add meta FM

Author: bamos

publications/all.bib

@@ -22,7 +22,7 @@ @misc{pooladian2023neural
   url={https://arxiv.org/abs/2406.00288},
   codeurl={https://github.com/facebookresearch/lagrangian-ot},
   abstract={
-We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting observations from a physical system, where the transport dynamics are influenced by the geometry of the system, such as obstacles, (e.g., incorporating barrier functions in the Lagrangian) and allows practitioners to incorporate a priori knowledge of the underlying system such as non-Euclidean geometries (e.g., paths must be circular). Our contributions are of computational interest, where we demonstrate the ability to efficiently compute geodesics and amortize spline-based paths, which has not been done before, even in low dimensional problems. Unlike prior work, we also output the resulting Lagrangian optimal transport map without requiring an ODE solver. We demonstrate the effectiveness of our formulation on low-dimensional examples taken from  prior work. 
+We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting observations from a physical system, where the transport dynamics are influenced by the geometry of the system, such as obstacles, (e.g., incorporating barrier functions in the Lagrangian) and allows practitioners to incorporate a priori knowledge of the underlying system such as non-Euclidean geometries (e.g., paths must be circular). Our contributions are of computational interest, where we demonstrate the ability to efficiently compute geodesics and amortize spline-based paths, which has not been done before, even in low dimensional problems. Unlike prior work, we also output the resulting Lagrangian optimal transport map without requiring an ODE solver. We demonstrate the effectiveness of our formulation on low-dimensional examples taken from  prior work.
   }
 }
 
@@ -51,6 +51,18 @@ @misc{silvestri2024score
   }
 }
 
+@inproceedings{atanackovic2024meta,
+  title={Meta Flow Matching:  Integrating Vector Fields on the Wasserstein Manifold},
+  author={Lazar Atanackovic and Xi Zhang and Brandon Amos and Mathieu Blanchette and Leo J Lee and Yoshua Bengio and Alexander Tong and Kirill Neklyudov},
+  booktitle={ICML 2024 Workshop on Geometry-grounded Representation Learning and Generative Modeling},
+  year={2024},
+  url={https://openreview.net/forum?id=f9GsKvLdzs},
+  _venue={ICML GRaM Workshop},
+  abstract={
+Numerous biological and physical processes can be modeled as systems of interacting samples evolving continuously over time, e.g. the dynamics of communicating cells or physical particles. Flow-based models allow for learning these dynamics at the population level --- they model the evolution of the entire distribution of samples. However, current flow-based models are limited to a single initial population and a set of predefined conditions which describe different dynamics. We propose (MFM), a practical approach to integrating along vector fields on the Wasserstein manifold by amortizing the flow model over the initial populations. We demonstrate empirically the ability of MFM to improve prediction of individual treatment responses on a large scale multi-patient single-cell drug screen dataset.
+  }
+}
+
 @misc{amos2023tutorial,
   title={Tutorial on amortized optimization},
   author={Brandon Amos},