Related papers: Universal Learning Theory
Reservoir computing is a versatile paradigm in computational neuroscience and machine learning, that exploits the non-linear dynamics of a dynamical system - the reservoir - to efficiently process time-dependent information. Since its…
The quest to comprehend the origins of intelligence raises intriguing questions about the evolution of learning abilities in natural systems. Why do living organisms possess an inherent drive to acquire knowledge of the unknown? Is this…
Deep learning models have lately shown great performance in various fields such as computer vision, speech recognition, speech translation, and natural language processing. However, alongside their state-of-the-art performance, it is still…
Einstein's contribution to relativity is reviewed. It is pointed out that Weyl gave first unified theory of gravitation and electromagnetism and it was different than the five dimensional theory of Kaluza. Einstein began his work on…
A simple pedagogical introduction to the Colombeau algebra of generalised functions is presented, leading the standard definition.
Like any field of empirical science, AI may be approached axiomatically. We formulate requirements for a general-purpose, human-level AI system in terms of postulates. We review the methodology of deep learning, examining the explicit and…
In this article we present a unification of the theory of algebraic, singular, topological and directional transition matrices by introducing the (generalized) transition matrix which encompasses each of the previous four. Some transition…
Semisupervised learning is a learning standard which deals with the study of how computers and natural systems such as human beings acquire knowledge in the presence of both labeled and unlabeled data. Semisupervised learning based methods…
With the emergence of generative artificial intelligence, an increasing number of individuals and organizations have begun exploring its potential to enhance productivity and improve product quality across various sectors. The field of…
Deep learning algorithms have made incredible strides in the past decade, yet due to their complexity, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of deep…
This is an old article of 2000. Its aim is to illustrate how a Lie-theoretic result of Zelmanov enables one to treat various problems in group theory.
Computational Thinking (CT) has been described as an essential skill which everyone should learn and can therefore include in their skill set. Seymour Papert is credited as concretising Computational Thinking in 1980 but since Wing…
Universal learning machine is a theory trying to study machine learning from mathematical point of view. The outside world is reflected inside an universal learning machine according to pattern of incoming data. This is subjective pattern…
When Kurt Goedel layed the foundations of theoretical computer science in 1931, he also introduced essential concepts of the theory of Artificial Intelligence (AI). Although much of subsequent AI research has focused on heuristics, which…
In his $1994$ survey, Kleinert defined formally and formulated the problem to obtain unit theorems for unit groups of orders in a semisimple algebra $A$. If $A$ is a group algebra $FG$, it boils down to classifying all finite groups $G$…
Machine learning has achieved remarkable success in many applications. However, existing studies are largely based on the closed-world assumption, which assumes that the environment is stationary, and the model is fixed once deployed. In…
Einstein's Special Theory of Relativity was proposed a little over a hundred years back. It remained a bedrock of twentieth century physics right up to Quantum Field Theory. However, the failure over several decades to provide a unified…
Universality is a key hypothesis in mechanistic interpretability -- that different models learn similar features and circuits when trained on similar tasks. In this work, we study the universality hypothesis by examining how small neural…
The orthodox interpretation of quantum theory treats the subject and the object on an equal footing. It has been suggested that the cyclical-time process, which resolves self-reference in consciousness, interconnects the observed universe…
The "unit theorem" to which the present mini-course is devoted is a theorem from algebra that has a combinatorial flavour, and that originated in fact from algebraic combinatorics. Beyond a proof, the course also addresses applications, one…