Title: Optimizing the Trade-off Between Symmetry and Efficiency in Graph Flow Matching

Abstract: In the realm of graph generative models, equivariance is a fundamental principle, ensuring that the architecture adheres to the permutation symmetry inherent in graphs. However, enforcing strict equivariance often leads to higher computational overhead due to rigid architectural requirements and can impede convergence speed, as the model is forced to maintain consistency across a vast array of potential node permutations. This paper investigates this specific trade-off. We begin with an equivariant discrete flow-matching framework and introduce a controllable symmetry modulation technique during training. This approach utilizes sinusoidal positional encodings and node permutations to relax equivariance constraints. Our experimental results reveal a dual nature to symmetry-breaking: while it can expedite the initial stages of training by offering a more accessible learning signal, it simultaneously promotes shortcut solutions that lead to overfitting, resulting in the generation of duplicate graphs from the training set. Conversely, strategically modulating the symmetry signal helps postpone overfitting and speeds up convergence. This balanced approach enables the model to achieve superior performance using only 19% of the training epochs required by the baseline.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC