Question: Impact of QuantileLoss on TFT optimization

I am wondering if the performance of the median prediction could depends on the others quantiles, using QuantilLoss.

It is clear that defining extra quantiles will results in a change in architecture of the later layers of the network, in order to generate extra outputs. Yet the upstream layers remain similar and are involved in all outputs predictions. Beside, the optimization process trains all quantiles at one go, meaning the resulting upstream layer should have different weights depending on the choice of the quantile.

So here are my questions:

Can we expect to improve median prediction depending on the choice of extra quantiles. Typically could we expect a median prediction error more centered around 0 with extra-quantiles such as 45% 55% ?

or could we get predicted quantile crossover ? Meaning the potential improvement on the median prediction would be very unsure.

Thank you all, in advance for your attention.

No files or tests are named. Start by examining QuantileLoss and the Temporal Fusion Transformer optimization path, then determine whether adding quantiles changes median predictions and can cause quantile crossover; done means documenting evidence-based conclusions.