Dynamic Voxel Grid Optimization for High-Fidelity RGB-D Supervised Surface Reconstruction

Direct optimization of interpolated features on multi-resolution voxel grids has emerged as a more efficient alternative to MLP-like modules. However, this approach is constrained by higher memory expenses and limited representation capabilities. In this paper, we introduce a novel dynamic grid optimization method for high-fidelity 3D surface reconstruction that incorporates both RGB and depth observations. Rather than treating each voxel equally, we optimize the process by dynamically modifying the grid and assigning more finer-scale voxels to regions with higher complexity, allowing us to capture more intricate details. Furthermore, we develop a scheme to quantify the dynamic subdivision of voxel grid during optimization without requiring any priors. The proposed approach is able to generate high-quality 3D reconstructions with fine details on both synthetic and real-world data, while maintaining computational efficiency, which is substantially faster than the baseline method NeuralRGBD.

Decentralized Riemannian Algorithm for Nonconvex Minimax Problems

The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has been actively applied to solve many problems, such as robust dimensionality reduction and deep neural networks with orthogonal weights (Stiefel manifold). Although many optimization algorithms for minimax problems have been developed in the Euclidean setting, it is difficult to convert them into Riemannian cases, and algorithms for nonconvex minimax problems with nonconvex constraints are even rare. On the other hand, to address the big data challenges, decentralized (serverless) training techniques have recently been emerging since they can reduce communications overhead and avoid the bottleneck problem on the server node. Nonetheless, the algorithm for decentralized Riemannian minimax problems has not been studied. In this paper, we study the distributed nonconvex-strongly-concave minimax optimization problem over the Stiefel manifold and propose both deterministic and stochastic minimax methods. The Steifel manifold is a non-convex set. The global function is represented as the finite sum of local functions. For the deterministic setting, we propose DRGDA and prove that our deterministic method achieves a gradient complexity of $O( \epsilon^{-2})$ under mild conditions. For the stochastic setting, we propose DRSGDA and prove that our stochastic method achieves a gradient complexity of $O(\epsilon^{-4})$. The DRGDA and DRSGDA are the first algorithms for distributed minimax optimization with nonconvex constraints with exact convergence. Extensive experimental results on the Deep Neural Networks (DNNs) training over the Stiefel manifold demonstrate the efficiency of our algorithms.

Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems

Bilevel Optimization has witnessed notable progress recently with new emerging efficient algorithms, yet it is underexplored in the Federated Learning setting. It is unclear how the challenges of Federated Learning affect the convergence of bilevel algorithms. In this work, we study Federated Bilevel Optimization problems. We first propose the FedBiO algorithm that solves the hyper-gradient estimation problem efficiently, then we propose FedBiOAcc to accelerate FedBiO. FedBiO has communication complexity $O(\epsilon^{-1.5})$ with linear speed up, while FedBiOAcc achieves communication complexity $O(\epsilon^{-1})$, sample complexity $O(\epsilon^{-1.5})$ and also the linear speed up. We also study Federated Bilevel Optimization problems with local lower level problems, and prove that FedBiO and FedBiOAcc converges at the same rate with some modification.

FedDA: Faster Framework of Local Adaptive Gradient Methods via Restarted Dual Averaging

Federated learning (FL) is an emerging learning paradigm to tackle massively distributed data. In Federated Learning, a set of clients jointly perform a machine learning task under the coordination of a server. The FedAvg algorithm is one of the most widely used methods to solve Federated Learning problems. In FedAvg, the learning rate is a constant rather than changing adaptively. The adaptive gradient methods show superior performance over the constant learning rate schedule; however, there is still no general framework to incorporate adaptive gradient methods into the federated setting. In this paper, we propose \textbf{FedDA}, a novel framework for local adaptive gradient methods. The framework adopts a restarted dual averaging technique and is flexible with various gradient estimation methods and adaptive learning rate formulations. In particular, we analyze \textbf{FedDA-MVR}, an instantiation of our framework, and show that it achieves gradient complexity $\tilde{O}(\epsilon^{-1.5})$ and communication complexity $\tilde{O}(\epsilon^{-1})$ for finding a stationary point $\epsilon$. This matches the best known rate for first-order FL algorithms and \textbf{FedDA-MVR} is the first adaptive FL algorithm that achieves this rate. We also perform extensive numerical experiments to verify the efficacy of our method.

A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization

In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic constraint. In particular, we propose a Newton-conjugate gradient (Newton-CG) based barrier-augmented Lagrangian method for finding an approximate SOSP of this problem. Under some mild assumptions, we show that our method enjoys a total inner iteration complexity of $\widetilde{\cal O}(\epsilon^{-11/2})$ and an operation complexity of $\widetilde{\cal O}(\epsilon^{-11/2}\min\{n,\epsilon^{-5/4}\})$ for finding an $(\epsilon,\sqrt{\epsilon})$-SOSP of general nonconvex conic optimization with high probability. Moreover, under a constraint qualification, these complexity bounds are improved to $\widetilde{\cal O}(\epsilon^{-7/2})$ and $\widetilde{\cal O}(\epsilon^{-7/2}\min\{n,\epsilon^{-3/4}\})$, respectively. To the best of our knowledge, this is the first study on the complexity of finding an approximate SOSP of general nonconvex conic optimization. Preliminary numerical results are presented to demonstrate superiority of the proposed method over first-order methods in terms of solution quality.

