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Large Language Models (LLMs) have attracted significant attention in recommender systems for their excellent world knowledge capabilities. However, existing methods that rely on Euclidean space struggle to capture the rich hierarchical…

Information Retrieval · Computer Science 2025-04-22 Wentao Cheng , Zhida Qin , Zexue Wu , Pengzhan Zhou , Tianyu Huang

Large language models (LLMs) have shown great success in text modeling tasks across domains. However, natural language exhibits inherent semantic hierarchies and nuanced geometric structure, which current LLMs do not capture completely…

Machine Learning · Computer Science 2025-11-07 Neil He , Rishabh Anand , Hiren Madhu , Ali Maatouk , Smita Krishnaswamy , Leandros Tassiulas , Menglin Yang , Rex Ying

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

Natural language text exhibits hierarchical structure in a variety of respects. Ideally, we could incorporate our prior knowledge of this hierarchical structure into unsupervised learning algorithms that work on text data. Recent work by…

Computation and Language · Computer Science 2018-06-13 Bhuwan Dhingra , Christopher J. Shallue , Mohammad Norouzi , Andrew M. Dai , George E. Dahl

The rapid advancement of large language models (LLMs) has enabled significant strides in various fields. This paper introduces a novel approach to evaluate the effectiveness of LLM embeddings in the context of inherent geometric properties.…

Computational Geometry · Computer Science 2025-12-29 Prakash Chourasia , Sarwan Ali , Murray Patterson

Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is…

Machine Learning · Computer Science 2024-07-24 Zhangyu Wang , Lantian Xu , Zhifeng Kong , Weilong Wang , Xuyu Peng , Enyang Zheng

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…

Machine Learning · Computer Science 2025-07-25 Neil He , Hiren Madhu , Ngoc Bui , Menglin Yang , Rex Ying

Hierarchical reinforcement learning deals with the problem of breaking down large tasks into meaningful sub-tasks. Autonomous discovery of these sub-tasks has remained a challenging problem. We propose a novel method of learning sub-tasks…

Machine Learning · Computer Science 2019-02-19 Saket Tiwari , M. Prannoy

Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this…

Machine Learning · Computer Science 2024-12-03 Aditya Sinha , Siqi Zeng , Makoto Yamada , Han Zhao

Metric learning plays a critical role in training image retrieval and classification. It is also a key algorithm in representation learning, e.g., for feature learning and its alignment in metric space. Hyperbolic embedding has been…

Computer Vision and Pattern Recognition · Computer Science 2023-10-24 Shiyang Yan , Zongxuan Liu , Lin Xu

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central…

Machine Learning · Computer Science 2023-05-31 Ya-Wei Eileen Lin , Ronald R. Coifman , Gal Mishne , Ronen Talmon

Language models are increasingly applied to biological sequences like proteins and mRNA, yet their default Euclidean geometry may mismatch the hierarchical structures inherent to biological data. While hyperbolic geometry provides a better…

Machine Learning · Computer Science 2025-11-05 Max van Spengler , Artem Moskalev , Tommaso Mansi , Mangal Prakash , Rui Liao

Learning embeddings of entities and relations existing in knowledge bases allows the discovery of hidden patterns in data. In this work, we examine the geometrical space's contribution to the task of knowledge base completion. We focus on…

Computation and Language · Computer Science 2019-08-20 Prodromos Kolyvakis , Alexandros Kalousis , Dimitris Kiritsis

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…

Machine Learning · Computer Science 2026-05-01 Sofía Pérez Casulo , Marcelo Fiori , Bernardo Marenco , Federico Larroca

Multi-step reasoning remains a central challenge for large language models: single-pass generation is efficient but lacks accuracy; tree-search methods explore multiple paths but are computation-heavy. We address this gap by distilling…

Artificial Intelligence · Computer Science 2026-05-29 Yuyu Liu , Haotian Xu , Yanan He , Sarang Rajendra Patil , Mengjia Xu , Tengfei Ma

Interpreting hierarchical structures latent in language is a key limitation of current language models (LMs). While previous research has implicitly leveraged these hierarchies to enhance LMs, approaches for their explicit encoding are yet…

Computation and Language · Computer Science 2024-11-22 Yuan He , Zhangdie Yuan , Jiaoyan Chen , Ian Horrocks

We are concerned with the discovery of hierarchical relationships from large-scale unstructured similarity scores. For this purpose, we study different models of hyperbolic space and find that learning embeddings in the Lorentz model is…

Artificial Intelligence · Computer Science 2018-07-10 Maximilian Nickel , Douwe Kiela

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…

Computer Vision and Pattern Recognition · Computer Science 2022-03-23 Aleksandr Ermolov , Leyla Mirvakhabova , Valentin Khrulkov , Nicu Sebe , Ivan Oseledets

Various neuroimaging studies suffer from small sample size problem which often limit their reliability. Meta-analysis addresses this challenge by aggregating findings from different studies to identify consistent patterns of brain activity.…

Machine Learning · Computer Science 2025-11-27 Seunghun Baek , Jaejin Lee , Jaeyoon Sim , Minjae Jeong , Won Hwa Kim

Different from the traditional classification tasks which assume mutual exclusion of labels, hierarchical multi-label classification (HMLC) aims to assign multiple labels to every instance with the labels organized under hierarchical…

Machine Learning · Computer Science 2019-09-05 Boli Chen , Xin Huang , Lin Xiao , Zixin Cai , Liping Jing
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