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Vector Symbolic Architectures (VSAs) are high-dimensional vector representations of objects (eg., words, image parts), relations (eg., sentence structures), and sequences for use with machine learning algorithms. They consist of a vector…
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
Recent interest in graph embedding methods has focused on learning a single representation for each node in the graph. But can nodes really be best described by a single vector representation? In this work, we propose a method for learning…
The arrival of AI coding assistants in educational settings presents a paradigm shift, introducing a "new kid in the classroom" for both students and instructors. Thus, understanding the perceptions of these key actors about this new…
Automated methods for essay scoring have made great progress in recent years, achieving accuracies very close to human annotators. However, a known weakness of such automated scorers is not taking into account the semantic relevance of the…
Asking questions during class time is one form of participation not commonly employed by members of underrepresented groups in large enrollment college classrooms, even though the form of participation is highly conducive to student…
High school science classrooms across the United States are answering calls to make computation a part of science learning. The problem is that there is little known about the barriers to learning that computation might bring to a science…
We cast visual imitation as a visual correspondence problem. Our robotic agent is rewarded when its actions result in better matching of relative spatial configurations for corresponding visual entities detected in its workspace and…
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
For the problem of 3D object recognition, researchers using deep learning methods have developed several very different input representations, including "multi-view" snapshots taken from discrete viewpoints around an object, as well as…
A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…
Motivated by children inventing creatively laws on how to add or multiply fractions, we introduce four fraction operations and discover some of their properties.
Learning to use math in physics involves combining (blending) our everyday experiences and the conceptual ideas of physics with symbolic mathematical representations. Graphs are one of the best ways to learn to build the blend. They are a…
We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's…
Vector Symbolic Architectures combine a high-dimensional vector space with a set of carefully designed operators in order to perform symbolic computations with large numerical vectors. Major goals are the exploitation of their…
We investigate the perception of visual variables on wall-sized tiled displays within an immersive environment. We designed and conducted two formal user studies focusing on elementary visualization reading tasks in VR. The first study…
We study the problem of computer-assisted teaching with explanations. Conventional approaches for machine teaching typically only provide feedback at the instance level e.g., the category or label of the instance. However, it is intuitive…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
The predominant approach to Visual Question Answering (VQA) demands that the model represents within its weights all of the information required to answer any question about any image. Learning this information from any real training set…
Large language models have become multimodal, and many of them are said to integrate their modalities using common representations. If this were true, a drawing of a car as an image, for instance, should map to a similar area in the latent…