The term gradient vanishing problem originates from the fields of artificial intelligence and digital transformation. It describes a challenge when training artificial neural networks, which form the basis of modern AI applications.
When a neural network learns, it gradually adjusts its "weights" using a mathematical method in order to deliver better and better results. This happens in many small steps that run from front to back through all layers of the network. The gradient vanishing problem occurs when these adjustment steps become so small at the very beginning of the network that they almost disappear. As a result, the network "forgets" almost everything that happens in the front layers - training stalls or is no longer possible at all.
A simple example: Imagine you want to inform a long line of people by shouting. If everyone barely passes on what they hear, nothing will get through in the end.
The gradient vanishing problem is particularly relevant for very deep neural networks, i.e. those comprising many layers. Solutions such as special building blocks (e.g. "LSTM" cells in speech AI) help to circumvent this problem.
Deutsch 
English (UK)