Related papers: The Role of General Intelligence in Mathematical R…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
Common-sense physical reasoning in the real world requires learning about the interactions of objects and their dynamics. The notion of an abstract object, however, encompasses a wide variety of physical objects that differ greatly in terms…
Object detection and recognition are fundamental functions underlying the success of species. Because the appearance of an object exhibits a large variability, the brain has to group these different stimuli under the same object identity, a…
As part of human core knowledge, the representation of objects is the building block of mental representation that supports high-level concepts and symbolic reasoning. While humans develop the ability of perceiving objects situated in 3D…
Mathematical reasoning is a fundamental aspect of human intelligence and is applicable in various fields, including science, engineering, finance, and everyday life. The development of artificial intelligence (AI) systems capable of solving…
Being mathematics a natural language to Mankind and to physics, it must be constantly adapted to our necessities and our natural perception. Then, mathematical concepts are not absolute to reality. Although mathematical theories are…
The overarching problem in artificial intelligence (AI) is that we do not understand the intelligence process well enough to enable the development of adequate computational models. Much work has been done in AI over the years at lower…
The article analyses foundational principles relevant to the creation of artificial general intelligence (AGI). Intelligence is understood as the ability to create novel skills that allow to achieve goals under previously unknown…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
Object perception is a fundamental sub-field of Computer Vision, covering a multitude of individual areas and having contributed high-impact results. While Machine Learning has been traditionally applied to address related problems, recent…
Reasoning about objects, relations, and physics is central to human intelligence, and a key goal of artificial intelligence. Here we introduce the interaction network, a model which can reason about how objects in complex systems interact,…
The idea behind object-centric representation learning is that natural scenes can better be modeled as compositions of objects and their relations as opposed to distributed representations. This inductive bias can be injected into neural…
One of the core components of our world models is 'intuitive physics' - an understanding of objects, space, and causality. This capability enables us to predict events, plan action and navigate environments, all of which rely on a composite…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
There is a significant lack of unified approaches to building generally intelligent machines. The majority of current artificial intelligence research operates within a very narrow field of focus, frequently without considering the…
A core function of intelligence is grounding, which is the process of connecting the natural language and abstract knowledge to the internal representation of the real world in an intelligent being, e.g., a human. Human cognition is…
Achieving visual reasoning is a long-term goal of artificial intelligence. In the last decade, several studies have applied deep neural networks (DNNs) to the task of learning visual relations from images, with modest results in terms of…
Recent advances in AI -- including generative approaches -- have resulted in technology that can support humans in scientific discovery and forming decisions, but may also disrupt democracies and target individuals. The responsible use of…
Recent progress in artificial intelligence (AI) is unlocking transformative capabilities for mathematics. There is great hope that AI will help solve major open problems and autonomously discover new mathematical concepts. In this essay, we…
Human perception is structured around objects which form the basis for our higher-level cognition and impressive systematic generalization abilities. Yet most work on representation learning focuses on feature learning without even…