debajyotidasgupta/repro-gnn-linear-sdp-bundle

Reproduction bundle — On the Expressive Power of GNNs to Solve Linear SDPs

Qian & Morris, ICML 2026 · arXiv 2604.27786 · OpenReview bjvLKXsTMK

This is a self-contained workspace that reproduces the six headline claims of the paper. It combines from-scratch Tier-A checks of the theory (WL colorings, sufficiency, complexity) with Tier-B neural experiments built on the authors' official GNN4SDP code.

Layout

src/sdp_core.py         from-scratch VC-WL / VC-2-WL / VC-2-FWL color refinement,
                        min-Frobenius-norm SDP solver (SCS/CLARABEL), Lemma C.15 spectral check
claims/                 Tier-A drivers (pure Python, CPU, deterministic)
  claim1_theorem23.py     Theorem 2.3 — VC-2-FWL sufficiency across a 14-instance battery
  claim2_counterexamples  Props 2.1 & 2.2 — VC-WL / VC-2-WL counterexamples
  claim6_complexity.py    Prop 2.4 — auxiliary-graph sizes, 1-WL≡VC-2-FWL, O((n^3+nnz)log n) scaling
ship/                   Tier-B drivers (neural; run on the official GNN4SDP models)
  gen_maxcut.py           synthetic Max-Cut SDP dataset generator (Table 1)
  gen_sdplib.py           SDPLIB Max-Cut (MCP*) processor -> HeteroData (Table 3)
  drive_train.py          multi-architecture trainer (ppgn/mpnn/2wl/ign/edge_gt)
  drive_sdplib.py         SDPLIB overfit test + saves ppgn checkpoint
  drive_warmstart.py      SCS warm-start speedup measurement (Table 5)
  requirements.txt        exact, verified dependency pins
GNN4SDP/                official code: models/, data/, utils/, trainer.py, config/
outputs/                Tier-A result JSONs (claim1, claim2, claim6)
results/                Tier-B result JSONs (maxcut, sdplib, warmstart)
poster.html             one-page reproduction poster (built with Chenruishuo/posterly)

Environment

python -m venv env && source env/bin/activate
pip install torch==2.8.0
# CPU wheels (macOS-ARM / Linux-CPU):
pip install torch_scatter torch_sparse -f https://data.pyg.org/whl/torch-2.8.0+cpu.html
# or CUDA 12.6:
pip install torch_scatter torch_sparse -f https://data.pyg.org/whl/torch-2.8.0+cu126.html
pip install -r ship/requirements.txt

Rerun

Tier A (theory, CPU, seconds):

python claims/claim2_counterexamples.py   # Props 2.1, 2.2   -> outputs/claim2/
python claims/claim1_theorem23.py         # Theorem 2.3      -> outputs/claim1/
python claims/claim6_complexity.py        # Prop 2.4         -> outputs/claim6/

Tier B (neural; run from inside GNN4SDP with PYTHONPATH set):

export PYTHONPATH=$PWD/GNN4SDP
# Claim 3 — Max-Cut expressivity gap
python ship/gen_maxcut.py  --root data/maxcut --n 30 --p 0.15 --num 500 --reg 1e-5
python ship/drive_train.py --datapath data/maxcut --models ppgn,mpnn,2wl,ign,edge_gt \
       --epochs 200 --hidden 64 --num_conv_layers 8 --no_mp 1 --no_dual 1
# Claim 4 — SDPLIB overfit (also trains the ppgn checkpoint used by Claim 5)
python ship/gen_sdplib.py  --root data/SDPLIB --pattern mcp --max_n 124 --reg 0
python ship/drive_sdplib.py --datapath data/SDPLIB --models ppgn,2wl,mpnn \
       --epochs 600 --hidden 64 --num_conv_layers 8 --ckpt_dir ckpt_sdplib
# Claim 5 — SCS warm-start speedup
python ship/drive_warmstart.py --datapath data/SDPLIB --ckpt ckpt_sdplib/ppgn_best.pt \
       --hidden 64 --num_conv_layers 8

Notes on scale

GPU provisioning (HF Jobs, then Vast.ai) was unavailable/unreliable during this run (HF Jobs returned HTTP 402; Vast.ai machines stalled on Docker Hub image pulls). The Tier-B neural experiments were therefore executed at reduced scale on CPU (smaller n, fewer instances / epochs than the paper) purely to fit the compute budget. The architecture code, data pipeline, loss, ground-truth SCS solver, and warm-start construction are the authors' originals, unmodified; only dataset size and training length were reduced. The reproduction targets the qualitative expressivity separations the paper asserts (the strong VC-2-FMPNN vs. the weaker baselines), which are visible at reduced scale. Every claim page in the logbook states its exact configuration.