Related papers: How the Brain might use Division
We consider the implications of the mathematical analysis of neurone-to-neurone dynamical complex networks. We show how the dynamical behaviour of small scale strongly connected networks lead naturally to non-binary information processing…
We revisit the planning problem in the blocks world, and we implement a known heuristic for this task. Importantly, our implementation is biologically plausible, in the sense that it is carried out exclusively through the spiking of…
This is the first in a series of connected papers discussing the problem of a dynamically reconfigurable universal learning neurocomputer that could serve as a computational model for the whole human brain. The whole series is entitled "The…
Neurons in the brain are often finely tuned for specific task variables. Moreover, such disentangled representations are highly sought after in machine learning. Here we mathematically prove that simple biological constraints on neurons,…
Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…
Neuroscience has focused on the detailed implementation of computation, studying neural codes, dynamics and circuits. In machine learning, however, artificial neural networks tend to eschew precisely designed codes, dynamics or circuits in…
Research has a long history of discussing what is superior in predicting certain outcomes: statistical methods or the human brain. This debate has repeatedly been sparked off by the remarkable technological advances in the field of…
Over the past decade, AI has made a remarkable progress. It is agreed that this is due to the recently revived Deep Learning technology. Deep Learning enables to process large amounts of data using simplified neuron networks that simulate…
Looking back at the history of calculators, one can see that they become less functional and more computationally expensive over time. A modern calculator runs on a personal computer and is drawn at 60 fps only to help us click a few digits…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…
The last two decades have seen tremendous advances in Artificial Intelligence. The exponential growth in terms of computation capabilities has given us hope of developing humans like robots. The question is: are we there yet? Maybe not.…
How do the synthetic neurons in language models create "thought categories" to segment and analyze their informational environment? What are the cognitive characteristics, at the very level of formal neurons, of this artificial categorical…
How do humans and other animals learn new tasks? A wave of brain recording studies has investigated how neural representations change during task learning, with a focus on how tasks can be acquired and coded in ways that minimise mutual…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
Although existing models can interact with humans and provide satisfactory responses, they lack the ability to act autonomously or engage in independent reasoning. Furthermore, input data in these models is typically provided as explicit…
Economies are complex man-made systems where organisms and markets interact according to motivations and principles not entirely understood yet. The increasing dissatisfaction with the postulates of traditional economics i.e. perfectly…
The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed…
We consider the following "partition and sum" operation on a natural number: Treating the number as a long string of digits insert several plus signs in between some of the digits and carry out the indicated sum. This results in a smaller…
Human reasoning can distill principles from observed patterns and generalize them to explain and solve novel problems. The most powerful artificial intelligence systems lack explainability and symbolic reasoning ability, and have therefore…
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…