Perhaps it's a bit pedantic, but the training is to adjust the electrical interface for the gddr5 8-bit data bus.  It finds the optimal drive & termination characteristics in order to avoid errors, but it doesn't adjust timing.  So for example when your card heats up from 20C to 80C, the resistance of the traces increase, which means more attenuation of the electrical signals.  That may lead to more CRC errors, and when they reach a threshold the memory controller will initiate a retrain.  The training sequence itself will then read and write fixed data patterns on the bus, trying things like increasing the output driver strength to overcome attenuation issues.  Increased driver strength may lead to data reflections causing more errors, which could be corrected with lowering the termination resistance on the receiving end.

Another tweak I've wondered about is monitoring memory die temps.  GDDR5 chips have internal thermal diodes similar to the GPU, and they can be enabled by setting a bit in mode register 7.  Knowing the temperature of each memory die could provide useful diagnostic info for problems such as a heatsink not having good contact with the chip.