KAIROS: Koopman-Aligned Invariant Representations for Open Dynamic Systems

A self-supervised framework for dynamic graph representation learning that achieves state-of-the-art anomaly detection across nine temporal graph benchmarks and competitive-to-winning node classification.

---

Benchmark scope

9 datasets:

Dataset	Nodes	Edges	Classes	Source
DBLP	25,387	185,480	10	CLDG (ICDE'23)
Bitcoinotc	5,881	35,592	3	CLDG
BITotc	4,863	28,473	7	CLDG
BITalpha	3,219	19,364	7	CLDG
TAX51	132,524	467,279	51	CLDG
Reddit	898,194	2,575,464	3	CLDG
MOOC	7,144	411,749	2	JODIE (KDD'19)
Arxiv	169,343	1,166,243	40	OGB
Elliptic	203,769	234,355	2 (fraud)	EvolveGCN / PyG

---

Running experiments

All experiment code lives under KAIROS/:

# KAIROS primary run on a single dataset
cd KAIROS
python ablate.py \
  --dataset dblp --task classification \
  --snapshots 4 --views 4 --strategy sequential \
  --dataloader_size 4096 --GPU 0 --epochs 200 --seed 24 \
  --ablation fixed_tau --tau_val 0.5 --backbone sage

# Simple baselines (LP/GCN/GAT/GraphSAGE/DGI/CCA-SSG)
python simple_baselines.py \
  --method gcn --dataset mooc --task classification --seed 24 --epochs 100

Regenerate all figures:

python make_figures.py

---

Dependencies

torch>=1.13          (CUDA build)
dgl                  (CUDA build)
scikit-learn>=1.0
scipy>=1.7
pandas>=1.3
numpy>=1.21
ogb                  (for Arxiv dataset)

Install: pip install -r requirements.txt

---

Repository layout

KAIROS/
├── README.md                    this file
├── make_figures.py              figure generator (8 figures)
├── bootstrap_best.py            bootstrap stat-sig analyzer
├── requirements.txt
├── KAIROS/                      model implementation
│   ├── main.py                  training loop + CLI
│   ├── models.py                KairosEncoder, KoopmanHead, LogReg
│   ├── utils.py                 graph loading, PPR, anomaly injection
│   ├── ablate.py                ablation runner (τ / backbone / Koopman)
│   ├── simple_baselines.py      LP/GCN/GAT/GraphSAGE/DGI/CCA-SSG
│   └── parallel_baselines.sh    batch runner for baselines
├── Data/                        datasets (symlinks to /tmp/ for large ones)
├── figures/                     generated PDFs and PNGs
└── runs/                        experiment logs (symlink to /tmp/)

---

Reproducibility

All experiments use 5 seeds: {24, 42, 7, 13, 99}. GPU non-determinism suppressed via torch.backends.cudnn.deterministic = True.