What Do Separable Physics-Informed Neural Networks Need from a Recurrent Block?

Sequence-model architectures combine interactions between tokens with nonlinear channel transformations, but the contributions of these components to physics-informed learning are difficult to distinguish. We study this question in separable physics-informed neural networks, where independent coordinate branches form a multidimensional field through a sum-of-products representation. We introduce Separable RWKV (S-RWKV), whose branches apply a smooth matrix-memory update to groups of learned Fourier features. Recurrence is confined to feature groups at a single coordinate and does not propagate between physical points. This construction allows us to remove the memory path while retaining the input encoding, channel transformations, field assembly, and training protocol. Across six benchmarks with repeated runs, the memory-free variant has lower mean errors than the full model on most scalar problems and requires fewer parameters and forward operations. Direct projection of the Fourier features, without chan nel transformations, produces larger errors and greater variation across runs on Convection and Wave. Comparisons with a separable multilayer perceptron show that the branch body remains important under matched input features and training conditions. Stage-wise results show that the main accuracy differences arise before output-projection refinement. Under the shared protocol, the memory-free model also outperforms the compared attention- and state-space-based networks on the scalar benchmarks. These results support lightweight nonlinear processing of grouped spectral features as an effective design for separable physics-informed learning