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i-Octree: A Fast, Lightweight, and Dynamic Octree for Proximity Search
Sep 15, 2023
Establishing the correspondences between newly acquired points and historically accumulated data (i.e., map) through nearest neighbors search is crucial in numerous robotic applications.However, static tree data structures are inadequate to handle large and dynamically growing maps in real-time.To address this issue, we present the i-Octree, a dynamic octree data structure that supports both fast nearest neighbor search and real-time dynamic updates, such as point insertion, deletion, and on-tree down-sampling. The i-Octree is built upon a leaf-based octree and has two key features: a local spatially continuous storing strategy that allows for fast access to points while minimizing memory usage, and local on-tree updates that significantly reduce computation time compared to existing static or dynamic tree structures.The experiments show that i-Octree surpasses state-of-the-art methods by reducing run-time by over 50% on real-world open datasets.
A Convergent ADMM Framework for Efficient Neural Network Training
Dec 22, 2021
As a well-known optimization framework, the Alternating Direction Method of Multipliers (ADMM) has achieved tremendous success in many classification and regression applications. Recently, it has attracted the attention of deep learning researchers and is considered to be a potential substitute to Gradient Descent (GD). However, as an emerging domain, several challenges remain unsolved, including 1) The lack of global convergence guarantees, 2) Slow convergence towards solutions, and 3) Cubic time complexity with regard to feature dimensions. In this paper, we propose a novel optimization framework to solve a general neural network training problem via ADMM (dlADMM) to address these challenges simultaneously. Specifically, the parameters in each layer are updated backward and then forward so that parameter information in each layer is exchanged efficiently. When the dlADMM is applied to specific architectures, the time complexity of subproblems is reduced from cubic to quadratic via a dedicated algorithm design utilizing quadratic approximations and backtracking techniques. Last but not least, we provide the first proof of convergence to a critical point sublinearly for an ADMM-type method (dlADMM) under mild conditions. Experiments on seven benchmark datasets demonstrate the convergence, efficiency, and effectiveness of our proposed dlADMM algorithm.
Community-based Layerwise Distributed Training of Graph Convolutional Networks
Dec 17, 2021
The Graph Convolutional Network (GCN) has been successfully applied to many graph-based applications. Training a large-scale GCN model, however, is still challenging: Due to the node dependency and layer dependency of the GCN architecture, a huge amount of computational time and memory is required in the training process. In this paper, we propose a parallel and distributed GCN training algorithm based on the Alternating Direction Method of Multipliers (ADMM) to tackle the two challenges simultaneously. We first split GCN layers into independent blocks to achieve layer parallelism. Furthermore, we reduce node dependency by dividing the graph into several dense communities such that each of them can be trained with an agent in parallel. Finally, we provide solutions for all subproblems in the community-based ADMM algorithm. Preliminary results demonstrate that our proposed community-based ADMM training algorithm can lead to more than triple speedup while achieving the best performance compared with state-of-the-art methods.
Towards Quantized Model Parallelism for Graph-Augmented MLPs Based on Gradient-Free ADMM framework
May 20, 2021
The Graph Augmented Multi-layer Perceptron (GA-MLP) model is an attractive alternative to Graph Neural Networks (GNNs). This is because it is resistant to the over-smoothing problem, and deeper GA-MLP models yield better performance. GA-MLP models are traditionally optimized by the Stochastic Gradient Descent (SGD). However, SGD suffers from the layer dependency problem, which prevents the gradients of different layers of GA-MLP models from being calculated in parallel. In this paper, we propose a parallel deep learning Alternating Direction Method of Multipliers (pdADMM) framework to achieve model parallelism: parameters in each layer of GA-MLP models can be updated in parallel. The extended pdADMM-Q algorithm reduces communication cost by utilizing the quantization technique. Theoretical convergence to a critical point of the pdADMM algorithm and the pdADMM-Q algorithm is provided with a sublinear convergence rate $o(1/k)$. Extensive experiments in six benchmark datasets demonstrate that the pdADMM can lead to high speedup, and outperforms all the existing state-of-the-art comparison methods.