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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…

Information Retrieval · Computer Science 2026-02-10 Hiren Madhu , Ngoc Bui , Ali Maatouk , Leandros Tassiulas , Smita Krishnaswamy , Menglin Yang , Sukanta Ganguly , Kiran Srinivasan , Rex Ying

Prototypical part networks offer interpretable alternatives to black-box deep learning models by learning visual prototypes for classification. This work provides a comprehensive analysis of prototype formulations, comparing point-based and…

Machine Learning · Computer Science 2026-01-08 Maximilian Xiling Li , Korbinian Franz Rudolf , Paul Mattes , Nils Blank , Rudolf Lioutikov

We consider the characteristic problem for the ultrahyperbolic equation in the Euclidean space. The value of a solution is prescribed on the characteristic hyperplane. A well-posed set-up of the problem is discussed. We obtain a certain…

Analysis of PDEs · Mathematics 2026-04-27 Maxim N. Demchenko

We consider the problem of multi-label classification where the labels lie in a hierarchy. However, unlike most existing works in hierarchical multi-label classification, we do not assume that the label-hierarchy is known. Encouraged by the…

Machine Learning · Computer Science 2021-01-14 Soumya Chatterjee , Ayush Maheshwari , Ganesh Ramakrishnan , Saketha Nath Jagaralpudi

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical…

Machine Learning · Computer Science 2020-05-05 Ines Chami , Adva Wolf , Da-Cheng Juan , Frederic Sala , Sujith Ravi , Christopher Ré

Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers…

Machine Learning · Computer Science 2019-10-30 Ines Chami , Rex Ying , Christopher Ré , Jure Leskovec

Language-enabled AI systems can answer complex, multi-hop questions to high accuracy, but supporting answers with evidence is a more challenging task which is important for the transparency and trustworthiness to users. Prior work in this…

Computation and Language · Computer Science 2022-01-11 Shane Storks , Qiaozi Gao , Aishwarya Reganti , Govind Thattai

Multimodal datasets contain an enormous amount of relational information, which grows exponentially with the introduction of new modalities. Learning representations in such a scenario is inherently complex due to the presence of multiple…

Machine Learning · Computer Science 2019-09-24 Devanshu Arya , Stevan Rudinac , Marcel Worring

Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and…

Artificial Intelligence · Computer Science 2025-12-09 Sarang Patil , Zeyong Zhang , Yiran Huang , Tengfei Ma , Mengjia Xu

Given an image set without any labels, our goal is to train a model that maps each image to a point in a feature space such that, not only proximity indicates visual similarity, but where it is located directly encodes how prototypical the…

Computer Vision and Pattern Recognition · Computer Science 2023-07-06 Yunhui Guo , Youren Zhang , Yubei Chen , Stella X. Yu

Heterogeneous graphs have attracted a lot of research interests recently due to the success for representing complex real-world systems. However, existing methods have two pain points in embedding them into low-dimensional spaces: the…

Machine Learning · Computer Science 2024-06-18 Qijie Bai , Changli Nie , Haiwei Zhang , Zhicheng Dou , Xiaojie Yuan

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable…

Computation and Language · Computer Science 2018-06-04 Mantong Zhou , Minlie Huang , Xiaoyan Zhu

Transformer model architectures have become an indispensable staple in deep learning lately for their effectiveness across a range of tasks. Recently, a surge of "X-former" models have been proposed which improve upon the original…

Computation and Language · Computer Science 2021-06-15 Zhe Liu , Yibin Xu

Multi-hop reasoning is an effective approach for query answering (QA) over incomplete knowledge graphs (KGs). The problem can be formulated in a reinforcement learning (RL) setup, where a policy-based agent sequentially extends its…

Artificial Intelligence · Computer Science 2018-09-13 Xi Victoria Lin , Richard Socher , Caiming Xiong

Explainable multi-hop question answering (QA) not only predicts answers but also identifies rationales, i. e. subsets of input sentences used to derive the answers. This problem has been extensively studied under the supervised setting,…

Computation and Language · Computer Science 2023-05-24 Wenting Zhao , Justin T. Chiu , Claire Cardie , Alexander M. Rush

Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling…

Machine Learning · Computer Science 2021-04-07 Li Sun , Zhongbao Zhang , Jiawei Zhang , Feiyang Wang , Hao Peng , Sen Su , Philip S. Yu

Graph theoretical approaches have been proven to be effective in the characterization of connected systems, as well as in quantifying their dysfunction due to perturbation. In this paper, we show the advantage of a non-Euclidean…

Quantitative Methods · Quantitative Biology 2024-06-10 Alice Longhena , Martin Guillemaud , Mario Chavez

Learning multi-hop reasoning has been a key challenge for reading comprehension models, leading to the design of datasets that explicitly focus on it. Ideally, a model should not be able to perform well on a multi-hop question answering…

Computation and Language · Computer Science 2019-04-30 Jifan Chen , Greg Durrett

Robust generalization beyond training distributions remains a critical challenge for deep neural networks. This is especially pronounced in medical image analysis, where data is often scarce and covariate shifts arise from different…

Computer Vision and Pattern Recognition · Computer Science 2026-02-04 Francesco Di Salvo , Sebastian Doerrich , Jonas Alle , Christian Ledig

Recently hyperbolic geometry has proven to be effective in building embeddings that encode hierarchical and entailment information. This makes it particularly suited to modelling the complex asymmetrical relationships between Chinese…

Computation and Language · Computer Science 2018-12-27 Marko Valentin Micic , Hugo Chu