Zhuo Sun

Zhuo Sun, Chris J. Oates, François-Xavier Briol

Control variates can be a powerful tool to reduce the variance of Monte Carlo estimators, but constructing effective control variates can be challenging when the number of samples is small. In this paper, we show that when a large number of related integrals need to be computed, it is possible to leverage the similarity between these integration tasks to improve performance even when the number of samples per task is very small. Our approach, called meta learning CVs (Meta-CVs), can be used for up to hundreds or thousands of tasks. Our empirical assessment indicates that Meta-CVs can lead to significant variance reduction in such settings, and our theoretical analysis establishes general conditions under which Meta-CVs can be successfully trained.

Xiaoyuan Cheng, Wenxuan Yuan, Yiming Yang et al.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

Xiaoxu Li, Jijie Wu, Zhuo Sun et al.

Few-shot learning for fine-grained image classification has gained recent attention in computer vision. Among the approaches for few-shot learning, due to the simplicity and effectiveness, metric-based methods are favorably state-of-the-art on many tasks. Most of the metric-based methods assume a single similarity measure and thus obtain a single feature space. However, if samples can simultaneously be well classified via two distinct similarity measures, the samples within a class can distribute more compactly in a smaller feature space, producing more discriminative feature maps. Motivated by this, we propose a so-called \textit{Bi-Similarity Network} (\textit{BSNet}) that consists of a single embedding module and a bi-similarity module of two similarity measures. After the support images and the query images pass through the convolution-based embedding module, the bi-similarity module learns feature maps according to two similarity measures of diverse characteristics. In this way, the model is enabled to learn more discriminative and less similarity-biased features from few shots of fine-grained images, such that the model generalization ability can be significantly improved. Through extensive experiments by slightly modifying established metric/similarity based networks, we show that the proposed approach produces a substantial improvement on several fine-grained image benchmark datasets. Codes are available at: https://github.com/spraise/BSNet

Xiaoxu Li, Zhuo Sun, Jing-Hao Xue et al.

Few-shot meta-learning has been recently reviving with expectations to mimic humanity's fast adaption to new concepts based on prior knowledge. In this short communication, we give a concise review on recent representative methods in few-shot meta-learning, which are categorized into four branches according to their technical characteristics. We conclude this review with some vital current challenges and future prospects in few-shot meta-learning.

Gang Xu, Zhigang Song, Zhuo Sun et al.

Histopathology image analysis plays a critical role in cancer diagnosis and treatment. To automatically segment the cancerous regions, fully supervised segmentation algorithms require labor-intensive and time-consuming labeling at the pixel level. In this research, we propose CAMEL, a weakly supervised learning framework for histopathology image segmentation using only image-level labels. Using multiple instance learning (MIL)-based label enrichment, CAMEL splits the image into latticed instances and automatically generates instance-level labels. After label enrichment, the instance-level labels are further assigned to the corresponding pixels, producing the approximate pixel-level labels and making fully supervised training of segmentation models possible. CAMEL achieves comparable performance with the fully supervised approaches in both instance-level classification and pixel-level segmentation on CAMELYON16 and a colorectal adenoma dataset. Moreover, the generality of the automatic labeling methodology may benefit future weakly supervised learning studies for histopathology image analysis.