Metric Flow Matching for Smooth Interpolations on the Data Manifold
Authors: Kacper Kapusniak, Peter Potaptchik, Teodora Reu, Leo Zhang, Alexander Tong, Michael Bronstein, Joey Bose, Francesco Di Giovanni
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We test METRIC FLOW MATCHING on different tasks: artificial dynamic reconstruction and navigation through Li DAR surfaces 5.1; unpaired image translation between classes in images 5.2; reconstruction of cell dynamics. Further results and experimental details can be found in Appendices D, E and F. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction. |
| Researcher Affiliation | Collaboration | 1University of Oxford, 2Mila, 3Université de Montréal, 4AITHYRA |
| Pseudocode | Yes | Algorithm 1 Pseudocode for training of geodesic interpolants. Algorithm 2 Pseudocode for METRIC FLOW MATCHING. |
| Open Source Code | Yes | Code is available at https://github.com/kksniak/metric-flow-matching |
| Open Datasets | Yes | We used the Animal Face dataset from Choi et al. [2020], adhering to the splitting predefined by dataset authors for train and validation sets, with validation treated as the test set. We utilized the Cite and Multi datasets from the Multimodal Single-cell Integration Challenge at Neur IPS 2022 Lance et al. [2022], preprocessed by Tong et al. [2023a]. |
| Dataset Splits | Yes | We used a 90%/10% train/validation split. We used a 90%/10% train/validation split, excluding left-out marginals from both sets. Training samples served as source and target distributions and for calculating the metrics, while validation samples were used for early stopping. |
| Hardware Specification | Yes | The unpaired translation experiment on AFHQ was trained on a GPU cluster with NVIDIA A100 and V100 GPUs. |
| Software Dependencies | No | The paper mentions software like PyTorch or Adam optimizer, but does not provide specific version numbers for software dependencies. |
| Experiment Setup | Yes | In the unpaired translation experiments, we utilized the U-Net architecture setup from Dhariwal and Nichol [2021] for both φt,η(x0, x1) and vt,θ(xt). The exact hyperparameters are reported in Table 5. We used the Adam optimizer Kingma and Ba [2014] for both networks and applied early stopping only for φt,η(x0, x1) based on training loss. For this experiment, we enforce stronger bending by using ( hα(x))8, in the loss function Lg RBF(η) in (11). |