# LSH Models in Federated Recommendation
## 1 Introduction  
Deep learning-based recommendation systems usually take data related to various kinds of users or items as model input, represent the hidden mapping relationship between the users and items, and generate the recommendation results. Three models named Generalized Matrix Factorization (GMF), Multilayer Perceptron (MLP), and Neural Matrix Factorization (NeuMF) are proposed [1]. One of the most common forms for constructing deep learning recommendation is MLP [2]. By increasing the number of layers and complexity of the deep neural network structure, Autoencoder is proposed [3]. Neural collaborative filtering (NCF) [4] has evolved through a rich feature crossover mode. In NCF, the simple inner product operations in the matrix decomposition have been dropped, more nonlinear features are introduced, which improves the learning ability of the sparse features. In addition, the deep interest network [5], as well as the deep interest evolution network [6], and the dynamic path selection multi-interest network [7] using the capsule network to extract the diverse interests of users all represent the current optimal deep learning recommendation model. Federated learning is a distributed machine learning environment. Under the coordination of central servers, multiple entities (clients) collaborate to complete the learning problems. Each client's raw data are stored locally, not exchanged or transmitted, and only in the aggregated update model. With the public attention on personal data privacy, it becomes increasingly important how the recommendation system to seek the optimal solution between personalization and privacy protection and data perturbation technology have been widely used in recommendation. [PERSON] [8] has proposed differential privacy(DP, including local DP and global DP) by adding Laplacian noise, which is used for the collaborative filtering algorithm. A localized DP-based perturbations on federated recommendation is proposed recently [9]. The traditional recommendation system is designed to protect the privacy of individual users by preventing the leakage of their original data and by encrypting the transmission of recommended original inputs. The federated recommendation system employs encryption of the gradient update of the recommendation model to safeguard privacy [10]. It also avoids the significant computational overhead of directly training the global model on the original data cipher domain. Furthermore, it effectively reduces the numerous privacy risks associated with data aggregation in traditional machine learning sources. The current federal recommendation system is still afflicted by two significant shortcomings: firstly, the addition of LDP has resulted in a reduction in the accuracy of recommendations, and secondly, the incorporation of Laplace noise has led to an increase in communication overhead [10]. Locality sensitive hash (LSH) is an approximate nearest neighbor (ANN) search and mapping technique. The locality hashing technique is employed to protect the client-uploaded model parameters throughout the training process of federated learning. The LSH primarily safeguards the local parameters of the model, which comprise sensitive information from the user. By hashing these local parameters, namely converting them to hash values, it is possible to ensure that when uploaded to the central server, even if the parameters are intercepted or leaked, the user-specific information cannot be directly obtained due to the unidirectional nature of the hash function. Consequently, LSH can safeguard user privacy and model security, even when federated learning clients are not deemed trustworthy or at risk. This paper presents three joint locality sensitive hashing (LSH) models combined with recommendation systems: GMF, MLP, and NeuMF. The LSH-enhanced federated learning model is the result of this combination.