Interfaces and Modules: A Scalable Representation for Weight-Space Learning across Architectures

Weight-space learning across architectures requires representations that respect parameter symmetries and scale to large networks. Existing equivariant tensor encoders require architecture-specific symmetry specifications, while neuron graphs make global attention costly. We introduce a typed graph organized around shared coordinate-permutation actions. Its nodes, called interfaces, represent coordinate spaces whose bound tensor axes must be permuted jointly; operation occurrences, called modules, form typed hyperedges. A compiler derives this graph from supported PyTorch models, with exact recovery of the permutation factors defined by its constraints. The Universal Weight Encoder (UWE) combines local equivariant updates to parameter features with global attention over invariant interface summaries. The small number of interfaces makes global attention practical, and a single encoder processes different supported architectures. UWE is competitive with architecture-specific state-of-the-art methods on established benchmarks. On a new zoo of 1,200 transformers spanning 100 architectures, it outperforms the evaluated baselines at ranking networks within unseen architectures, including architectures larger than those used for training, while using substantially less memory.