Are the Bosses' affinity DMG bonuses persistent?

[FreddyTheMonkey]

Do they carry over in NG+? So far, aside from the third boss, I defeated them all before finding the hidden memory, be it for deciphering the riddle too late (first 2 biomes) or not getting the riddle at all before the boss (fourth biome, I retried it a handful of times but didn't find enough lore before beating the boss).

It's def not a big deal if they don't, because beating the bosses without them means I was good enough for that particular boss, but I was just wondering if I'll get the chance to use them in NG+. Or if lore carries over and thus I'll be able to immediately unlock them.

[Derpykat5]

They seem to.

[Omegatherion]

The DMG bonus is permanent just like the heirlooms. You get it once and it will always be active.