Datasets:
license: cc-by-4.0
task_categories:
- tabular-regression
tags:
- sparse-matrices
- linear-systems
- preconditioners
- numerical-linear-algebra
- suitesparse
- scientific-computing
- benchmark
size_categories:
- n<1K
configs:
- config_name: manifest
data_files: manifest.parquet
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).
Dataset Description
- Source: SuiteSparse Matrix Collection
- License: CC-BY 4.0
- Total matrices: 867
- Format: Matrix Market (.mtx)
- Size on disk: ~5.7 GB (1.9 GB compressed)
| 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. Usehf_hub_downloadorsnapshot_downloadfor 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)