This paper investigates the impact of multiscale data on machine learning algorithms, particularly in the context of deep learning. A dataset is multiscale if its distribution shows large variations in scale across different directions. This paper reveals multiscale structures in the loss landscape, including its gradients and Hessians inherited from the data. Correspondingly, it introduces a novel gradient descent approach, drawing inspiration from multiscale algorithms used in scientific computing. This approach seeks to transcend empirical learning rate selection, offering a more systematic, data-informed strategy to enhance training efficiency, especially in the later stages.

We propose a new framework for the sampling, compression, and analysis of distributions of point sets and other geometric objects embedded in Euclidean spaces. Our approach involves constructing a tensor called the RaySense sketch, which captures nearest neighbors from the underlying geometry of points along a set of rays. We explore various operations that can be performed on the RaySense sketch, leading to different properties and potential applications. Statistical information about the data set can be extracted from the sketch, independent of the ray set. Line integrals on point sets can be efficiently computed using the sketch. We also present several examples illustrating applications of the proposed strategy in practical scenarios.

In this paper, we study linear regression applied to data structured on a manifold. We assume that the data manifold is smooth and is embedded in a Euclidean space, and our objective is to reveal the impact of the data manifold's extrinsic geometry on the regression. Specifically, we analyze the impact of the manifold's curvatures (or higher order nonlinearity in the parameterization when the curvatures are locally zero) on the uniqueness of the regression solution. Our findings suggest that the corresponding linear regression does not have a unique solution when the embedded submanifold is flat in some dimensions. Otherwise, the manifold's curvature (or higher order nonlinearity in the embedding) may contribute significantly, particularly in the solution associated with the normal directions of the manifold. Our findings thus reveal the role of data manifold geometry in ensuring the stability of regression models for out-of-distribution inferences.

To contribute to automating the medical vision-language model, we propose a novel Chest-Xray Difference Visual Question Answering (VQA) task. Given a pair of main and reference images, this task attempts to answer several questions on both diseases and, more importantly, the differences between them. This is consistent with the radiologist's diagnosis practice that compares the current image with the reference before concluding the report. We collect a new dataset, namely MIMIC-Diff-VQA, including 700,703 QA pairs from 164,324 pairs of main and reference images. Compared to existing medical VQA datasets, our questions are tailored to the Assessment-Diagnosis-Intervention-Evaluation treatment procedure used by clinical professionals. Meanwhile, we also propose a novel expert knowledge-aware graph representation learning model to address this task. The proposed baseline model leverages expert knowledge such as anatomical structure prior, semantic, and spatial knowledge to construct a multi-relationship graph, representing the image differences between two images for the image difference VQA task. The dataset and code can be found at https://github.com/Holipori/MIMIC-Diff-VQA. We believe this work would further push forward the medical vision language model.

In recommender systems, the user-item interaction data is usually sparse and not sufficient for learning comprehensive user/item representations for recommendation. To address this problem, we propose a novel dual-bridging recommendation model (DBRec). DBRec performs latent user/item group discovery simultaneously with collaborative filtering, and interacts group information with users/items for bridging similar users/items. Therefore, a user's preference over an unobserved item, in DBRec, can be bridged by the users within the same group who have rated the item, or the user-rated items that share the same group with the unobserved item. In addition, we propose to jointly learn user-user group (item-item group) hierarchies, so that we can effectively discover latent groups and learn compact user/item representations. We jointly integrate collaborative filtering, latent group discovering and hierarchical modelling into a unified framework, so that all the model parameters can be learned toward the optimization of the objective function. We validate the effectiveness of the proposed model with two real datasets, and demonstrate its advantage over the state-of-the-art recommendation models with extensive experiments.