Csed-dev/matrixpfn-suitesparse

MatrixPFN SuiteSparse Evaluation Set

A curated subset of the SuiteSparse Matrix Collection for benchmarking learned preconditioners on sparse linear systems, matching the evaluation criteria from the GNP paper (arXiv 2406.00809v3).

Property	Value
Rows/Cols	1,000 - 100,000
Nonzeros	1,314 - 1,990,919
Shape	Square
Type	Real, non-SPD
Problem domains	50 categories

Domain Distribution (top 10)

Count	Domain
123	Circuit simulation
75	Computational fluid dynamics
69	Optimization
67	Optimal control
59	Economic
49	Chemical process simulation
47	Undirected weighted graph
32	Circuit simulation (frequency-domain)
31	2D/3D problem
30	Eigenvalue/model reduction

Dataset Structure

.
├── README.md
├── manifest.parquet              # Matrix metadata (browsable in HF Dataset Viewer)
├── suitesparse_manifest.json     # Full manifest with all 867 matrix metadata
├── suitesparse.tar.gz            # All 867 matrices (1.9 GB compressed, ~5.7 GB extracted)
│   └── suitesparse/
│       ├── 2D_27628_bjtcai/
│       │   └── 2D_27628_bjtcai.mtx
│       ├── ACTIVSg2000/
│       │   └── ACTIVSg2000.mtx
│       └── ...                   # 867 matrix directories
├── benchmark_results/
│   └── benchmark_gnp_paper.jsonl  # FGMRES benchmark: 838 matrices × 6 preconditioners
└── ablation_results/
    ├── ablation_edge_features.json     # Study 1: 3 seeds, 500 epochs (original)
    ├── ablation_edge_features_v2.json  # Study 2: 3 seeds, 500 epochs (pre-Dirichlet fix)
    └── ablation_edge_features_v3.json  # Study 3: 5 seeds, 1000 epochs (definitive)

manifest.parquet

Browsable in the HuggingFace Dataset Viewer. Fields:

Column	Type	Description
id	int	SuiteSparse matrix ID
group	str	Collection group (e.g. "HB", "SNAP")
name	str	Matrix name
rows	int	Number of rows
cols	int	Number of columns
nnz	int	Number of nonzeros
kind	str	Problem domain

benchmark_results/

JSONL file with FGMRES solver results for 838/867 matrices (29 timed out/OOM) using 6 preconditioners.

FGMRES settings (matching GNP paper): restart=10, max_iters=100, rtol=1e-8.

Per-entry fields: matrix properties (symmetry, diagonal dominance, scaling factor, zero diagonal count), and per-preconditioner results (construction time/status, convergence, iterations, residual history, Iter-AUC, Time-AUC).

Benchmark Results Summary

Preconditioner	Converged	Construction Failed	Not Converged
ILU(0)	376 (44.9%)	309 (36.9%)	153 (18.3%)
AMG (AIR)	206 (24.6%)	16 (1.9%)	616 (73.5%)
GMRES-Inner	107 (12.8%)	0 (0.0%)	731 (87.2%)
None	64 (7.6%)	0 (0.0%)	774 (92.4%)
Block Jacobi	41 (4.9%)	577 (68.9%)	220 (26.3%)
Jacobi	33 (3.9%)	603 (72.0%)	202 (24.1%)

Iter-AUC win rates (best preconditioner per matrix): ILU 41.1% · GMRES-Inner 33.9% · AMG 24.4% · Rest 0.5%

Key findings:

• 525/838 (62.6%) matrices solved by at least one preconditioner
• 313/838 (37.4%) matrices unsolved by any classical method
• 72% of matrices have zero diagonal entries (→ Jacobi family construction failure)
• ILU dominates small matrices (<5K), AMG becomes competitive at >10K
• ILU ∪ AMG covers 511/838 (61.0%); 327 matrices (39.0%) have both ILU and AMG failing

Comparison with GNP paper (arXiv 2406.00809v3, same 867 matrices):

Metric	Ours	GNP paper
ILU construction failures	309 (36.9%)	348 (40.1%)
AMG construction failures	16 (1.9%)	62 (7.2%)
ILU iter-AUC win rate	41.1%	~40%
AMG iter-AUC win rate	24.4%	~25%
GNP iter-AUC win rate	—	~25%
GNP construction failures	—	0 (0.0%)

ablation_results/

GCN vs MPNN ablation studies comparing ContextResGCN (GCN with Gershgorin-normalized adjacency) against ContextResMPNN (explicit edge function with sum aggregation).

