Flow Matching on General Geometries
Authors: Ricky T. Q. Chen, Yaron Lipman
ICLR 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Empirically, we find that Riemannian Flow Matching achieves state-of-the-art performance on manifold datasets across various settings, being on par or outperforming competitive baselines. We also demonstrate that our approach scales to higher dimensions without sacrificing performance, thanks to our scalable closed-form training objective. Moreover, we present the first successful training of continuous-time deep generative models on non-trivial geometries, including those imposed by discrete triangular meshes and manifolds with non-trivial boundaries that represent challenging constraints on maze-shaped manifolds. |
| Researcher Affiliation | Collaboration | Ricky T. Q. Chen FAIR, Meta rtqichen@meta.com Yaron Lipman FAIR, Meta and Weizmann Institute of Science ylipman@meta.com |
| Pseudocode | Yes | Algorithm 1 Riemannian CFM |
| Open Source Code | Yes | Details regarding the more complex mesh manifolds can be found in the open source code, which we release for reproducibility1. 1https://github.com/facebookresearch/riemannian-fm |
| Open Datasets | Yes | We make use of the publicly sourced datasets (NOAA, 2020a;b; Brakenridge, 2017; EOSDIS, 2020) compiled by Mathieu & Nickel (2020). [...] We make use of the preprocessed protein (Lovell et al., 2003) and RNA (Murray et al., 2003) datasets compiled by Huang et al. (2022). |
| Dataset Splits | Yes | We followed their procedure and split the data according to 80% train, 10% val, and 10% test. |
| Hardware Specification | Yes | All experiments are run on a single NVIDIA V100 GPU with 32GB memory. |
| Software Dependencies | No | The paper lists several software packages and libraries (e.g., Py Torch, Py Torch Lightning, Hydra, Jupyter, Matplotlib, numpy, Sci Py, pandas, geopandas, torchdiffeq, libigl, Py EVTK) but does not specify their version numbers. Citations to papers describing software (e.g., Paszke et al., 2019 for PyTorch) do not count as specific version numbers of the software used. |
| Experiment Setup | Yes | We generally used 512 hidden units and tuned the number of layers for each type of experiment, ranging from 6 to 12 layers. We used the Swish activation function (Ramachandran et al., 2017) with a learnable parameter. We used Adam with a learning rate of 1e-4 and an exponential moving averaging on the weights (Polyak & Juditsky, 1992) with a decay of 0.999 for all of our experiments. |