how can an AI be trained if we human beings are not telling it its calculation is correct?
What you are looking for is called self-supervised learning. Yann LeCun, one of the originators behind modern neural network systems, has suggested that machines can reason usefully even in the absence of human-provided labels simply by learning auxiliary tasks, the answers for which are already encoded in the data samples. Self-supervision has already been successfully applied to a variety of tasks, showing improvement in multitask performance due to self-supervision. Unsupervised learning would in general be a subset of self-supervision.
Self-supervision can be performed in a variety of ways. One of the most common is to use parts of the data as input and other parts as labels, and using the "input" subset of the data to predict the labels.
Supervised learning looks like this:
The human_labels correspond to entries in various_data, which we expect the model to predict.
Meanwhile, self-supervised learning can look something like this:
(Using Python array slice notation, some of the input data are used as training labels.)
For example, a machine could use half of the pixels in an image of a handwritten digit to try to predict the missing pixels. This is a form of self-supervision: Since the machine knows which pixels belong together in the same sample, it can "automatically" produce its own labeled data from the input itself, simply by using some inputs as outputs.
However, predicting pixels from other pixels is often not the desired task.
So instead, a neural network is often pretrained using self-supervised or unsupervised learning techniques, and then subsequently trained on some amount of human-labeled data as a form of transfer learning.
What the summary of the hypothetical news article promises is that self-supervision made the learning more efficient, not that it outgrew the need for any kind of human intervention. This is exactly what we get from successful self-supervision in pretraining.
In the best possible case, the machine learns to "recognize" each class of digit 0-9 but it still does not know how to ground its own internal labels to the human's labels. Then a human supplying the mapping between the machine's labels and the human-specified IDs would be the only step necessary to upgrade the self-supervised machine to one that is directly useful for digit recognition.
There will always be a need for humans to train a machine via direct supervision in order for the machine to learn the intended task. In order to solve a specific problem, a sufficient degree of supervision is always required, and sufficient labels to reflect the intention must be provided.