The paper introduces *Clifford-Steerable Convolutional Neural Networks* (CS-CNNs), a novel class of equivariant CNNs designed to process multivector fields on pseudo-Euclidean spaces. CS-CNNs are equivariant to the pseudo-Euclidean group \( \mathrm{E}(p, q) \), which includes transformations such as translations and Lorentz boosts. The key innovation is the implicit parametrization of \( \mathrm{O}(p, q) \)-steerable kernels via Clifford group equivariant neural networks. This approach allows CS-CNNs to handle complex field types, such as those encountered in physics, while maintaining equivariance. The paper demonstrates the effectiveness of CS-CNNs through experiments on fluid dynamics and relativistic electrodynamics forecasting tasks. CS-CNNs outperform baseline methods, including conventional steerable CNNs and non-equivariant Clifford CNNs, in terms of performance and sample efficiency. The models consistently achieve better results, even with smaller datasets, and show consistent performance across different spacetime dimensions. The main contributions of the work include: 1. Processing full multivector fields on pseudo-Euclidean spaces. 2. Developing an implicit implementation of \( \mathrm{O}(p, q) \)-steerable kernels via \( \mathrm{O}(p, q) \)-equivariant MLPs. 3. Evaluating E(p, q)-equivariant CNNs on various PDE simulation tasks, consistently outperforming strong baselines. The paper also discusses the theoretical background, including pseudo-Euclidean spaces, feature vector fields, steerable CNNs, and the Clifford algebra. It provides a detailed explanation of how CS-CNNs are constructed and how they achieve equivariance. Experimental results show that CS-CNNs are effective in simulating physical systems, particularly in higher-dimensional spacetime settings.The paper introduces *Clifford-Steerable Convolutional Neural Networks* (CS-CNNs), a novel class of equivariant CNNs designed to process multivector fields on pseudo-Euclidean spaces. CS-CNNs are equivariant to the pseudo-Euclidean group \( \mathrm{E}(p, q) \), which includes transformations such as translations and Lorentz boosts. The key innovation is the implicit parametrization of \( \mathrm{O}(p, q) \)-steerable kernels via Clifford group equivariant neural networks. This approach allows CS-CNNs to handle complex field types, such as those encountered in physics, while maintaining equivariance. The paper demonstrates the effectiveness of CS-CNNs through experiments on fluid dynamics and relativistic electrodynamics forecasting tasks. CS-CNNs outperform baseline methods, including conventional steerable CNNs and non-equivariant Clifford CNNs, in terms of performance and sample efficiency. The models consistently achieve better results, even with smaller datasets, and show consistent performance across different spacetime dimensions. The main contributions of the work include: 1. Processing full multivector fields on pseudo-Euclidean spaces. 2. Developing an implicit implementation of \( \mathrm{O}(p, q) \)-steerable kernels via \( \mathrm{O}(p, q) \)-equivariant MLPs. 3. Evaluating E(p, q)-equivariant CNNs on various PDE simulation tasks, consistently outperforming strong baselines. The paper also discusses the theoretical background, including pseudo-Euclidean spaces, feature vector fields, steerable CNNs, and the Clifford algebra. It provides a detailed explanation of how CS-CNNs are constructed and how they achieve equivariance. Experimental results show that CS-CNNs are effective in simulating physical systems, particularly in higher-dimensional spacetime settings.