Registering an object shape to a sequence of point clouds undergoing non-rigid deformation is a long-standing challenge. The key difficulties stem from two factors: (i) the presence of local minima due to the non-convexity of registration objectives, especially under noisy or partial inputs, which hinders accurate and robust deformation estimation, and (ii) error accumulation over long sequences, leading to tracking failures. To address these challenges, we introduce to adopt a scalable data-driven approach and propose \methodname, an efficient feed-forward model trained on large deformation datasets.It is designed to handle noisy and partial inputs while effectively leveraging temporal information for accurate and consistent sequential registration. The key to our design is predicting a sequence of deformation graphs through a two-stage pipeline, which first estimates frame-wise coarse graph nodes for robust initialization, before refining their trajectories over time in a sliding-window fashion. Extensive experiments show that our proposed approach (i) outperforms previous state of the art on both the DeformingThings4D and D-FAUST datasets, and (ii) achieves more than 4x speedup compared to the previous best, offering significant efficiency improvement.
论文检索
输入标题、作者或关键词，从 619 篇学术成果中精准定位
Outliers are ubiquitous in geometric vision contexts such as pose estimation and mapping, leading to inaccurate estimates. While robust loss functions can tackle outliers, it is challenging to make the estimation robust to the choice of initialization and to estimate the appropriate robust loss shape parameter that allows distinguishing inliers from outliers. Graduated non-convexity (GNC) often mitigates these issues. However, typical GNC uses a fixed annealing factor to update the shape parameter, which can lead to low-quality or inefficient estimates. This paper proposes a novel approach to adaptively anneal the shape parameter within a GNC framework. We developed a search strategy that incorporates a sampling of annealing choices and model scorings to select the most promising shape parameter at each GNC iteration. Additionally, we propose new stopping criteria and an initialization technique that improves performance for diverse data, and we show the benefits of combining discrete and continuous robust estimation strategies. We evaluate our method using synthetic and real-world data in two problems: 3D registration and pose graph optimization in SLAM sequences. Our results demonstrate greater efficiency and robustness compared to previous GNC schemes. Code and other resources are available at https://www.merl.com/research/highlights/sac-gnc.
FedDifRC: Unlocking the Potential of Text-to-Image Diffusion Models in Heterogeneous Federated Learning
PDF ↗Federated learning aims at training models collaboratively across participants while protecting privacy. However, one major challenge for this paradigm is the data heterogeneity issue, where biased data preferences across multiple clients, harming the model's convergence and performance. In this paper, we first introduce powerful diffusion models into the federated learning paradigm and show that diffusion representations are effective steers during federated training. To explore the possibility of using diffusion representations in handling data heterogeneity, we propose a novel diffusion-inspired Federated paradigm with Diffusion Representation Collaboration, termed FedDifRC, leveraging meaningful guidance of diffusion models to mitigate data heterogeneity. The key idea is to construct text-driven diffusion contrasting and noise-driven diffusion regularization, aiming to provide abundant class-related semantic information and consistent convergence signals. On the one hand, we exploit the conditional feedback from the diffusion model for different text prompts to build a text-driven contrastive learning strategy. On the other hand, we introduce a noise-driven consistency regularization to align local instances with diffusion denoising representations, constraining the optimization region in the feature space. In addition, FedDifRC can be extended to a self-supervised scheme without relying on any labeled data. We also provide a theoretical analysis for FedDifRC to ensure convergence under non-convex objectives. The experiments on different scenarios validate the effectiveness of FedDifRC and the efficiency of crucial components.
The rapid proliferation of multi-view data has necessitated robust and scalable clustering techniques capable of capturing complex, high-dimensional patterns. While Multi-view Bipartite Graph Clustering (MVBGC) has shown promising results, existing approaches often overlook that the generated bipartite graph is susceptible to disturbances from complex structures and noise. To address these challenges, we propose RTGD-MVC, a novel framework for Robust Tensor Learning with Graph Diffusion tailored for efficient and scalable multi-view graph clustering. RTGD-MVC integrates a graph diffusion mechanism to suppress noise propagation and employs cross-view diffusion to enhance global consistency while capturing complementary information across views. Additionally, a non-convex Tensor Exponential Norm (TEN) is introduced as a tighter surrogate for the tensor rank, enabling the learning of more discriminative and noise-robust representations. By embedding these components into a unified optimization model with linear computational complexity, RTGD-MVC achieves both theoretical efficiency and practical scalability. Extensive experiments on diverse benchmark datasets demonstrate that RTGD-MVC significantly outperforms state-of-the-art methods, highlighting its superior ability to capture intricate multi-view correlations and structural patterns.
Physics-based Generative Models for Geometrically Consistent and Interpretable Wireless Channel Synthesis
PDF ↗In recent years, machine learning (ML) methods have become increasingly popular in wireless communication systems for several applications. A critical bottleneck for designing ML systems for wireless communications is the availability of realistic wireless channel datasets, which are extremely resource-intensive to produce. To this end, the generation of realistic wireless channels plays a key role in the subsequent design of effective ML algorithms for wireless communication systems. Generative models have been proposed to synthesize channel matrices, but outputs produced by such methods may not correspond to geometrically viable channels and do not provide any insight into the scenario being generated. In this work, we aim to address both these issues by integrating established parametric, physics-based geometric channel (PPGC) modeling frameworks with generative methods to produce realistic channel matrices with interpretable representations in the parameter domain. We show that the generative model converges to prohibitively suboptimal stationary points when learning the underlying prior directly over the parameters due to the non-convex PPGC model. To address this limitation, we propose a linearized reformulation of the problem to ensure smooth gradient flow during generative model training, while also providing insights into the underlying physical environment. We evaluate our model against prior baselines by comparing the generated, scenario-specific samples in terms of the 2-Wasserstein distance and through its utility when used for downstream compression tasks.
Dyn-D^2P: Dynamic Differentially Private Decentralized Learning with Provable Utility Guarantee
PDF ↗Most existing decentralized learning methods with differential privacy (DP) guarantee rely on constant gradient clipping bounds and fixed-level DP Gaussian noises for each node throughout the training process, leading to a significant accuracy degradation compared to non-private counterparts. In this paper, we propose a new Dynamic Differentially Private Decentralized learning approach (termed Dyn-D^2P) tailored for general time-varying directed networks. Leveraging the Gaussian DP (GDP) framework for privacy accounting, Dyn-D^2P dynamically adjusts gradient clipping bounds and noise levels based on gradient convergence. This proposed dynamic noise strategy enables us to enhance model accuracy while preserving the total privacy budget. Extensive experiments on benchmark datasets demonstrate the superiority of Dyn-D^2P over its counterparts employing fixed-level noises, especially under strong privacy guarantees. Furthermore, we provide a provable utility bound for Dyn-D^2P that establishes an explicit dependency on network-related parameters, with a scaling factor of 1/sqrt{n} in terms of the number of nodes n up to a bias error term induced by gradient clipping. To our knowledge, this is the first model utility analysis for differentially private decentralized non-convex optimization with dynamic gradient clipping bounds and noise levels.
A Priori Estimation of the Approximation, Optimization and Generalization Errors of Random Neural Networks for Solving Partial Differential Equations
PDF ↗In recent years, neural networks have achieved remarkable progress in various fields and have also drawn much attention in applying them on scientific problems. A line of methods involving neural networks for solving partial differential equations (PDEs), such as Physics-Informed Neural Networks (PINNs) and the Deep Ritz Method (DRM), has emerged. Although these methods outperform classical numerical methods in certain cases, the optimization problems involving neural networks are typically non-convex and non-smooth, which can result in unsatisfactory solutions for PDEs. In contrast to deterministic neural networks, the hidden weights of random neural networks are sampled from some prior distribution and only the output weights participate in training. This makes training much simpler, but it remains unclear how to select the prior distribution. In this paper, we focus on Barron type functions and approximate them under Sobolev norms by random neural networks with clear prior distribution. In addition to the approximation error, we also derive bounds for the optimization and generalization errors of random neural networks for solving PDEs when the solutions are Barron type functions.
The use of estimators instead of stochastic gradients for updates has been shown to improve algorithm convergence rates of, but their impact on generalization remains under-explored. In this paper, we investigate how estimators influence generalization. Our focus is on two widely studied problems: stochastic optimization (SO) and stochastic compositional optimization (SCO), both under convex and non-convex settings. For SO problems, we first analyze the generalization error of the STORM algorithm as a foundational step. We then extend our analysis to SCO problems by introducing an algorithmic framework that encompasses several popular algorithmic approaches. Through this framework, we conduct a generalization analysis, uncovering new insights into the impact of estimators on generalization. Subsequently, we provide a detailed analysis of three specific algorithms within this framework: SCGD, SCSC, and COVER, to explore the effects of different estimator strategies. Furthermore, in the context of SCO, we propose a novel definition of stability and a new decomposition of excess risk in the non-convex setting. Our analysis indicates two key findings: (1) In SCO problems, eliminating the estimator for the gradient of the inner function does not impact generalization performance while significantly reducing computational and storage overhead. (2) Faster convergence rates are consistently associated with better generalization performance.
