A prior map serves as a foundational reference for localization in context-aware applications such as augmented reality (AR). Providing valuable contextual information about the environment, the prior map is a vital tool for mitigating drift. In this paper, we propose a map-based visual-inertial localization algorithm (NeRF-VIO) with initialization using neural radiance fields (NeRF). Our algorithm utilizes a multilayer perceptron model and redefines the loss function as the geodesic distance on \(SE(3)\), ensuring the invariance of the initialization model under a frame change within \(\mathfrak{se}(3)\). The evaluation demonstrates that our model outperforms existing NeRF-based initialization solution in both accuracy and efficiency. By integrating a two-stage update mechanism within a multi-state constraint Kalman filter (MSCKF) framework, the state of NeRF-VIO is constrained by both captured images from an onboard camera and rendered images from a pre-trained NeRF model. The proposed algorithm is validated using a real-world AR dataset, the results indicate that our two-stage update pipeline outperforms MSCKF across all data sequences.

We describe a graph-based neural acceleration technique for nonnegative matrix factorization that builds upon a connection between matrices and bipartite graphs that is well-known in certain fields, e.g., sparse linear algebra, but has not yet been exploited to design graph neural networks for matrix computations. We first consider low-rank factorization more broadly and propose a graph representation of the problem suited for graph neural networks. Then, we focus on the task of nonnegative matrix factorization and propose a graph neural network that interleaves bipartite self-attention layers with updates based on the alternating direction method of multipliers. Our empirical evaluation on synthetic and two real-world datasets shows that we attain substantial acceleration, even though we only train in an unsupervised fashion on smaller synthetic instances.