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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…

Deep metric learning algorithms have been utilized to learn discriminative and generalizable models which are effective for classifying unseen classes. In this paper, a novel noise tolerant deep metric learning algorithm is proposed. The…

Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical…

Computer vision tasks such as image classification, image retrieval and few-shot learning are currently dominated by Euclidean and spherical embeddings, so that the final decisions about class belongings or the degree of similarity are made…

A novel regularization technique, AdaCubic, is proposed that adapts the weight of the cubic term. The heart of AdaCubic is an auxiliary optimization problem with cubic constraints that dynamically adjusts the weight of the cubic term in…

Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…

Existing methods for solving Riemannian bilevel optimization (RBO) problems require prior knowledge of the problem's first- and second-order information and curvature parameter of the Riemannian manifold to determine step sizes, which poses…

By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…

Alternating Direction Method of Multipliers (ADMM) has been used successfully in many conventional machine learning applications and is considered to be a useful alternative to Stochastic Gradient Descent (SGD) as a deep learning optimizer.…

The progress in hyperbolic neural networks (HNNs) research is hindered by their absence of inductive bias mechanisms, which are essential for generalizing to new tasks and facilitating scalable learning over large datasets. In this paper,…

Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…

This paper presents a hardness-aware deep metric learning (HDML) framework. Most previous deep metric learning methods employ the hard negative mining strategy to alleviate the lack of informative samples for training. However, this mining…

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…

Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…

The exponential volume growth of hyperbolic geometry can embed the hierarchical relationships between states in reinforcement learning (RL) with far less distortion than Euclidean space. However, hyperbolic deep RL faces severe optimization…

Deep Learning has revolutionized machine learning and artificial intelligence, achieving superhuman performance in several standard benchmarks. It is well-known that deep learning models are inefficient to train; they learn by processing…

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…

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…

Autonomous robots are increasingly becoming a strong fixture in social environments. Effective crowd navigation requires not only safe yet fast planning, but should also enable interpretability and computational efficiency for working in…