Permutation-Equivariant Flow Matching for Alignment-Free Neural Weight Generation

A trained neural network can be represented by a parameter vector in high dimensions. Learning distributions over these vectors enables the generation of new models across various tasks and architectures. A central challenge is permutation symmetry: permuting hidden neurons can produce distant parameter vectors representing the same function. This introduces variations that a generative model must account for when learning from trained networks. Existing methods typically address this using networks derived from a common base model or costly approximate neuron alignment. We instead parameterize a flow-matching velocity field with a permutation-equivariant Graph Meta Network, enabling direct learning from independently trained networks without alignment. Extensive experiments show that our method closely reproduces the joint statistics of accuracy, functional similarity, and weight similarity of independently trained collections, providing evidence of generation beyond checkpoint memorization. A single conditional model also generates task-specific networks on heterogeneous architectures and generalizes to unseen hidden-width configurations. On a tabular domain-shift task, intermediate conditioning produces individual networks with performance comparable to logit ensembles across both domains. Taken together, our results show how permutation equivariance enables learning from diverse collections of independently trained networks without permutation alignment.