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Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph…
Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a…
Open-ended learning benefits immensely from the use of symbolic methods for goal representation as they offer ways to structure knowledge for efficient and transferable learning. However, the existing Hierarchical Reinforcement Learning…
Anomaly detection on the attributed network has recently received increasing attention in many research fields, such as cybernetic anomaly detection and financial fraud detection. With the wide application of deep learning on graph…
Graph contrastive learning (GCL) has recently emerged as a new concept which allows for capitalizing on the strengths of graph neural networks (GNNs) to learn rich representations in a wide variety of applications which involve abundant…
Hierarchy is a natural representation of semantic taxonomies, including the ones routinely used in image segmentation. Indeed, recent work on semantic segmentation reports improved accuracy from supervised training leveraging hierarchical…
We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric…
While representation learning has yielded a great success on many graph learning tasks, there is little understanding behind the structures that are being captured by these embeddings. For example, we wonder if the topological features,…
Foundation models pre-trained on massive datasets, including large language models (LLMs), vision-language models (VLMs), and large multimodal models, have demonstrated remarkable success in diverse downstream tasks. However, recent studies…
Image-text representation learning forms a cornerstone in vision-language models, where pairs of images and textual descriptions are contrastively aligned in a shared embedding space. Since visual and textual concepts are naturally…
The persistence diagram is a central object in the study of persistent homology and has also been investigated in the context of random topology. The more recent notion of the verbose diagram (a.k.a. verbose barcode) is a refinement of the…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
Structuring latent representations in a hierarchical manner enables models to learn patterns at multiple levels of abstraction. However, most prevalent image understanding models focus on visual similarity, and learning visual hierarchies…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…
Learning structures of 3D shapes is a fundamental problem in the field of computer graphics and geometry processing. We present a simple yet interpretable unsupervised method for learning a new structural representation in the form of 3D…
Creating representations of shapes that are invari-ant to isometric or almost-isometric transforma-tions has long been an area of interest in shape anal-ysis, since enforcing invariance allows the learningof more effective and robust shape…
Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain largely confined to Euclidean space. However, natural language exhibits hierarchical structure from broad…
Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence modules. We consider various classes of persistence modules,…
We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and…
The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to…