Research map / Probabilistic and scientific modeling / Molecules and proteins
GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics
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Introduces GENOT, a flow-matching neural solver that learns conditional distributions of linear, quadratic, unbalanced and fused entropic OT couplings for any cost, applied to single-cell genomics.
Problem
Neural OT solvers for single-cell genomics are limited to deterministic Monge maps, squared Euclidean cost, balanced mass, and linear OT; they cannot handle stochastic, non-Euclidean, unbalanced, or Gromov-Wasserstein/fused problems needed for cell trajectory, perturbation and modality-translation t
Approach
Learn entropic OT couplings by conditioning a flow-matching model on each source point x, so that each conditional distribution pi(.|x) is generated from Gaussian noise; the coupling is obtained from discrete entropic solvers on mini-batches, allowing any cost, quadratic/fused objectives, and unbalanced extensions via learned re-weighting functions.
Key results
- GENOT-L outperforms all considered baselines on the simulated linear EOT benchmark, which is designed for balanced problems with the squared Euclidean cost.
- GENOT-Q gives Sinkhorn divergences that are orders of magnitude better than discrete GW-LR on ATAC-to-RNA translation, while FOSCTTM is competitive only in low dimensions for GW-LR.
- U-GENOT-L increases prediction accuracy for nine cancer drugs by allowing mass variation, and the model is well calibrated for 117 of 163 drugs.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the geodesic distance on the data manifold instead of the squared Euclidean cost | GENOT-L · Developing mouse pancreas trajectory inference | TSI score | Helped |
| allow mass variation with U-GENOT | GENOT-L · Cancer drug perturbations | prediction accuracy | Helped |
| use geodesic intra-domain costs instead of squared Euclidean costs | GENOT-Q · ATAC-seq to RNA-seq translation | FOSCTTM | Helped |
| use GENOT-Q instead of GW-LR | ATAC-seq to RNA-seq translation · Low-dimensional modality translation | FOSCTTM | Mixed |
| use GENOT-Q instead of GW-LR | ATAC-seq to RNA-seq translation · Modality translation | Sinkhorn divergence | Helped |
| add a fused feature penalty | GENOT-Q · ATAC-seq to RNA-seq translation | alignment | Helped |
| use batch-wise independent couplings instead of OT couplings (ablation) | GENOT modality translation · ATAC-seq to RNA-seq translation | cell-type clustering | Hurt |
| use U-GENOT-F in the unbalanced setting | GENOT-F · Unbalanced modality translation | accuracy | Helped |
| increase dimensionality | GENOT-Q and U-GENOT-Q · Gaussian simulated data | entropic OT plan learning performance | Hurt |
| use a fused term rather than pure GW | GENOT-F · Single-cell modality alignment | alignment stability | Helped |
| use a neural initialization scheme based on the previous iteration's coupling (ablation) | GENOT-Q · Quadratic OT | simulation-free training | Hurt |
Surprising findings
- GW-LR remains competitive with GENOT-Q in FOSCTTM for low-dimensional ATAC-to-RNA translation.
- GENOT-Q's performance decreases with increasing dimensionality on Gaussian EOT benchmarks.
Limitations
- GW and fused GW solutions are non-unique, so orientation is not maintained across iterations, requiring fused terms or initialization schemes.
- Choosing unbalancedness hyperparameters tau is mostly empirical.
- No evidence that cells evolve according to entropic OT plans; evaluation relies on task-specific biological proxies.
Experimental setup
Datasets: mouse pancreas scRNA-seq (E14.5 to E15.5) cancer drug single-cell RNA-seq (163 drugs) bone marrow ATAC-RNA multiome simulated Gaussian and benchmark data
Benchmarks: mouse pancreas trajectory (TSI, CT error) cancer drug response prediction bone marrow ATAC-to-RNA translation simulated Gaussian EOT benchmark
Metrics: FOSCTTM Sinkhorn divergence accuracy TSI score CT error cos-var uncertainty
Baselines: GW-LR bridge matching mini-batch OT flow matching discrete Gromov-Wasserstein solver
Builds on: flow matching Sinkhorn algorithm unbalanced optimal transport entropic Gromov-Wasserstein
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