Related papers: Position: Beyond Euclidean -- Foundation Models Sh…

Graphs are a widely used paradigm for representing non-Euclidean data, with applications ranging from social network analysis to biomolecular prediction. While graph learning has achieved remarkable progress, real-world graph data presents…

Euclidean Distance Matrix (EDM), which consists of pairwise squared Euclidean distances of a given point configuration, finds many applications in modern machine learning. This paper considers the setting where only a set of anchor nodes is…

Applying AI foundation models directly to geospatial datasets remains challenging due to their limited ability to represent and reason with geographical entities, specifically vector-based geometries and natural language descriptions of…

Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…

These lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470]. We introduce and study basic aspects of non-Euclidean geometries from a coordinate-free viewpoint.

Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be…

Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable…

Laplacian-based methods are popular for the dimensionality reduction of data lying in $\mathbb{R}^N$. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance…

Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional methods frequently struggle with the inherent complexity,…

Large language models (LLMs) exhibit remarkable flexibility: they can adapt to novel tasks from in-context examples without any parameter updates, a capability known as in-context learning (ICL). Prior work on synthetic tasks has shown that…

A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is…

The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…

Foundation models pretrained on diverse data at scale have demonstrated extraordinary capabilities in a wide range of vision and language tasks. When such models are deployed in real world environments, they inevitably interface with other…

3D scene modeling techniques serve as the bedrocks in the geospatial engineering and computer science, which drives many applications ranging from automated driving, terrain mapping, navigation, virtual, augmented, mixed, and extended…

Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…

The advancement of large language models (LLMs) for real-world applications hinges critically on enhancing their reasoning capabilities. In this work, we explore the reasoning abilities of large language models (LLMs) through their…

In cognitive science and AI, a longstanding question is whether machines learn representations that align with those of the human mind. While current models show promise, it remains an open question whether this alignment is superficial or…

Machine learning (ML)-based solutions are rapidly changing the landscape of many fields, including structural engineering. Despite their promising performance, these approaches are usually only demonstrated as proof-of-concept in structural…

Foundation models, including Large Language Models (LLMs), Multimodal Large Language Models (MLLMs), Image Generative Models (i.e, Text-to-Image Models and Image-Editing Models), and Video Generative Models, have become essential tools with…

This review explores the potential of foundation models to advance laboratory automation in the materials and chemical sciences. It emphasizes the dual roles of these models: cognitive functions for experimental planning and data analysis,…