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In neural architecture search (NAS) methods based on latent space optimization (LSO), a deep generative model is trained to embed discrete neural architectures into a continuous latent space. In this case, different optimization algorithms that operate in the continuous space can be implemented to search neural architectures. However, the optimization of latent variables is challenging for gradient-based LSO since the mapping from the latent space to the architecture performance is generally non-convex. To tackle this problem, this paper develops a convexity regularized latent space optimization (CR-LSO) method, which aims to regularize the learning process of latent space in order to obtain a convex architecture performance mapping. Specifically, CR-LSO trains a graph variational autoencoder (G-VAE) to learn the continuous representations of discrete architectures. Simultaneously, the learning process of latent space is regularized by the guaranteed convexity of input convex neural networks (ICNNs). In this way, the G-VAE is forced to learn a convex mapping from the architecture representation to the architecture performance. Hereafter, the CR-LSO approximates the performance mapping using the ICNN and leverages the estimated gradient to optimize neural architecture representations. Experimental results on three popular NAS benchmarks show that CR-LSO achieves competitive evaluation results in terms of both computational complexity and architecture performance.