Antibodies are crucial proteins produced by the immune system to eliminate harmful foreign substances and have become pivotal therapeutic agents for treating human diseases.

Structured state space models (SSMs), the core engine behind prominent neural networks such as S4 and Mamba, are linear dynamical systems adhering to a specified structure, most notably diagonal. In contrast to typical neural network modules, whose parameterizations are real, SSMs often use complex parameter-izations. Theoretically explaining the benefits of complex parameterizations for SSMs is an open problem. The current paper takes a step towards its resolution, by establishing formal gaps between real and complex diagonal SSMs.