Degradation mechanism of hydroxymethylfurfural to 2,5-dioxo-3-hexenal and 4-oxopentanoic acid
Here is a link to a detailed reference on HMF.  In section 3.3 (page 32) they show a mechanism for the acid catalyzed degradation of HMF.  As you noted, they do propose two pathways for decomposition, one leads to polymeric materials, the other leads to 2,5-dioxo-3-hexenal, which then can react further to produce 4-oxopentanoic acid. The work they describe was done by Horvat (Horvat, J.; Klaič, B.; Metelko, B.; Sunjic, V. Tetrahedron Lett. 1985, 26, 2111).

I don't want to reproduce their drawing, but follow the link and look for Scheme 17.  Most of the steps involve protonation of either 


a double bond to form a resonance stabilized carbocation followed by addition of water and elimination of a proton to yield an alcohol
a hydroxyl group followed by elimination of water to yield a resonance stabilized carbocation followed by elimination of a proton to yield a double bond
or protonation of the furan oxygen followed by ring opening to generate a protonated, resonance stabilized carbonyl


If you have any specific questions on the mechanism, just post back here.