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PhyloGFN: Phylogenetic inference with generative flow networks
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Adapts GFlowNets with trajectory balance to sample tree topologies bottom-up, using Fitch/Felsenstein-inspired features, for Bayesian marginal likelihood estimation and parsimony analysis on eight DNA benchmark datasets.
Problem
Phylogenetic inference (Bayesian posterior over tree topologies and branch lengths, and large parsimony) is hard because tree space is superexponential and MCMC/VI methods either restrict the tree space or underperform in marginal likelihood estimation.
Approach
Treat tree construction as a bottom-up sequential decision process (joining pairs of rooted trees) and train a GFlowNet with trajectory balance, using Felsenstein (Bayesian) and Fitch (parsimony) per-site features as order-invariant state representations that add no learnable parameters.
Key results
- PhyloGFN-Bayesian MLL on DS1 of -7108.95 ± 0.06, close to MrBayes SS (-7108.42) and above phi-CSMC (-7290.36) on all datasets; GeoPhy better on DS7.
- Pearson correlation on 50% random VBPI-GNN-generated trees: PhyloGFN 0.955 on DS1 vs VBPI-GNN 0.512, showing better fit on low-probability trees.
- PhyloGFN-Continuous (Gaussian mixture branch lengths) matches or beats MrBayes and VBPI-GNN on most datasets, e.g., DS1 -7108.40 ± 0.04.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PhyloGFN instead of φ-CSMC | Bayesian phylogenetic inference · DS1–DS6 and DS8 | marginal log-likelihood | Helped |
| Use PhyloGFN instead of GeoPhy | Bayesian phylogenetic inference · DS1, DS4–DS6 and DS8 | marginal log-likelihood | Helped |
| Use PhyloGFN instead of GeoPhy | Bayesian phylogenetic inference · DS2 and DS3 | marginal log-likelihood | No clear effect |
| Use PhyloGFN instead of GeoPhy | Bayesian phylogenetic inference · DS7 | marginal log-likelihood | Hurt |
| Use PhyloGFN instead of VBPI-GNN on lower-posterior-probability trees | Bayesian phylogenetic inference · DS1–DS8, 30% and 50% random trees | Pearson correlation | Helped |
| Use PhyloGFN instead of VBPI-GNN on high-probability trees | Bayesian phylogenetic inference · DS2, DS3 and DS7 | Pearson correlation | Hurt |
| Replace discrete branch-length distributions with Gaussian-mixture continuous modeling | PhyloGFN-Bayesian · DS1–DS8 | marginal log-likelihood | Helped |
| Use 40% of the training trajectories instead of the full training data | PhyloGFN-Bayesian · DS1–DS8 | marginal log-likelihood | No clear effect |
| Use PhyloGFN-Parsimony instead of PAUP* | Parsimony inference · All benchmark datasets | optimal tree solutions | No clear effect |
| Condition the PhyloGFN-Parsimony policy on temperature | PhyloGFN-Parsimony · DS1 | Pearson correlation between sampling log-probability and log-reward | Helped |
Surprising findings
- VBPI-GNN achieves higher correlation on high-probability trees but its correlation drops sharply on lower-probability trees (e.g., 0.512 at 50% random on DS1).
- PhyloGFN with only 8% of training trajectories still outperforms GeoPhy and phi-CSMC on DS1 MLL.
Limitations
- Training is expensive: full runs take 3 to 8 days per dataset (up to 190 hours on DS8) on V100/A100 GPUs.
- Branch lengths in the initial discrete version are quantized; continuous version is only in appendix.
- Amortizes only over a single fixed sequence dataset; does not generalize to unseen sequence sets.
Experimental setup
Datasets: DS1 DS2 DS3 DS4 DS5 DS6 DS7 DS8
Benchmarks: DS1-DS8 marginal log-likelihood DS1-DS8 parsimony optimal trees
Metrics: marginal log-likelihood (importance-weighted bound) Pearson correlation of sampling log-density vs unnormalized parsimony score
Baselines: MrBayes SS VBPI-GNN phi-CSMC GeoPhy PAUP*
Builds on: generative flow networks trajectory balance VBPI-GNN Felsenstein pruning algorithm Fitch algorithm
Closest papers by meaning
- PhyloGen: Language Model-Enhanced Phylogenetic Inference via Graph Structure Generation (NeurIPS 2024 · similarity 0.93)
- Likelihood-free inference of phylogenetic tree posterior distributions (NeurIPS 2026 · similarity 0.90)
- Deep Generative Models for Phylogenetic Inference with Complex Evolutionary Processes (NeurIPS 2026 · similarity 0.90)
- PhyloVAE: Unsupervised Learning of Phylogenetic Trees via Variational Autoencoders (ICLR 2025 · similarity 0.88)
- PhyloLM: Inferring the Phylogeny of Large Language Models and Predicting their Performances in Benchmarks (ICLR 2025 · similarity 0.86)
- gfnx: Fast and Scalable Library for Generative Flow Networks in JAX (NeurIPS 2026 · similarity 0.85)
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