Related papers: Mental Geometry
We will present several examples in which ideas from ergodic theory can be useful to study some problems in arithmetic and algebraic geometry.
This paper introduces a method for learning to generate line drawings from 3D models. Our architecture incorporates a differentiable module operating on geometric features of the 3D model, and an image-based module operating on view-based…
The concept of abstraction has been independently developed both in the context of AI Planning and discounted Markov Decision Processes (MDPs). However, the way abstractions are built and used in the context of Planning and MDPs is…
A simple Neural Network model is presented for end-to-end visual learning of arithmetic operations from pictures of numbers. The input consists of two pictures, each showing a 7-digit number. The output, also a picture, displays the number…
Cartoons are an important part of our entertainment culture. Though drawing a cartoon is not for everyone, creating it using an arrangement of basic geometric primitives that approximates that character is a fairly frequent technique in…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
Originating in psychology, $\textit{Theory of Mind}$ (ToM) has attracted significant attention across multiple research communities, especially logic, economics, and robotics. Most psychological work does not aim at formalizing those…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
The initial techniques developed in Euclid's Elements, well before the use of the parallel postulate, are reexamined in order to clarify even the most obscure details, particularly those related to equality, superposition and angle…
The leading idea of the paper is to treat the theorem of Wigner with methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Geometry constitutes a core set of intuitions present in all humans, regardless of their language or schooling [1]. Could brain's built in machinery for processing geometric information take part in uncertainty representation? For decades…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Understanding intelligence is a central pursuit in neuroscience, cognitive science, and artificial intelligence. Intelligence encompasses learning, problem-solving, creativity, and even consciousness. Recent advancements in geometric…
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
Alchemy is a new meta-learning environment rich enough to contain interesting abstractions, yet simple enough to make fine-grained analysis tractable. Further, Alchemy provides an optional symbolic interface that enables meta-RL research…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
The Artificial Intelligence field is flooded with optimisation methods. In this paper, we change the focus to developing modelling methods with the aim of getting us closer to Artificial General Intelligence. To do so, we propose a novel…
When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric…
This article provides a pedagogically oriented introduction to geometric (Clifford) calculus on pseudo-Riemannian manifolds. Unlike usual approaches to the topic, which rely on embedding the geometric algebra either within a tensor algebra…