Related papers: Exploring a Cognitive Architecture for Learning Ar…
Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have…
Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we…
Neural networks can approximate complex functions, but they struggle to perform exact arithmetic operations over real numbers. The lack of inductive bias for arithmetic operations leaves neural networks without the underlying logic…
Intelligence necessitates memory. Without memory, humans fail to perform various nontrivial tasks such as reading novels, playing games or solving maths. As the ultimate goal of machine learning is to derive intelligent systems that learn…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Learning underlies nearly all human behavior and is central to education and education reform. Although recent advances in neuroscience have revealed the fundamental structure of learning processes, these insights have yet to be integrated…
Learning to count is an important example of the broader human capacity for systematic generalization, and the development of counting is often characterized by an inflection point when children rapidly acquire proficiency with the…
For complex life to evolve, a sophisticated nervous system for handling its complexities was fundamental. The demand resulted in the emergence of brain's computational facility, the neuronal network. This facet of the brain is attested…
This article addresses an open problem in the area of cognitive systems and architectures: namely the problem of handling (in terms of processing and reasoning capabilities) complex knowledge structures that can be at least plausibly…
We envision a machine capable of solving mathematical problems. Dividing the quantitative reasoning system into two parts: thought processes and cognitive processes, we provide probabilistic descriptions of the architecture.
Over the last decades, deep neural networks based-models became the dominant paradigm in machine learning. Further, the use of artificial neural networks in symbolic learning has been seen as increasingly relevant recently. To study the…
Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…
In this paper a neural network is trained to perform simple arithmetic using images of concatenated handwritten digit pairs. A convolutional neural network was trained with images consisting of two side-by-side handwritten digits, where the…
Analogy is core to human cognition. It allows us to solve problems based on prior experience, it governs the way we conceptualize new information, and it even influences our visual perception. The importance of analogy to humans has made it…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Continual learning is a challenge for models with static architecture, as they fail to adapt to when data distributions evolve across tasks. We introduce a mathematical framework that jointly models architecture and weights in a Sobolev…
Algorithms based on deep network models are being used for many pattern recognition and decision-making tasks in robotics and AI. Training these models requires a large labeled dataset and considerable computational resources, which are not…
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 recently has been shown as a hard challenge for neural systems. Abilities including expression translation, logical reasoning, and mathematics knowledge acquiring appear to be essential to overcome the challenge. This…
Despite incredible progress, many neural architectures fail to properly generalize beyond their training distribution. As such, learning to reason in a correct and generalizable way is one of the current fundamental challenges in machine…