arXiv subjects
Publications and source records attributed to Xiaohan Guo.
The present paper is devoted to study 2-local derivations on the Block-type Lie algebra which is an infinite-dimensional Lie algebra with some outer derivations. We prove that every 2-local derivation on the Block-type Lie algebra is a derivation.
Enabling large-scale generative models to continuously learn new visual concepts is essential for personalizing pre-trained models to meet individual user preferences. Existing approaches for continual visual concept learning are constrained by two fundamental challenges: catastrophic forgetting and parameter expansion. In this paper, we propose Redundancy-Removal Mixture of Experts (R^2MoE), a parameter-efficient framework for lifelong visual concept learning that effectively learns new concepts while incurring minimal parameter overhead. Our framework includes three key innovative contributions: First, we propose a mixture-of-experts framework with a routing distillation mechanism that enables experts to acquire concept-specific knowledge while preserving the gating network's routing capability, thereby effectively mitigating catastrophic forgetting. Second, we propose a strategy for eliminating redundant layer-wise experts that reduces the number of expert parameters by fully utilizing previously learned experts. Third, we employ a hierarchical local attention-guided inference approach to mitigate interference between generated visual concepts. Extensive experiments have demonstrated that our method generates images with superior conceptual fidelity compared to the state-of-the-art (SOTA) method, achieving an impressive 87.8\% reduction in forgetting rates and 63.3\% fewer parameters on the CustomConcept 101 dataset. Our code is available at {https://github.com/learninginvision/R2MoE}
Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we focus on the hitherto unconsidered setting where phase variation of the component functions are spatially correlated. We propose an algorithm to optimize a metric-based objective function for registration with a novel penalty term that incorporates the spatial correlation between the component phase variations through a kriging estimate of an appropriate phase random field. The penalty term encourages the overall phase at a particular location to be similar to the spatially weighted average phase in its neighbourhood, and thus engenders a regularization that prevents over-alignment. Utility of the registration method, and its superior performance compared to methods that fail to account for the spatial correlation, is demonstrated through performance on simulated examples and two multivariate functional datasets pertaining to EEG signals and ozone concentrations. The generality of the framework opens up the possibility for extension to settings involving different forms of correlation between the component functions and their phases.
Disentanglement, a critical concern in interpretable machine learning, has also garnered significant attention from the computer vision community. Many existing GAN-based class disentanglement (unsupervised) approaches, such as InfoGAN and its variants, primarily aim to maximize the mutual information (MI) between the generated image and its latent codes. However, this focus may lead to a tendency for the network to generate highly similar images when presented with the same latent class factor, potentially resulting in mode collapse or mode dropping. To alleviate this problem, we propose \texttt{CoDeGAN} (Contrastive Disentanglement for Generative Adversarial Networks), where we relax similarity constraints for disentanglement from the image domain to the feature domain. This modification not only enhances the stability of GAN training but also improves their disentangling capabilities. Moreover, we integrate self-supervised pre-training into CoDeGAN to learn semantic representations, significantly facilitating unsupervised disentanglement. Extensive experimental results demonstrate the superiority of our method over state-of-the-art approaches across multiple benchmarks. The code is available at https://github.com/learninginvision/CoDeGAN.
Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace variogram, which quantifies spatial variation, can be misleading when analysing misaligned functional data with phase variation. To remedy this, we describe a framework that extends amplitude-phase separation methods in functional data to the spatial setting, with a view towards performing clustering and spatial prediction. We propose a decomposition of the trace variogram into amplitude and phase components and quantify how spatial correlations between functional observations manifest in their respective amplitude and phase components. This enables us to generate separate amplitude and phase clustering methods for spatial functional data, and develop a novel spatial functional interpolant at unobserved locations based on combining separate amplitude and phase predictions. Through simulations and real data analyses, we found that the proposed methods result in more accurate predictions and more interpretable clustering results.