Federated Learning (FL) provides a flexible distributed platform where numerous clients with high data and system heterogeneity can collaborate to learn a model. While previous research has shown that FL can handle diverse data, it often completely assumes idealized conditions. In practice, real-world factors make it hard to predict or design individual client participation. This complexity results in an unknown participation pattern - arbitrary client participation (ACP). Hence, the key open problem is to understand the impact of client participation and develop a lightweight mechanism to support ACP in FL. In this paper, we first empirically investigate the client participation's influence in FL, revealing that FL algorithms are adversely impacted by ACP. To alleviate the impact, we propose a lightweight solution, Federated Average with Snapshot (FAST), that supports almost ACP for FL and can seamlessly integrate with other classic FL algorithms. Specifically, FAST enforces clients to take a snapshot once in a while and facilitates ACP for the majority of training processes. We prove that the convergence rates of FAST in non-convex and strongly-convex cases match those under ideal client participation. Furthermore, we empirically introduce an adaptive strategy to dynamically configure the snapshot frequency, tailored to accommodate diverse FL systems. Extensive experiments show that FAST significantly improves performance under ACP and high data heterogeneity.
Reinforcement Learning (RL) has made significant strides in various domains, and policy gradient methods like Proximal Policy Optimization (PPO) have gained popularity due to their balance in performance, training stability, and computational efficiency. These methods directly optimize policies through gradient-based updates. However, developing effective control policies for environments with complex and non-linear dynamics remains a challenge. High variance in gradient estimates and non-convex optimization landscapes often lead to unstable learning trajectories. Koopman Operator Theory has emerged as a powerful framework for studying non-linear systems through an infinite-dimensional linear operator that acts on a higher-dimensional space of measurement functions. In contrast with their non-linear counterparts, linear systems are simpler, more predictable, and easier to analyze. In this paper, we present Koopman-Inspired Proximal Policy Optimization (KIPPO), which learns an approximately linear latent-space representation of the underlying system’s dynamics while retaining essential features for effective policy learning. This is achieved through a Koopman-approximation auxiliary network that can be added to the baseline policy optimization algorithms without altering the architecture of the core policy or value function. Extensive experimental results demonstrate consistent improvements over the PPO baseline with 6–60% increased performance while reducing variability by up to 91% when evaluated on various continuous control tasks.
Many important scientific problems involve multivariate optimization coupled with slow and laborious experimental measurements. These high-dimensional searches can be defined by complex, non-convex optimization landscapes that resemble needle-in-a-haystack surfaces, leading to entrapment in local minima. Contextualizing optimizers with human domain knowledge is a powerful approach to guide searches to localized fruitful regions. However, this approach is susceptible to human confirmation bias. It is also challenging for domain experts to keep track of the rapidly expanding scientific literature. Here, we propose the use of Large Language Models (LLMs) for contextualizing Bayesian optimization (BO) via a hybrid optimization framework that intelligently and economically blends stochastic inference with domain knowledge-based insights from the LLM, which is used to suggest new, better-performing areas of the search space for exploration. Our method fosters user engagement by offering real-time commentary on the optimization progress, explaining the reasoning behind the search strategies. We validate the effectiveness of our approach on synthetic benchmarks with up to 15 variables and demonstrate the ability of LLMs to reason in four real-world experimental tasks where context-aware suggestions boost optimization performance substantially.
Machine Learning (ML) algorithms are increasingly used in our daily lives, yet often exhibit discrimination against protected groups. In this talk, I discuss the growing concern of bias in ML and overview existing approaches to address fairness issues. Then, I present three novel approaches developed by my research group. The first leverages generative AI to eliminate biases in training datasets, the second tackles non-convex problems arise in fair learning, and the third introduces a matrix decomposition-based post-processing approach to identify and eliminate unfair model components.
