where K is the convolution filter, parameterized via A, B, and C (see Supplementary Material for a detailed derivation). This convolutional representation reveals a key aspect of state-space models: they learn explicitly from the entire sequence (via global convolution) while preserving recurrent generation capabilities (Figure ). Learning the optimal parameters of a discrete state-space system, however, introduces vanishing gradient problems both in recurrent and convolutional formulations. Structured state-space sequence models, (S4s) , tackle those issues by introducing additional structure to the model parameters (via the so-called high-order polynomial projection operators ) and reducing the unstable computations to the stable Cauchy kernel computation (see for more detail). Ablation studies have During the generation, S4 switches to the recurrent formulation (via the same parameters, (equation ( )) and produces SMILES strings element-by-element for more efficient and effective chemical space exploration. (c) Computational pipeline, where S4 was used to learn from known SMILES strings and generate new molecules de novo.