Quantized Gromov-Wasserstein

The Gromov-Wasserstein (GW) framework adapts ideas from optimal transport to allow for the comparison of probability distributions defined on different metric spaces. Scalable computation GW distances and associated matchings graphs point clouds have recently been made possible by state-of-the-art algorithms such as S-GWL MREC. Each these algorithmic breakthroughs relies decomposing underlying spaces into parts performing parts, adding recursion needed. While very successful in practice, theoretical guarantees methods are limited. Inspired recent advances theory quantization measure spaces, we define Quantized Gromov Wasserstein (qGW): a that treats fundamental objects fits hierarchy upper bounds problem. This formulation motivates new algorithm approximating which yields speedups reductions memory complexity. Consequently, able go beyond outperforming apply matching at scales an order magnitude larger than existing literature, including datasets containing over 1M points.