph signals. Data credit to SOURCE
• sensor_graph : G drive link here to download and store the graph adjacency files

(b) Run aut(G)-equivariant DCRNN with the default set-up (c.f. Table 3):

python dcrnn_train_pytorch.py --config_filename=data/model/dcrnn_la_aut_gc_false_t3.yaml --aut True

• To use the sparsified graph adjacency, change the above to config_filename=data/model/dcrnn_la_sp_aut_gc_false_t3.yaml
• To compare with the vanilla DCRNN, remove --aut True

File directory:

./DCRNN_PyTorch

• orbit_idx.p : store the 2-cluster assignments
• orbit_idx_9.p: store the 9-cluster assignment
• dcrnn_train_pytorch.py : main file to run the experiment

./DCRNN_Pytorch/data/model

• dcrnn_la_aut_gc_false_t3.yaml : config file to run experiments on the original traffic graph
• dcrnn_la_sp_aut_gc_false_t3.yaml : config file to run experiments on the sparsified traffic graph

./DCRNN_Pytorch/model/pytorch

• dcrnn_supervisor.py : training script
• dcrnn_model.py : DCRNN spatial-temporal GNN script
• dcrnn_cell.py : modified basic graph convolution block to allow (approximate) aut(G) equivariance

3. Human Pose Estimation

See folder ./Human_Pose_Est The model architecture and data are adapted from: https://github.com/garyzhao/SemGCN

(a) Download data following instructions here

(b) Run models with different symmetry choices, using $\mathcal{G}$-Net(gc+ew) with graph convolution and learnable edge weights (c.f. Table 4):

• $\mathcal{S}_{16}$ (Default SemGCN setup): python3 main_gcn_aut.py --epochs 30 --hid_dim 128 --checkpoint "./checkpoints"
• Relax-$\mathcal{S}_{16}$: python3 main_gcn_aut.py --no_tie --epochs 30 --hid_dim 128 --checkpoint "./checkpoints"
• $\mathcal{S}_2^2$ (aut(G)): python3 main_gcn_aut.py --aut --epochs 30 --hid_dim 128 --checkpoint "./checkpoints"
• Trivial: python3 main_gcn_aut.py --triv --epochs 30 --hid_dim 128 --checkpoint "./checkpoints"

(c) Run different model variants (c.f. Table 5):

• Vanilla $\mathcal{G}$-Net: python3 main_gcn_aut.py --no_gc --no_ew --epochs 30 --hid_dim 128 --checkpoint "./checkpoints"
• $\mathcal{G}$-Net(gc): python3 main_gcn_aut.py --no_ew --epochs 30 --hid_dim 128 --checkpoint "./checkpoints"
• $\mathcal{G}$-Net(pt): python3 main_gcn_aut.py --no_gc --no_ew --pointwise --epochs 30 --hid_dim 128 --checkpoint "./checkpoints"