On page 7 of the LTC3631 datasheet, the diagram shows a comparator with two noninverting inputs. What does such a comparator do?
In this context, it means that the comparator can be triggered by comparison of the inverting input against both of the two non-inverting inputs. My impression (though I'm not 100% certain on this) is that the inverting input needs to exceed both of the non-inverting inputs to switch the output. The input hooked to the soft-start pin is dominant at start up, but during normal operation, the 800 mV reference is dominant. This means that at start-up, the inductor current cycles more slowly than during normal operation.
Here's the description from the datasheet of the what the comparator does during normal operation:
The inductor current increases until either the current exceeds the peak current comparator threshold or the voltage on the VFB pin exceeds 800mV, at which time the high side power switch is turned off, and the low side power switch (N-channel MOSFET) turns on. The inductor current ramps down until the reverse current comparator trips, signaling that the current is close to zero. If the voltage on the VFB pin is still less than the 800mV reference, the high side power switch is turned on again and another cycle commences.