It says "mAP result values on the WIDERFACE validation dataset:"

If your professor is working in on object detection they know what mAP is - all the major datasets use it as their standard evaluation criteria.

> What makes it state of the art

Generally it means something roughly like "the best known approach for this specific problem". Often it means "the best known approach for this specific dataset" (eg "SOTA on ImageNet").

> why is lower accuracy acceptable?

Lower accuracy is worse, but these numbers look close enough that it's probably acceptable for most people.

There are plenty of environments where TF is preferable to MXNet (eg, you have TPUs/want to use TFLite on mobile/want to slice the model weights up and use it for your own custom TF model).

It's probably lower accuracy because it wasn't trained as long. Those extra couple of points could take days (or more) of training.

The paper that presents this algorithm has the best known accuracy on the widerface dataset, which is why it is called state of the art. The authors of the paper published an implementation of this algorithm based on mxnet, but a lot people and companies use tensorflow instead of mxnet in their work, so just using the mxnet implemenation is not an option. Thats why I converted it to TF, with a slight decrease in accuracy on widerface. Then what is "acceptable" depends on your judgement, but the widerface dataset is extremely challenging, with many pictures having hundreds of small faces. In some of these pictures my implementation will miss a few faces, or find them but with lower probability. Overall for the vast majority of face detection applications, the two implementations will yield extremely similar results. I havent yet found a picture with a few dozen faces where the TF implementation performed not as well as the original one !