Preheat and precool for increased comfort and economy.
In more details. Lets say my home takes 20 minutes to reach 21 degrees from the current temperature once I start the heating and maybe 30 minutes to go below my comfort temperature after I turn the radiant heating off (winter mode). Lets also say that I only want a warm house only for my breakfast time, say 7-8am. A dumb thermostat would turn it on @ 7 and off @ 8. This means it will reach my desired 21 degrees @ 7:20. Thats just silly. Additionally if I leave the house @ 8:00 the house will remain warm for 30 more minutes. That's a waste of money if noone is in the house.
A smart thermostat should "know" (continously monitor the house's response to heating and cooling compared to outside temperature) and start and stop earlier. For the above scenario the heating should be kept on from 6:40 to 7:30 and everybody should be happy!
In more realistic scenarios with radiant heating, the temperature keeps increasing for a bit even after the heating is turned off so in the above example a dumb themostat would turn off once the temperature reaches 21 but the temperature may reach 24 before is starts falling again. PI thermostats learn how long does this rise take and how high they reach and react proactively to maintain a steady temperature saving at the same time, money! This learning process is continuous throughout the day and night as parameters change. The continuous averaging of the 8 previous events predicts the optimal future behaviour.