When asked if Kemper Profiler uses Impulse Responses, which they claim they don't:

They do use IRs. They use 256 point IRs augmented with parametric EQ. This is easily demonstrated by examining the data structure of the profile and by measuring the device (or by using their IR converter which converts long IRs to 256 point IR plus EQ). What they say is "we use something more advanced" or something like that. By "more advanced" they mean they augment the IR with parametric EQ. However they must augment the IR with parametric EQ because the IR is too short to reproduce low frequencies accurately. The frequency resolution of an IR is proportional to its length: the longer the IR the better the resolution. To accurately reproduce a guitar cabinet requires at least 1000 points from my research. (Note: I'm using the term "parametric EQ" as a substitute for IIR filter since most people don't know what an IIR filter is.)

This technique has been around since the early days of modelers (I believe the Pod 2.0 was the first to do this). The impetus for this is that it uses much less processing power since the amount of processing power required is directly proportional to the length of the IR. A 256 point IR plus, for example, an 8-band EQ can be equivalent to a 512 point IR but uses less processing power. The downside is the phase response isn't the same but that is usually inaudible.

In their specific case the amplifier output frequency response and cabinet frequency response are combined into a single IR plus EQ since they aren't measured separately. See my MIMIC whitepaper for more information on frequency response, etc. You can make assumptions about the amplifier output frequency response in order to separate it from the cabinet response. In their case I believe they assume there is a 6 dB resonance at 125 Hz plus a 6 dB highshelf (incidentally this is the same power amp frequency response model that the Marshall JMP-1 used albeit using analog filters). For many amplifiers this is a reasonable approximation.

The Axe-Fx II IRs are 2048 sample (eight times the resolution) and don't require augmentation.