S4 is a structured state space sequence model that efficiently models long-range dependencies (LRDs) in sequence data. The paper introduces S4, which is based on a new parameterization of the state space model (SSM), allowing for efficient computation while preserving the theoretical strengths of SSMs. S4 addresses the computational and memory challenges of previous SSM-based models by conditioning the state matrix A with a low-rank correction, enabling it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. This results in a computational complexity of $\tilde{O}(N + L)$ and memory usage of $O(N + L)$, which is essentially tight for sequence models. S4 achieves strong empirical results across a diverse range of established benchmarks. It achieves 91% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet. It substantially closes the gap to Transformers on image and language modeling tasks while performing generation 60× faster. S4 also sets the state-of-the-art on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors. The paper also discusses the theoretical foundations of SSMs, including the HiPPO framework for continuous-time memorization and the use of the SSM convolution kernel. The S4 parameterization is shown to be effective for a wide range of tasks, including large-scale generative modeling, fast autoregressive generation, and sampling resolution change. S4 is also shown to be effective in learning with weaker inductive biases, outperforming other models on tasks such as speech classification and time-series forecasting. The paper concludes that S4 has the potential to be an effective general sequence modeling solution, capable of handling a wide range of tasks across different modalities and domains. The results across established benchmarks suggest that S4 is a promising approach for sequence modeling, particularly for tasks that require efficient handling of long-range dependencies.S4 is a structured state space sequence model that efficiently models long-range dependencies (LRDs) in sequence data. The paper introduces S4, which is based on a new parameterization of the state space model (SSM), allowing for efficient computation while preserving the theoretical strengths of SSMs. S4 addresses the computational and memory challenges of previous SSM-based models by conditioning the state matrix A with a low-rank correction, enabling it to be diagonalized stably and reducing the SSM to the well-studied computation of a Cauchy kernel. This results in a computational complexity of $\tilde{O}(N + L)$ and memory usage of $O(N + L)$, which is essentially tight for sequence models. S4 achieves strong empirical results across a diverse range of established benchmarks. It achieves 91% accuracy on sequential CIFAR-10 with no data augmentation or auxiliary losses, on par with a larger 2-D ResNet. It substantially closes the gap to Transformers on image and language modeling tasks while performing generation 60× faster. S4 also sets the state-of-the-art on every task from the Long Range Arena benchmark, including solving the challenging Path-X task of length 16k that all prior work fails on, while being as efficient as all competitors. The paper also discusses the theoretical foundations of SSMs, including the HiPPO framework for continuous-time memorization and the use of the SSM convolution kernel. The S4 parameterization is shown to be effective for a wide range of tasks, including large-scale generative modeling, fast autoregressive generation, and sampling resolution change. S4 is also shown to be effective in learning with weaker inductive biases, outperforming other models on tasks such as speech classification and time-series forecasting. The paper concludes that S4 has the potential to be an effective general sequence modeling solution, capable of handling a wide range of tasks across different modalities and domains. The results across established benchmarks suggest that S4 is a promising approach for sequence modeling, particularly for tasks that require efficient handling of long-range dependencies.