Artificial Intelligence has become very present in the media in the last couple of years. At the end of 2022, ChatGPT has captured the world’s attention, showing at least a hundred million users around the globe the extraordinary potential of large language models. Large language models such as LLaMA, Bard and ChatGPT mimic intelligent behavior equivalent to, or indistinguishable from, that of a human in specific areas (i.e., Imitation Game or Turing Test). Stephen Wolfram has written an article about how ChatGPT works.

Year-end 2022 might therefore be a watershed moment for human mankind since Artificial Intelligence has now the potential to change the way how humans think and work

… All these achievements have one thing in common – they are build on a model using an Artificial Neural Networks (ANN). … ANN are very good function approximators provided that big data of the corresponding domain is available. Almost all practical problems such as playing a game of Go or mimic intelligent behavior can be represented by mathematical functions.

The corresponding theorem that formulates this basic idea of approximation is called Universal Approximation Theorem. It is a fundamental result in the field of ANN, which states that certain types of neural network can approximate certain function to any desired degree of accuracy. This theorem suggest that a neural network is capable of learning complex patterns and relationships in data as long as certain conditions are fulfilled.

The Universal Approximation Theorem is the root-cause why ANN are so successful and capable in solving a wide range of problems in machine learning and other fields. — Read More