---
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](https://sparse.tamu.edu/) for benchmarking learned preconditioners on sparse linear systems, matching the evaluation criteria from the GNP paper ([arXiv 2406.00809v3](https://arxiv.org/abs/2406.00809v3)).

## Dataset Description

- **Source:** [SuiteSparse Matrix Collection](https://sparse.tamu.edu/)
- **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](https://github.com/Csed-dev/MatrixPFN/blob/main/docs/adr/04-gcn-over-mpnn.md) and [ADR-08](https://github.com/Csed-dev/MatrixPFN/blob/main/docs/adr/08-mpnn-generalization-failure.md).

## 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](https://sparse.tamu.edu/), downloaded unmodified in Matrix Market format via [ssgetpy](https://github.com/drdarshan/ssgetpy).

## Usage

### Download and extract all matrices

```python
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

```python
from scipy.io import mmread

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

### Browse the manifest

```python
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:**

```bibtex
@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)