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Symmetry-Aware GFlowNets

ICML 2025 · Probabilistic and scientific modeling › Molecules and proteins · approach: Equivariant and disentangled latent representations · 0 citations (OpenAlex)

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Proposes SA-GFN, which corrects GFlowNet sampling bias from graph automorphisms (equivalent actions) by scaling terminal rewards by automorphism group sizes, avoiding per-transition isomorphism tests.

Problem

GFlowNets sampling graphs suffer systematic bias because equivalent actions (leading to isomorphic states) are not accounted for in transition probabilities, skewing sampling toward graphs with fewer symmetries (node-by-node) or symmetric fragments (fragment-based).

Approach

Show that the bias from equivalent actions reduces to a ratio of automorphism group sizes, so scaling the reward by |Aut(G)| (or dividing by fragment automorphisms for fragment-based generation) makes TB and DB objectives sample proportionally to reward, with an unbiased likelihood estimator via automorphism counting.

Key results

• In the fragment-based task, the vanilla model generated 5220 cyclohexane fragments among 5000 sampled molecules versus 1042 for the corrected method.
• Reward Scaling with exact correction yields top-K reward 1.091 vs vanilla 1.09 in atom-based task and uniqueness fraction 1.0 vs 0.93.
• In the synthetic uniform-reward environment, the vanilla model's Z was 26706 versus the true 112 with reward scaling recovering 112.

Measured effects reported in the paper

Surprising findings

• Reward scaling is sufficient for both TB and DB objectives, avoiding per-transition automorphism counting.
• Atom-based molecule task showed limited improvement, possibly because rewards are negatively correlated with symmetry counts in QM9.

Limitations

• Theoretical guarantees rely on a specific predefined set of graph actions and permutation-equivariant policies.
• Validated mainly on TB and DB objectives and molecule-related datasets.
• Reward scaling is slower to converge under DB because corrections are only applied at trajectory end.

Experimental setup

Datasets: QM9 ZINC250k

Benchmarks: atom-based molecule generation (HOMO-LUMO gap proxy) fragment-based molecule generation (sEH proxy) synthetic graph environments with exact terminating probabilities

Metrics: L1 error diversity top-K diversity top-K reward unique fraction Pearson correlation of log-likelihood and log-reward

Baselines: Vanilla GFlowNet Transition Correction PE (positional encoding correction) Flow Scaling

Builds on: trajectory balance detailed balance GFlowNet molecule generation (Bengio et al. 2021 style atom/fragment environment positional encoding orbit-based equivalent action correction

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