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Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an equivariant flow instead of short-trajectory MCMC sampling | LJ-13 metastable-state discovery · LJ-13, low-energy minima | unique minima discovered: 2.70±3.80 -> 38.30±2.49; 7.70±3.23 -> 41.50±2.50; 0.90±0.30 -> 1.00±0.00 | Helped |
| Use an equivariant flow instead of a long MCMC trajectory | LJ-13 metastable-state discovery · LJ-13, u(x) in (-70, -60) | unique minima discovered: 64.60±6.11 -> 38.30±2.49 | Hurt |
| Replace the kernel-flow potential with a simple MLP potential (ablation) | Equivariant gradient flow · DW-4 and LJ-13 | training and sampling time: 0.879 ± 0.012 -> 2.58 ± 0.091; 0.498 ± 0.010 -> 1.760 ± 0.056; 0.222 ± 0.003 -> 4.18 ± 0.112; 0.178 ± 0.002 -> 6.670 ± 0 | Hurt |
| Replace the kernel-flow potential with a SchNet potential (ablation) | Equivariant gradient flow · DW-4 and LJ-13 | training and sampling time: 0.879 ± 0.012 -> 6.140 ± 0.583; 0.498 ± 0.010 -> 4.770 ± 0.500; 0.222 ± 0.003 -> 7.690 ± 0.018; 0.178 ± 0.002 -> 25.400 | Hurt |
| Use a non-equivariant flow instead of an equivariant flow (ablation) | Density estimation · DW-4 and LJ-13 | test log-likelihood and generalization | Hurt |
| Add random rotation and permutation data augmentation to a non-equivariant flow (ablation) | Non-equivariant density-estimation flow · DW-4 and LJ-13 | test log-likelihood and fitting | Hurt |
| Use the non-equivariant flow with data augmentation instead of the equivariant flow (ablation) | Boltzmann-generating flow · DW-4 | target-density reweighting | Hurt |
| Use a non-equivariant flow without data augmentation (ablation) | Boltzmann-generating flow · DW-4 | asymptotically unbiased sampling: 10.85 and 11.40 | Hurt |
| Estimate divergence with the Hutchinson estimator instead of computing it exactly (ablation) | Boltzmann-generating flow · DW-2 and growing particle systems | importance reweighting | Hurt |
| Train with OTD instead of DTO (ablation) | Equivariant flow · DW-4 | log-likelihood and training efficiency | No clear effect |
| Train the equivariant flow on one perturbed DW-4 minimum rather than equilibrium data | Equivariant flow · DW-4 metastable-state discovery | distinct minima discovered | Helped |
| Train a non-equivariant flow on one perturbed DW-4 minimum (ablation) | Non-equivariant flow · DW-4 metastable-state discovery | distinct minima discovered | Hurt |
Closest papers by meaning
- Equivariant flow matching (NeurIPS 2023 · similarity 0.94)
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- SymDrift: One-Shot Generative Modeling under Symmetries (NeurIPS 2026 · similarity 0.87)
- Controlled Generation with Equivariant Variational Flow Matching (ICML 2025 · similarity 0.87)
- A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrödinger Equation (AAAI 2025 · similarity 0.87)
- Scalable Equilibrium Sampling with Sequential Boltzmann Generators (ICML 2025 · similarity 0.86)
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