In decision-making problems under uncertainty, predicting unknown parameters is often considered independent of the optimization part. Decision-focused learning (DFL) is a task-oriented framework that integrates prediction and optimization by adapting the predictive model to give better decisions for the corresponding task. Here, an inevitable challenge arises when computing the gradients of the optimal decision with respect to the parameters. Existing research copes with this issue by smoothly reforming surrogate optimization or constructing surrogate loss functions that mimic task loss. However, they are applied to restricted optimization domains. In this paper, we propose Locally Convex Global Loss Network (LCGLN), a global surrogate loss model that can be implemented in a general DFL paradigm. LCGLN learns task loss via a partial input convex neural network which is guaranteed to be convex for chosen inputs while keeping the non-convex global structure for the other inputs. This enables LCGLN to admit general DFL through only a single surrogate loss without any sense for choosing appropriate parametric forms. We confirm the effectiveness and flexibility of LCGLN by evaluating our proposed model with three stochastic decision-making problems.
In this paper, we study the problem of (finite sum) minimax optimization in the Differential Privacy (DP) model. Unlike most of the previous studies on the (strongly) convex-concave settings or loss functions satisfying the Polyak-Lojasiewicz condition, here we mainly focus on the nonconvex-strongly-concave one, which encapsulates many models in deep learning such as deep AUC maximization. Specifically, we first analyze a DP version of Stochastic Gradient Descent Ascent (SGDA) and show the utility bound in terms of the Euclidean norm of the gradient for the empirical risk function. We then propose a new method with less gradient noise variance and improve the upper bound to the best-known result for DP Empirical Risk Minimization with non-convex loss. We also discussed several lower bounds of private minimax optimization. Finally, experiments on AUC maximization, generative adversarial networks, and temporal difference learning with real-world data support our theoretical analysis.
pFedES: Generalized Proxy Feature Extractor Sharing for Model Heterogeneous Personalized Federated Learning
PDF ↗Federated learning (FL), as a privacy-preserving collaborative machine learning paradigm, has attracted significant interest from industry and academia. To allow each data owner (FL client) to train a heterogeneous and personalized local model based on its local data distribution, system resources and requirements on model structure, the field of model-heterogeneous personalized federated learning (MHPFL) has emerged. Existing MHPFL approaches either rely on the availability of a public dataset with special characteristics to facilitate knowledge transfer, incur high computational and communication costs, or face potential model leakage risks. To address these limitations, we propose a model-heterogeneous personalized Federated learning approach based on generalized proxy feature Extractor Sharing (pFedES) for supervised image classification tasks. (1) We devise a shared small proxy homogeneous feature extractor before each client's heterogeneous local model. (2) Clients train them via the proposed iterative learning to enable the exchange of global generalized knowledge and local personalized knowledge. (3) The small proxy local homogeneous extractors produced after local training are uploaded to the server for aggregation to facilitate knowledge fusion across clients. We theoretically prove pFedES converges with a non-convex convergence rate O(1/T). Experiments on 3 benchmark datasets against 9 baselines demonstrate that pFedES performs state-of-the-art model accuracy while maintaining efficient communication and computation.
Distributed machine learning (DML) is promising for training large models on large datasets. In DML, multiple workers collaborate on the training of neural networks, significantly reducing the time required for neural network training. The efficiency of DML is heavily influenced by communication, making it crucial to balance the trade-off between communication cost and model performance in current research. Local methods are excellent at reducing communication costs, yet face degradation in accuracy and generalizability. Indeed, global knowledge is valuable for improving performance in local methods. However, the theoretical analysis of global knowledge validity is lacking, and global knowledge can currently only be used in the global aggregation of local methods due to communication limitations and staleness. To this end, in this paper, we establish the mechanism of global knowledge guidance and propose Adaptive Global Knowledge Guided Distributed Stochastic Gradient Descent (AdaGK-SGD) to extend the guidance of global knowledge to the whole distributed training process without any additional communication. Specifically, we define the maximum lifetime of global knowledge based on the mechanism, and establish a correlation between the maximum lifetime and the validity of global knowledge to circumvent the adverse effects of global knowledge staleness. The Maximum Lifetime of Global Knowledge module of our algorithm can be applied separately to other algorithms. In addition, considering the application, we provide a straightforward and efficient strategy for achieving the maximum lifetime adaptive setting. We establish the convergence rate of AdaGK-SGD for convex and non-convex scenarios. Numerically, we find that AdaGK-SGD can significantly improve the accuracy and generalizability of distributed algorithms compared with existing methods.
