New Sliced GW Distance Tackles High-Dimensional Alignment
Solving GW's 1D closed-form gap with rotational invariance for big data.
Deep Dive
Gong, Rioux, and Goldfeld propose a sliced inner product Gromov-Wasserstein (IGW) distance that resolves the lack of closed-form solutions for one-dimensional GW problems with inner product cost. It enjoys a natural rotational invariance property and is studied for its structural and computational properties. Numerical experiments validate the theory, with applications to heterogeneous clustering of text data and language model representation comparison.
Key Points
- Resolves the absence of closed-form 1D solutions for GW with inner product cost (IGW).
- Achieves rotational invariance and computational scalability for high-dimensional data.
- Demonstrated on heterogeneous text clustering and comparing language model representations.
Why It Matters
Enables efficient geometric alignment of high-dimensional, heterogeneous datasets without explicit correspondences, boosting mult-modal ML scalability.