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Many problems in robotics are fundamentally problems of geometry, which lead to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie…
Significant strides have been made toward designing better generative models in recent years. Despite this progress, however, state-of-the-art approaches are still largely unable to capture complex global structure in data. For example,…
Creating and understanding art has long been a hallmark of human ability. When presented with finished digital artwork, professional graphic artists can intuitively deconstruct and replicate it using various drawing tools, such as the line…
Incorporating geometric transformations that reflect the relative position changes between an observer and an object into computer vision and deep learning models has attracted much attention in recent years. However, the existing proposals…
This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
This course design aims to develop and research a handwriting matrix recognition and step-by-step visual calculation process display system, addressing the issue of abstract formulas and complex calculation steps that students find…
Due to its amazing three-dimensional effects, holography is a very motivating, yet very demanding subject for physics classes at the upper level in school. For this reason an instruction unit on holography that supplement holographic…
Knowledge graph embeddings (KGE) have been extensively studied to embed large-scale relational data for many real-world applications. Existing methods have long ignored the fact many KGs contain two fundamentally different views: high-level…
We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the…
Realizing generalizable dynamic object manipulation on conveyor systems is important for enhancing manufacturing efficiency, as it eliminates specialized engineering for different scenarios. To this end, imitation learning emerges as a…
This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…
A good teacher should not only be knowledgeable, but should also be able to communicate in a way that the student understands -- to share the student's representation of the world. In this work, we introduce a new controlled experimental…
Sketching is used as a ubiquitous tool of expression by novices and experts alike. In this thesis I explore two methods that help a system provide a geometric machine-understanding of sketches, and in-turn help a user accomplish a…
A fundamental operation in many vision tasks, including motion understanding, stereopsis, visual odometry, or invariant recognition, is establishing correspondences between images or between images and data from other modalities. We present…
Multimodal tasks, such as image-text retrieval and generation, require embedding data from diverse modalities into a shared representation space. Aligning embeddings from heterogeneous sources while preserving shared and modality-specific…
Empowered by large-scale training, vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited. Recent advances try to…
Learning structured task representations from human demonstrations is essential for understanding long-horizon manipulation behaviors, particularly in bimanual settings where action ordering, object involvement, and interaction geometry can…
Current medical image synthetic augmentation techniques rely on intensive use of generative adversarial networks (GANs). However, the nature of GAN architecture leads to heavy computational resources to produce synthetic images and the…
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the…