Halliday & Matthiessen (1999: 174-5):
This type of circumstance relates to projection rather than expansion, and specifically to the projecting not the projected component Hence there is no agnate participant; instead, the Angle corresponds to the process of saying (grammatically, the projecting verbal clause in a 'locution' nexus) or the process of sensing (grammatically, the projecting mental clause in an 'idea' nexus). Thus according to the newspaper corresponds to the newspaper says; and to her students corresponds to her students think.