Adversarial Weight Perturbation Improves Generalization in Graph Neural Network

A lot of theoretical and empirical evidence shows that the flatter local minima tend to improve generalization. Adversarial Weight Perturbation (AWP) is an emerging technique to efficiently and effectively find such minima. In AWP we minimize the loss w.r.t. a bounded worst-case perturbation of the model parameters thereby favoring local minima with a small loss in a neighborhood around them. The benefits of AWP, and more generally the connections between flatness and generalization, have been extensively studied for i.i.d. data such as images. In this paper, we extensively study this phenomenon for graph data. Along the way, we first derive a generalization bound for non-i.i.d. node classification tasks. Then we identify a vanishing-gradient issue with all existing formulations of AWP and we propose a new Weighted Truncated AWP (WT-AWP) to alleviate this issue. We show that regularizing graph neural networks with WT-AWP consistently improves both natural and robust generalization across many different graph learning tasks and models.

Faster Adaptive Federated Learning

Federated learning has attracted increasing attention with the emergence of distributed data. While extensive federated learning algorithms have been proposed for the non-convex distributed problem, the federated learning in practice still faces numerous challenges, such as the large training iterations to converge since the sizes of models and datasets keep increasing, and the lack of adaptivity by SGD-based model updates. Meanwhile, the study of adaptive methods in federated learning is scarce and existing works either lack a complete theoretical convergence guarantee or have slow sample complexity. In this paper, we propose an efficient adaptive algorithm (i.e., FAFED) based on the momentum-based variance reduced technique in cross-silo FL. We first explore how to design the adaptive algorithm in the FL setting. By providing a counter-example, we prove that a simple combination of FL and adaptive methods could lead to divergence. More importantly, we provide a convergence analysis for our method and prove that our algorithm is the first adaptive FL algorithm to reach the best-known samples $O(\epsilon^{-3})$ and $O(\epsilon^{-2})$ communication rounds to find an $\epsilon$-stationary point without large batches. The experimental results on the language modeling task and image classification task with heterogeneous data demonstrate the efficiency of our algorithms.

Towards Robust Dataset Learning

Adversarial training has been actively studied in recent computer vision research to improve the robustness of models. However, due to the huge computational cost of generating adversarial samples, adversarial training methods are often slow. In this paper, we study the problem of learning a robust dataset such that any classifier naturally trained on the dataset is adversarially robust. Such a dataset benefits the downstream tasks as natural training is much faster than adversarial training, and demonstrates that the desired property of robustness is transferable between models and data. In this work, we propose a principled, tri-level optimization to formulate the robust dataset learning problem. We show that, under an abstraction model that characterizes robust vs. non-robust features, the proposed method provably learns a robust dataset. Extensive experiments on MNIST, CIFAR10, and TinyImageNet demostrate the effectiveness of our algorithm with different network initializations and architectures.

BI AVAN: Brain inspired Adversarial Visual Attention Network

Visual attention is a fundamental mechanism in the human brain, and it inspires the design of attention mechanisms in deep neural networks. However, most of the visual attention studies adopted eye-tracking data rather than the direct measurement of brain activity to characterize human visual attention. In addition, the adversarial relationship between the attention-related objects and attention-neglected background in the human visual system was not fully exploited. To bridge these gaps, we propose a novel brain-inspired adversarial visual attention network (BI-AVAN) to characterize human visual attention directly from functional brain activity. Our BI-AVAN model imitates the biased competition process between attention-related/neglected objects to identify and locate the visual objects in a movie frame the human brain focuses on in an unsupervised manner. We use independent eye-tracking data as ground truth for validation and experimental results show that our model achieves robust and promising results when inferring meaningful human visual attention and mapping the relationship between brain activities and visual stimuli. Our BI-AVAN model contributes to the emerging field of leveraging the brain's functional architecture to inspire and guide the model design in artificial intelligence (AI), e.g., deep neural networks.

FedGRec: Federated Graph Recommender System with Lazy Update of Latent Embeddings

Recommender systems are widely used in industry to improve user experience. Despite great success, they have recently been criticized for collecting private user data. Federated Learning (FL) is a new paradigm for learning on distributed data without direct data sharing. Therefore, Federated Recommender (FedRec) systems are proposed to mitigate privacy concerns to non-distributed recommender systems. However, FedRec systems have a performance gap to its non-distributed counterpart. The main reason is that local clients have an incomplete user-item interaction graph, thus FedRec systems cannot utilize indirect user-item interactions well. In this paper, we propose the Federated Graph Recommender System (FedGRec) to mitigate this gap. Our FedGRec system can effectively exploit the indirect user-item interactions. More precisely, in our system, users and the server explicitly store latent embeddings for users and items, where the latent embeddings summarize different orders of indirect user-item interactions and are used as a proxy of missing interaction graph during local training. We perform extensive empirical evaluations to verify the efficacy of using latent embeddings as a proxy of missing interaction graph; the experimental results show superior performance of our system compared to various baselines. A short version of the paper is presented in \href{https://federated-learning.org/fl-neurips-2022/}{the FL-NeurIPS'22 workshop}.