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Baking Symmetry into GFlowNets

George Ma, Emmanuel Bengio, Yoshua Bengio, Dinghuai Zhang

TL;DR

This paper identifies symmetry as an underutilized aspect of GFlowNets, showing that isomorphic states and actions can inflate sample complexity and skew flow estimates. It proposes two state-invariance strategies (group averaging and canonical representation) and two action-invariance strategies (isomorphism testing and graph-level/node- or edge-level positional encodings) to enforce symmetry during training. Across synthetic experiments, these approaches improve flow accuracy and downstream rewards while reducing computation compared to naive enumeration. The work advances GFlowNets toward more efficient, diverse candidate generation in symmetry-rich domains such as graphs and molecules.

Abstract

GFlowNets have exhibited promising performance in generating diverse candidates with high rewards. These networks generate objects incrementally and aim to learn a policy that assigns probability of sampling objects in proportion to rewards. However, the current training pipelines of GFlowNets do not consider the presence of isomorphic actions, which are actions resulting in symmetric or isomorphic states. This lack of symmetry increases the amount of samples required for training GFlowNets and can result in inefficient and potentially incorrect flow functions. As a consequence, the reward and diversity of the generated objects decrease. In this study, our objective is to integrate symmetries into GFlowNets by identifying equivalent actions during the generation process. Experimental results using synthetic data demonstrate the promising performance of our proposed approaches.

Baking Symmetry into GFlowNets

TL;DR

This paper identifies symmetry as an underutilized aspect of GFlowNets, showing that isomorphic states and actions can inflate sample complexity and skew flow estimates. It proposes two state-invariance strategies (group averaging and canonical representation) and two action-invariance strategies (isomorphism testing and graph-level/node- or edge-level positional encodings) to enforce symmetry during training. Across synthetic experiments, these approaches improve flow accuracy and downstream rewards while reducing computation compared to naive enumeration. The work advances GFlowNets toward more efficient, diverse candidate generation in symmetry-rich domains such as graphs and molecules.

Abstract

GFlowNets have exhibited promising performance in generating diverse candidates with high rewards. These networks generate objects incrementally and aim to learn a policy that assigns probability of sampling objects in proportion to rewards. However, the current training pipelines of GFlowNets do not consider the presence of isomorphic actions, which are actions resulting in symmetric or isomorphic states. This lack of symmetry increases the amount of samples required for training GFlowNets and can result in inefficient and potentially incorrect flow functions. As a consequence, the reward and diversity of the generated objects decrease. In this study, our objective is to integrate symmetries into GFlowNets by identifying equivalent actions during the generation process. Experimental results using synthetic data demonstrate the promising performance of our proposed approaches.
Paper Structure (19 sections, 7 equations, 9 figures, 1 table)

This paper contains 19 sections, 7 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. GFlowNets training criteria
  4. Flow matching (FM).
  5. Detailed balance (DB).
  6. Trajectory balance (TB).
  7. Method
  8. State invariance
  9. Symmetrization via group averaging
  10. Symmetrization via canonical representation
  11. Action invariance
  12. Symmetrization via isomorphism testing
  13. Symmetrization via graph-level positional encoding
  14. Symmetrization via node-level and edge-level positional encoding
  15. Experiments
  16. ...and 4 more sections

Figures (9)

  • Figure 1: An example of action symmetry. There are three possible actions leading from the left graph to the right graph, but only one action leading backwards.
  • Figure 2: An example where two actions with different edge-level PEs could lead to isomorphic graphs.
  • Figure 3: The HyperGrid environment.
  • Figure 4: Results of the baseline, our method 1 (enumration based), and our method 2 (canonization based) on the hypergrid environment. We test with $\mathrm{horizon}=16$, $\mathrm{dimension}=3$, $R_0=0.001$.
  • Figure 5: The JS divergence between $p(x)$ and $p_\theta(x)$ during offline GFlowNet training.
  • ...and 4 more figures