Multi-objective optimization (MOO) lies at the core of many machine learning (ML) applications that involve multiple, potentially conflicting objectives (e.g., multi-task learning, multi-objective reinforcement learning, among many others). Despite the long history of MOO, recent years have witnessed a surge in interest within the ML community in the development of gradient manipulation algorithms for MOO, thanks to the availability of gradient information in many ML problems. However, existing gradient manipulation methods for MOO often suffer from long training times, primarily due to the need for computing dynamic weights by solving an additional optimization problem to determine a common descent direction that can decrease all objectives simultaneously. To address this challenge, we propose a new and efficient algorithm called Periodic Stochastic Multi-Gradient Descent (PSMGD) to accelerate MOO. PSMGD is motivated by the key observation that dynamic weights across objectives exhibit small changes under minor updates over short intervals during the optimization process. Consequently, our PSMGD algorithm is designed to periodically compute these dynamic weights and utilizes them repeatedly, thereby effectively reducing the computational overload. Theoretically, we prove that PSMGD can achieve state-of-the-art convergence rates for strongly-convex, general convex, and non-convex functions. Additionally, we introduce a new computational complexity measure, termed backpropagation complexity, and demonstrate that PSMGD could achieve an objective-independent backpropagation complexity. Through extensive experiments, we verify that PSMGD can provide comparable or superior performance to state-of-the-art MOO algorithms while significantly reducing training time.
Motivated by the settings where sensing the entire tensor is infeasible, this paper proposes a novel tensor compressed sensing model, where measurements are only obtained from sensing each lateral slice via mutually independent matrices. Leveraging the low tubal rank structure, we reparameterize the unknown tensor ?* using two compact tensor factors and formulate the recovery problem as a nonconvex minimization problem. To solve the problem, we first propose an alternating minimization algorithm, termed Alt-PGD-Min, that iteratively optimizes the two factors using a projected gradient descent and an exact minimization step, respectively. Despite nonconvexity, we prove that Alt-PGD-Min achieves ϵ-accuracy recovery with ?(?²log1/?) iteration complexity and ?(?⁶rn₃logn₃(?²r(n₁+n₂)+n₁log1/ε)) sample complexity, where ? denotes tensor condition number of ?*. To further accelerate the convergence, especially when the tensor is ill-conditioned with large ?, we prove Alt-ScalePGD-Min that preconditions the gradient update using an approximate Hessian that can be computed efficiently. We show that Alt-ScalePGD-Min achieves ? independent iteration complexity ?(log1/ε) and improves the sample complexity to ?(?⁴rn₃log n₃(?⁴ r(n₁ + n₂)+n₁log 1/ε)). Experiments validate the effectiveness of the proposed methods.
Hybrid Decentralized Optimization: Leveraging Both First- and Zeroth-Order Optimizers for Faster Convergence
PDF ↗Distributed optimization is the standard way of speeding up machine learning training, and most of the research in the area focuses on distributed first-order, gradient-based methods. Yet, there are settings where some computationally-bounded nodes may not be able to implement first-order, gradient-based optimization, while they could still contribute to joint optimization tasks. In this paper, we initiate the study of hybrid decentralized optimization, studying settings where nodes with zeroth-order and first-order optimization capabilities co-exist in a distributed system, and attempt to jointly solve an optimization task over some data distribution. We essentially show that, under reasonable parameter settings, such a system can not only withstand noisier zeroth-order agents but can even benefit from integrating such agents into the optimization process, rather than ignoring their information. At the core of our approach is a new analysis of distributed optimization with noisy and possibly-biased gradient estimators, which may be of independent interest. Our results hold for both convex and non-convex objectives. Experimental results on standard optimization tasks confirm our analysis, showing that hybrid first-zeroth order optimization can be practical, even when training deep neural networks.
This work presents a novel approach to low-rank matrix factorization in a federated learning context, where multiple clients collaboratively solve a matrix decomposition problem without sharing their local data. The algorithm introduces a power initialization technique for the global factorization matrix and combines it with local gradient descent updates to achieve strong theoretical and practical guarantees. Considering this power initialization, we rewrite the previous smooth non-convex problem into a smooth strongly-convex problem that we solve using a parallel Nesterov gradient descent potentially requiring a single step of communication at the initialization step. We provide a linear rate of convergence of the excess loss, our results improve the rates of convergence given in the literature. We provide an upper bound on the Frobenius-norm error of reconstruction under the power initialization strategy. We complete our analysis with experiments on both synthetic and real data.