Related papers: Visual thinking and simplicity in proof
Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions.…
Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
Spatially-sparse predictors are good models for brain decoding: they give accurate predictions and their weight maps are interpretable as they focus on a small number of regions. However, the state of the art, based on total variation or…
Objects are a centerpiece of the mathematical realm and our interaction with and reasoning about it, just as they are of the physical one (if not more). And humans' mathematical reasoning must ultimately be grounded in our general…
The concept of metaphor, in particular graphical (or visual) metaphor, is central to the field of information visualization. Information graphics and interactive information visualization systems employ a variety of metaphorical devices to…
Visualization as a discipline often grapples with generalization by reasoning about how study results on the efficacy of a tool in one context might apply to another context. This work offers an account of the logic of generalization in…
This paper presents a hybrid approach to spatial indexing of two dimensional data. It sheds new light on the age old problem by thinking of the traditional algorithms as working with images. Inspiration is drawn from an analogous situation…
Video spatial reasoning requires accumulating viewpoint-dependent evidence over time while retaining information useful to the question being asked. Existing spatial video-language models improve geometric perception and long-range context…
Building patterns are important urban structures that reflect the effect of the urban material and social-economic on a region. Previous researches are mostly based on the graph isomorphism method and use rules to recognize building…
Multimodal Reasoning Models (MRMs) leveraging Chain-of-Thought (CoT) based thinking have revolutionized mathematical and logical problem-solving. However, we show that this paradigm struggles with generalized spatial intelligence. We…
The simple concept of a SIC poses a very deep problem in algebraic number theory, as soon as the dimension of Hilbert space exceeds three. A detailed description of the simplest possible example is given.
Motivated by applications in robotics and computer vision, we study problems related to spatial reasoning of a 3D environment using sublevel sets of polynomials. These include: tightly containing a cloud of points (e.g., representing an…
Spatial reasoning in vision language models (VLMs) remains fragile when semantics hinge on subtle temporal or geometric cues. We introduce a synthetic benchmark that probes two complementary skills: situational awareness (recognizing…
The visual representation of a concept varies significantly depending on its meaning and the context where it occurs; this poses multiple challenges both for vision and multimodal models. Our study focuses on concreteness, a well-researched…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Natural language provides a widely accessible and expressive interface for robotic agents. To understand language in complex environments, agents must reason about the full range of language inputs and their correspondence to the world.…
In decision-support systems, the visual component is important for On Line Analysis Processing (OLAP). In this paper, we propose a new approach that faces the visualization problem due to data sparsity. We use the results of a Multiple…
We investigate integral representation of vector-valued function spaces, i.e., of subspaces $H\subset C(K,E)$, where $K$ is a compact space and $E$ is a (real or complex) Banach space. We point out that there are two possible ways of…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…