LRIM Graph Benchmark

LRIM

Node Regression Dataset page ↗

Structure

1,000Graphs
256Nodes
512Edges
1Node Feature Dim

Coverage

8Results
10Variants
2Papers
Node regression Long-Range Ising Model benchmark for per-node energy prediction on periodic 2D grid graphs with controllable long-range interactions. Uses spins on a periodic 2D grid with controllable long-range couplings. Evaluated by log-MSE.

Dataset details

Task

Long-Range Ising Model benchmark for per-node energy prediction on periodic 2D grid graphs with controllable long-range interactions. The primary catalog metric is log-MSE.

Data

Long-Range Ising Model benchmark for per-node energy prediction on periodic 2D grid graphs with controllable long-range interactions. The cataloged artifact reports 10,000 graphs.

Features

Nodes occupy a periodic two-dimensional grid and carry spin/state inputs. Edges or interaction terms encode distance-dependent Ising couplings; the release controls interaction range and system size.

Splits and evaluation

The catalog records these protocols or variants: LRIM-16-hard, LRIM-16-easy, LRIM-32-hard, LRIM-32-easy, LRIM-64-hard, LRIM-64-easy, LRIM-128-hard, LRIM-128-easy, LRIM-256-hard, LRIM-256-easy. Evaluation uses log-MSE (lower is better). Exact masks or folds must come from the cited release.

Quirks and pitfalls

Periodic boundaries and long-range couplings distinguish this benchmark from nearest-neighbor grids. Energy conventions, coupling normalization, lattice size, temperature sampling, and interaction cutoff must be reported.

Sources

Variant Structure

1,000Graphs
256Nodes
512Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-16-hard

#Modellog-MSE ↓Paper
1
GPS-RWSE
Hyb baseline
-4.3450 ± 0.0650
From Message-Passing to Linearized Graph Sequence Models no code
May 2026 May '26
2
GPS-Base
GT baseline
-4.3400 ± 0.1010
From Message-Passing to Linearized Graph Sequence Models no code
May 2026 May '26
3
LGSM
Hyb ★ proposed
-4.2840 ± 0.1330
From Message-Passing to Linearized Graph Sequence Models no code
May 2026 May '26
4
GPS-LapPE
Hyb baseline
-4.2480 ± 0.1100
From Message-Passing to Linearized Graph Sequence Models no code
May 2026 May '26
5
GHR-GatedGCN
baseline
-4.1950 ± 0.0610
Graph Hierarchical Recurrence for Long-Range Generalization no code
May 2026 May '26
6
GatedGCN
GNN baseline
-3.9190 ± 0.2230
From Message-Passing to Linearized Graph Sequence Models no code
May 2026 May '26
7
GatedGCN-VN_G
GNN baseline
-3.7560 ± 0.0630
From Message-Passing to Linearized Graph Sequence Models no code
May 2026 May '26
8
GIN
GNN baseline
-2.4060 ± 0.1480
From Message-Passing to Linearized Graph Sequence Models no code
May 2026 May '26
SOTA performance set a new SOTA at the time matched the SOTA at the time

Variant Structure

1,000Graphs
256Nodes
512Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-16-easy

SOTA performance set a new SOTA at the time matched the SOTA at the time

Variant Structure

1,000Graphs
1,024Nodes
2,048Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-32-easy

SOTA performance set a new SOTA at the time matched the SOTA at the time

Variant Structure

1,000Graphs
1,024Nodes
2,048Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-32-hard

SOTA performance set a new SOTA at the time matched the SOTA at the time

Variant Structure

1,000Graphs
4,096Nodes
8,192Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-64-easy

SOTA performance set a new SOTA at the time matched the SOTA at the time

Variant Structure

1,000Graphs
4,096Nodes
8,192Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-64-hard

SOTA performance set a new SOTA at the time matched the SOTA at the time

Variant Structure

1,000Graphs
16,384Nodes
32,768Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-128-easy

SOTA performance set a new SOTA at the time matched the SOTA at the time

Variant Structure

1,000Graphs
16,384Nodes
32,768Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-128-hard

SOTA performance set a new SOTA at the time matched the SOTA at the time

Variant Structure

1,000Graphs
65,536Nodes
131,072Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-256-easy

SOTA performance set a new SOTA at the time matched the SOTA at the time

Variant Structure

1,000Graphs
65,536Nodes
131,072Edges
1Node Feature Dim

SOTA Progression

new SOTA matches SOTA at that time other proposed result other baseline result

Leaderboard — LRIM-256-hard

SOTA performance set a new SOTA at the time matched the SOTA at the time