Summary of Neural Optimal Transport with Lagrangian Costs, by Aram-alexandre Pooladian et al.
Neural Optimal Transport with Lagrangian Costs
by Aram-Alexandre Pooladian, Carles Domingo-Enrich, Ricky T. Q. Chen, Brandon Amos
First submitted to arxiv on: 1 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper investigates the optimal transport problem between probability measures, considering a least action principle (Lagrangian cost) that accounts for geometric constraints in physical systems. The authors demonstrate efficient computation of geodesics and spline-based paths, which has not been achieved before even in low-dimensional problems. The formulation also outputs Lagrangian optimal transport maps without requiring an ODE solver, unlike prior work. The paper’s effectiveness is demonstrated on low-dimensional examples from prior research. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how to move probability measures between two points in a way that uses the least amount of energy. This is important when studying systems where the movement is affected by obstacles or non-Euclidean shapes. The authors found a way to efficiently calculate these movements, which was not possible before even for simple problems. They also showed how to get the final result without needing special computer programs. |
Keywords
» Artificial intelligence » Probability
