We provide theoretical guarantees for label consistency in generalized k-means problems, with an emphasis on the overfitted case where the number of clusters used by the algorithm is more than the ground truth. We provide conditions under which the estimated labels are close to a refinement of the true cluster labels. We consider both exact and approximate recovery of the labels. Our results hold for any constant-factor approximation to the k-means problem. The results are also model-free and only based on bounds on the maximum or average distance of the data points to the true cluster centers. These centers themselves are loosely defined and can be taken to be any set of points for which the aforementioned distances can be controlled. We show the usefulness of the results with applications to some manifold clustering problems.

We consider both exact andapproximate recoveryofthelabels. Our results hold for anyconstant-factor approximation tothek-means problem.

We provide theoretical guarantees for label consistency in generalized $k$-means problems, with an emphasis on the overfitted case where the number of clusters used by the algorithm is more than the ground truth. We provide conditions under which the estimated labels are close to a refinement of the true cluster labels. We consider both exact and approximate recovery of the labels. Our results hold for any constant-factor approximation to the $k$-means problem. The results are also model-free and only based on bounds on the maximum or average distance of the data points to the true cluster centers. These centers themselves are loosely defined and can be taken to be any set of points for which the aforementioned distances can be controlled. We show the usefulness of the results with applications to some manifold clustering problems.

Recent advances in conditional generative modeling have introduced Continuous conditional Generative Adversarial Network (CcGAN) and Continuous Conditional Diffusion Model (CCDM) for estimating high-dimensional data distributions conditioned on scalar, continuous regression labels (e.g., angles, ages, or temperatures). However, these approaches face fundamental limitations: CcGAN suffers from data imbalance due to fixed-size vicinity constraints, while CCDM requires computationally expensive iterative sampling. To address these issues, we propose CcGAN-AVAR, an enhanced CcGAN framework featuring (1) two novel components for handling data imbalance - an adaptive vicinity mechanism that dynamically adjusts vicinity size and a multi-task discriminator that enhances generator training through auxiliary regression and density ratio estimation - and (2) the GAN framework's native one-step generator, enable 30x-2000x faster inference than CCDM. Extensive experiments on four benchmark datasets (64x64 to 256x256 resolution) across eleven challenging settings demonstrate that CcGAN-AVAR achieves state-of-the-art generation quality while maintaining sampling efficiency.

To deal with distribution shifts in graph data, various graph out-of-distribution (OOD) generalization techniques have been recently proposed. These methods often employ a two-step strategy that first creates augmented environments and subsequently identifies invariant subgraphs to improve generalizability. Nevertheless, this approach could be suboptimal from the perspective of consistency. First, the process of augmenting environments by altering the graphs while preserving labels may lead to graphs that are not realistic or meaningfully related to the origin distribution, thus lacking distribution consistency. Second, the extracted subgraphs are obtained from directly modifying graphs, and may not necessarily maintain a consistent predictive relationship with their labels, thereby impacting label consistency. In response to these challenges, we introduce an innovative approach that aims to enhance these two types of consistency for graph OOD generalization. We propose a modifier to obtain both augmented and invariant graphs in a unified manner. With the augmented graphs, we enrich the training data without compromising the integrity of label-graph relationships. The label consistency enhancement in our framework further preserves the supervision information in the invariant graph. We conduct extensive experiments on real-world datasets to demonstrate the superiority of our framework over other state-of-the-art baselines.

We provide theoretical guarantees for label consistency in generalized k -means problems, with an emphasis on the overfitted case where the number of clusters used by the algorithm is more than the ground truth. We provide conditions under which the estimated labels are close to a refinement of the true cluster labels. We consider both exact and approximate recovery of the labels. Our results hold for any constant-factor approximation to the k -means problem. The results are also model-free and only based on bounds on the maximum or average distance of the data points to the true cluster centers.

Existing 3D point-based dynamic point detection and removal methods have a significant time overhead, making them difficult to adapt to LiDAR-inertial odometry systems. This paper proposes a label consistency based dynamic point detection and removal method for handling moving vehicles and pedestrians in autonomous driving scenarios, and embeds the proposed dynamic point detection and removal method into a self-designed LiDAR-inertial odometry system. Experimental results on three public datasets demonstrate that our method can accomplish the dynamic point detection and removal with extremely low computational overhead (i.e., 1$\sim$9ms) in LIO systems, meanwhile achieve comparable preservation rate and rejection rate to state-of-the-art methods and significantly enhance the accuracy of pose estimation. We have released the source code of this work for the development of the community.

Continuous Conditional Generative Modeling (CCGM) aims to estimate the distribution of high-dimensional data, typically images, conditioned on scalar continuous variables known as regression labels. While Continuous conditional Generative Adversarial Networks (CcGANs) were initially designed for this task, their adversarial training mechanism remains vulnerable to extremely sparse or imbalanced data, resulting in suboptimal outcomes. To enhance the quality of generated images, a promising alternative is to replace CcGANs with Conditional Diffusion Models (CDMs), renowned for their stable training process and ability to produce more realistic images. However, existing CDMs encounter challenges when applied to CCGM tasks due to several limitations such as inadequate U-Net architectures and deficient model fitting mechanisms for handling regression labels. In this paper, we introduce Continuous Conditional Diffusion Models (CCDMs), the first CDM designed specifically for the CCGM task. CCDMs address the limitations of existing CDMs by introducing specially designed conditional diffusion processes, a modified denoising U-Net with a custom-made conditioning mechanism, a novel hard vicinal loss for model fitting, and an efficient conditional sampling procedure. With comprehensive experiments on four datasets with varying resolutions ranging from 64x64 to 192x192, we demonstrate the superiority of the proposed CCDM over state-of-the-art CCGM models, establishing new benchmarks in CCGM. Extensive ablation studies validate the model design and implementation configuration of the proposed CCDM. Our code is publicly available at https://github.com/UBCDingXin/CCDM.

The continuous evolution of pre-trained large language models with ever-growing parameters and corpus sizes has augmented their capacity to solve complex tasks. This ability, which obviates the necessity for task-specific training or fine-tuning, relies on providing the model with a language description or some task exemplars -- referred to the prompt -- that guide the desired autoregressive generation. Despite the remarkable success, the underlying mechanisms that facilitate such exceptional generalization abilities remain an open question. In this paper, we present a novel framework that formally conceptualizes answer generation for complex natural language tasks as a hierarchical ``template-content'' structure. According to our modeling, there exist pre-trained models that can automatically decompose tasks into constituent steps during autoregressive generation, through language modeling on a sufficiently large corpus, thereby solving them. Our framework offers an explanatory tool for the complex reasoning abilities of large language models from the perspective of modeling autoregressive generation tasks. Our experiments show that practical models exhibit different behaviors for ``template'' and ``content'' providing support for our modeling.

Inter-Annotator Agreement (IAA) is commonly used as a measure of label consistency in natural language processing tasks. However, in real-world scenarios, IAA has various roles and implications beyond its traditional usage. In this paper, we not only consider IAA as a measure of consistency but also as a versatile tool that can be effectively utilized in practical applications. Moreover, we discuss various considerations and potential concerns when applying IAA and suggest strategies for effectively navigating these challenges.