FGMRES settings: restart=30, max_iters=300, rtol=1e-6. Training on diffusion + advection only, evaluated on diffusion, advection, and graph_laplacian (OOD). Grid sizes: 16, 24, 32 (train) + 48 (OOD).

Study 3 Results (definitive, 5 seeds × 1000 epochs)

Domain	Model	Convergence	Avg Iterations
Diffusion	GCN	800/800 (100%)	90.5
Diffusion	MPNN	800/800 (100%)	85.7
Advection	GCN	800/800 (100%)	87.2
Advection	MPNN	800/800 (100%)	83.0
Graph Laplacian (OOD)	GCN	400/400 (100%)	63.1
Graph Laplacian (OOD)	MPNN	0/400 (0%)	—

Training loss (nearly identical): GCN 0.091 vs MPNN 0.092.

MPNN is competitive on in-distribution domains but catastrophically fails on OOD graph topology (Barabási-Albert graphs with power-law degree distribution). Root cause: MPNN's explicit edge function overfits to training topology; GCN's Gershgorin-normalized adjacency is degree-invariant by construction. See ADR-04 and ADR-08.

Dataset Creation

Selection Criteria

Matches the GNP paper evaluation set:

• Square matrices only (rows == cols)
• Real-valued (not complex)
• Non-SPD (not symmetric positive definite)
• 1,000 to 100,000 rows
• Less than 2,000,000 nonzeros

Source Data

All matrices originate from the SuiteSparse Matrix Collection, downloaded unmodified in Matrix Market format via ssgetpy.

Usage

Download and extract all matrices

import subprocess
from pathlib import Path
from huggingface_hub import hf_hub_download

DATA_DIR = Path("data")
DATA_DIR.mkdir(exist_ok=True)

hf_hub_download(
    repo_id="Csed-dev/matrixpfn-suitesparse",
    repo_type="dataset",
    filename="suitesparse.tar.gz",
    local_dir=DATA_DIR,
)
subprocess.run(["tar", "xzf", str(DATA_DIR / "suitesparse.tar.gz"), "-C", str(DATA_DIR)], check=True)
(DATA_DIR / "suitesparse.tar.gz").unlink()

Load a single matrix

from scipy.io import mmread

matrix = mmread("data/suitesparse/ACTIVSg2000/ACTIVSg2000.mtx")
print(f"Shape: {matrix.shape}, NNZ: {matrix.nnz}")

Browse the manifest

from datasets import load_dataset

manifest = load_dataset("Csed-dev/matrixpfn-suitesparse", "manifest")
print(manifest["train"].to_pandas().head())

Considerations

• Matrix Market (.mtx) files are not natively streamable via datasets. Use hf_hub_download or snapshot_download for the sparse matrices.
• Some matrices may have near-singular or zero diagonals, causing preconditioner construction failures (documented in benchmark results).
• The benchmark results use spectral-radius scaling (dividing by the infinity norm) before solving.

Citation

This dataset is a redistribution of matrices from the SuiteSparse Matrix Collection under the CC-BY 4.0 license.

Required citations:

@article{Davis2011,
  author  = {Timothy A. Davis and Yifan Hu},
  title   = {The University of Florida Sparse Matrix Collection},
  journal = {ACM Transactions on Mathematical Software},
  volume  = {38},
  number  = {1},
  year    = {2011},
  doi     = {10.1145/2049662.2049663}
}

@article{Kolodziej2019,
  author  = {Scott P. Kolodziej and Mohsen Aznaveh and Matthew Bullock and Jarrett David and Timothy A. Davis and Matthew Henderson and Yifan Hu and Read Sandstrom},
  title   = {The SuiteSparse Matrix Collection Website Interface},
  journal = {Journal of Open Source Software},
  volume  = {4},
  number  = {35},
  pages   = {1244},
  year    = {2019},
  doi     = {10.21105/joss.01244}
}

Individual matrices may have additional citations. See https://sparse.tamu.edu/ for per-matrix metadata.

License

CC-BY 4.0 (inherited from SuiteSparse Matrix Collection)