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Accurate identification of important objects in the scene is a prerequisite for safe and high-quality decision making and motion planning of intelligent agents (e.g., autonomous vehicles) that navigate in complex and dynamic environments.…

In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…

In this paper, we consider the problem of estimating self-tuning histograms using query workloads. To this end, we propose a general learning theoretic formulation. Specifically, we use query feedback from a workload as training data to…

Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…

As personalized learning gains increasing attention in mathematics education, there is a growing demand for intelligent systems that can assess complex student responses and provide individualized feedback in real time. In this study, we…

Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…

Recently, deep metric learning techniques received attention, as the learned distance representations are useful to capture the similarity relationship among samples and further improve the performance of various of supervised or…

Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the…

Representation Learning of words and Knowledge Graphs (KG) into low dimensional vector spaces along with its applications to many real-world scenarios have recently gained momentum. In order to make use of multiple KG embeddings for…

In this paper, we evaluate the accuracy of deep learning approaches on geospatial vector geometry classification tasks. The purpose of this evaluation is to investigate the ability of deep learning models to learn from geometry coordinates…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

Understanding how explicit theoretical features are encoded in opaque neural systems is a central challenge now common to neuroscience and AI. We introduce Metric Learning Encoding Models (MLEMs) to address this challenge most directly as a…

We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms…

Standard LLM evaluation practices compress diverse abilities into single scores, obscuring their inherently multidimensional nature. We present JE-IRT, a geometric item-response framework that embeds both LLMs and questions in a shared…

In lifelong learning, tasks (or classes) to be learned arrive sequentially over time in arbitrary order. During training, knowledge from previous tasks can be captured and transferred to subsequent ones to improve sample efficiency. We…

Learning a set of tasks over time, also known as continual learning (CL), is one of the most challenging problems in artificial intelligence. While recent approaches achieve some degree of CL in deep neural networks, they either (1) grow…

Overfitting and generalization is an important concept in Machine Learning as only models that generalize are interesting for general applications. Yet some students have trouble learning this important concept through lectures and…

Understanding convergent learning -- the degree to which independently trained neural systems -- whether multiple artificial networks or brains and models -- arrive at similar internal representations -- is crucial for both neuroscience and…

In the realm of robotics, numerous downstream robotics tasks leverage machine learning methods for processing, modeling, or synthesizing data. Often, this data comprises variables that inherently carry geometric constraints, such as the…

The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of…