Related papers: Visual thinking and simplicity in proof
The main aim of the work presented here is to contribute to computer science advances in the multimodal usability area, in-as-much as it addresses one of the major issues relating to the generation of effective oral system messages: how to…
Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…
Network clustering requires making many decisions manually, such as the number of groups and a statistical model to be used. Even after filtering using an information criterion or regularizing with a nonparametric framework, we are commonly…
Financial companies continuously analyze the state of the markets to rethink and adjust their investment strategies. While the analysis is done on the digital form of data, decisions are often made based on graphical representations in…
Consider a rational map from a projective space to a product of projective spaces, induced by a collection of linear projections. Motivated by the the theory of limit linear series and Abel-Jacobi maps, we study the basic properties of the…
Visual Spatial Reasoning (VSR) is a core human cognitive ability and a critical requirement for advancing embodied intelligence and autonomous systems. Despite recent progress in Vision-Language Models (VLMs), achieving human-level VSR…
Spatial world models, representations that support flexible reasoning about spatial relations, are central to developing computational models that could operate in the physical world, but their precise mechanistic underpinnings are nuanced…
Symbolic learning represents the most straightforward approach to interpretable modeling, but its applications have been hampered by a single structural design choice: the adoption of propositional logic as the underlying language.…
Any counterexample to the two-dimensional Jacobian Conjecture gives a rational map from one projective plane to another. We use some ideas of the Minimal Model Program to study the combinatorial structure of a rational surface, that is…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
Unfamiliar or esoteric visual forms arise in many areas of visualization. While such forms can be intriguing, it can be unclear how to make effective use of them without long periods of practice or costly user studies. In this work we…
Vision-language models (VLMs) work well in tasks ranging from image captioning to visual question answering (VQA), yet they struggle with spatial reasoning, a key skill for understanding our physical world that humans excel at. We find that…
Reasoning about spatial relationships between objects is essential for many real-world robotic tasks, such as fetch-and-delivery, object rearrangement, and object search. The ability to detect and disambiguate different objects and identify…
One of the most famous results in Complex Analysis is the Little Picard Theorem, that characterizes the image set of an arbitrary entire function. Specifically, the theorem states that this image set is either the whole complex plane or the…
Simplification is one of the fundamental operations used in geoinformation science (GIS) to reduce size or representation complexity of geometric objects. Although different simplification methods can be applied depending on one's purpose,…
Modern extended reality XR systems provide rich analysis of image data and fusion of sensor input and demand AR/VR applications that can reason about 3D scenes in a semantic manner. We present a spatial reasoning framework that bridges…
Spatial reasoning over text is challenging as the models not only need to extract the direct spatial information from the text but also reason over those and infer implicit spatial relations. Recent studies highlight the struggles even…
We present an effective method for visualizing flat surfaces using ray marching. Our approach provides an intuitive way to explore translation surfaces, mirror rooms, unfolded polyhedra, and translation prisms while maintaining…
Vision-language models (VLMs) achieve strong performance on spatial reasoning benchmarks, yet it remains unclear whether this reflects structured 3D understanding or reliance on statistical shortcuts in natural images. We introduce a…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…