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The field of artificial intelligence (AI) represents an enormous endeavour of humankind that is currently transforming our societies down to their very foundations. Its task, building truly intelligent systems, is underpinned by a vast…
The latest improvements in artificial intelligence (AI) raise new challenges for intellectual property laws, particularly concerning the inventorship issue in AI-assisted inventions - that is, those in which AI is used in the inventive…
As progress in AI continues to advance, it is important to know how advanced systems will make choices and in what ways they may fail. Machines can already outsmart humans in some domains, and understanding how to safely build ones which…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed $k$, the method finds a convex polytope with $k$ vertices, called archetype points, such that the polytope is…
Computation fundamentally separates time from space: nondeterministic search is exponential in time but polynomially simulable in space (Savitch's Theorem). We propose that the brain physically instantiates a biological variant of this…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…
In this work, a 2D contour generation algorithm is proposed for irregular regions. The contour of the physical domain is approximated by mesh segments using the known coordinates of the contour. For this purpose, the algorithm uses a…
Advances in experimental neuroscience have transformed our ability to explore the structure and function of neural circuits. At the same time, advances in machine learning have unleashed the remarkable computational power of artificial…
In fine art, especially painting, humans have mastered the skill to create unique visual experiences through composing a complex interplay between the content and style of an image. Thus far the algorithmic basis of this process is unknown…
Solving math word problem (MWP) with AI techniques has recently made great progress with the success of deep neural networks (DNN), but it is far from being solved. We argue that the ability of learning by analogy is essential for an MWP…
Let $n\geq 3$ and $r_n$ be a $3$-polytopal graph such that for every $3\leq i\leq n$, $r_n$ has at least one vertex of degree $i$. We find the minimal vertex count for $r_n$. We then describe an algorithm to construct the graphs $r_n$. A…
AI-assisted research is crossing a threshold: fully automated systems can now generate research papers for as little as $15, while long-horizon agents can execute experiments, draft manuscripts, and simulate critique with minimal human…
Producing an artificial general intelligence (AGI) has been an elusive goal in artificial intelligence (AI) research for some time. An AGI would have the capability, like a human, to be exposed to a new problem domain, learn about it and…
We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If…
{\bf Abstract.} The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to a well-known open problem. It has two objectives. The first is to reconcile the way of…
We study the geometry of centrally-symmetric random polytopes, generated by $N$ independent copies of a random vector $X$ taking values in $\mathbb{R}^n$. We show that under minimal assumptions on $X$, for $N \gtrsim n$ and with high…
Santos' construction of the first known counterexample to the Hirsch conjecture, for bounded polytopes, follows the strategy of first finding a counterexample to the nonrevisiting conjecture. Santos constructs a $5$-dimensional…
We consider the problem of computing a lightest derivation of a global structure using a set of weighted rules. A large variety of inference problems in AI can be formulated in this framework. We generalize A* search and heuristics derived…