This paper presents a nonparametric construction for deep learning compatible modern Hopfield models and introduces an efficient variant with sub-quadratic complexity. The key contribution is interpreting memory storage and retrieval in modern Hopfield models as a nonparametric regression problem with query-memory pairs. This framework recovers the known results from the original dense modern Hopfield model and introduces sparse-structured models with sub-quadratic complexity. The sparse model inherits the theoretical properties of its dense counterpart, including connection to transformer attention, fixed point convergence, and exponential memory capacity, without requiring knowledge of the Hopfield energy function. The framework is extended to construct a family of modern Hopfield models, including linear, random masked, top-K, and positive random feature models. Empirically, the framework is validated in both synthetic and realistic settings. Theoretical analysis shows that the sparse model has tighter retrieval error bounds, stronger noise robustness, and exponential memory capacity compared to the dense model. The framework also supports efficient implementations with various kernel functions, including linear and positive random features. The work addresses three key challenges in modern Hopfield models: computational efficiency, rigorous analysis of sparsity, and integration with attention mechanisms. The proposed framework provides a nonparametric approach for constructing modern Hopfield models with theoretical guarantees and practical efficiency.This paper presents a nonparametric construction for deep learning compatible modern Hopfield models and introduces an efficient variant with sub-quadratic complexity. The key contribution is interpreting memory storage and retrieval in modern Hopfield models as a nonparametric regression problem with query-memory pairs. This framework recovers the known results from the original dense modern Hopfield model and introduces sparse-structured models with sub-quadratic complexity. The sparse model inherits the theoretical properties of its dense counterpart, including connection to transformer attention, fixed point convergence, and exponential memory capacity, without requiring knowledge of the Hopfield energy function. The framework is extended to construct a family of modern Hopfield models, including linear, random masked, top-K, and positive random feature models. Empirically, the framework is validated in both synthetic and realistic settings. Theoretical analysis shows that the sparse model has tighter retrieval error bounds, stronger noise robustness, and exponential memory capacity compared to the dense model. The framework also supports efficient implementations with various kernel functions, including linear and positive random features. The work addresses three key challenges in modern Hopfield models: computational efficiency, rigorous analysis of sparsity, and integration with attention mechanisms. The proposed framework provides a nonparametric approach for constructing modern Hopfield models with theoretical guarantees and practical efficiency.