Benchmark

Task: align a 2D Archimedean spiral to a 3D Swiss roll with the same angular parameterization. Quality metric: Spearman rank correlation between matched angular positions (1.0 = perfect alignment).

Large-Scale Results

End-to-end wall-clock time using distance_mode="landmark" and mixed_precision=True.

NVIDIA H100 80 GB HBM3:

Scale	Time	Spearman ρ	GPU Memory
4,000 × 5,000	0.8 s	0.999	0.7 GB
10,000 × 12,000	4.1 s	0.999	3.9 GB
20,000 × 25,000	4.6 s	0.999	16 GB
30,000 × 35,000	9.3 s	0.999	34 GB
40,000 × 50,000	17 s	0.999	64 GB
45,000 × 45,000	18 s	0.999	65 GB

NVIDIA L40S 48 GB:

Scale	Time	Spearman ρ	GPU Memory
4,000 × 5,000	2.4 s	0.999	1.1 GB
10,000 × 12,000	3.0 s	0.999	6.7 GB
20,000 × 25,000	12 s	0.999	18 GB
30,000 × 35,000	25 s	0.999	34 GB
35,000 × 40,000	34 s	0.999	45 GB

Alignment quality (Spearman ≥ 0.999) is maintained across all scales. Maximum scale is bounded by GPU memory for the dense N×K transport plan; stable operation requires ≤ 80% VRAM utilization.

TorchGW vs POT

Scale	Method	Time	Spearman ρ
400 × 500	POT entropic_gromov_wasserstein	1.6 s	0.999
400 × 500	TorchGW sampled_gw	0.9 s	0.998
4,000 × 5,000	POT entropic_gromov_wasserstein	183 s	0.999
4,000 × 5,000	TorchGW sampled_gw	1.0 s	0.999

At 4,000×5,000, TorchGW is ~175× faster than POT with equal quality. At larger scales POT runs out of memory; TorchGW scales to 45k×45k on a single GPU.

Visualization

Reproducing

# Large-scale benchmark (TorchGW only)
python examples/benchmark_scale.py

# POT comparison (requires: pip install pot)
python examples/demo_spiral_to_swissroll.py