Direct addition of pulled garden weeds into lasagna layering system.

I have a lasagna layering system as taught by a webinar from the Rodale Institute (https://rodaleinstitute.org/wp-content/uploads/Backyard-Composting-Cheatsheet.pdf). I’m wondering specifically about garden weeds and if they can go directly into my cylinder or if I need to put them in my intermediate bucket of greens (with all my food scraps, etc) so it starts decomposing first, then add it to the lasagna layer in the appropriate way. Just wondering if it’s necessary to do that or if I can make it easier for myself in this way, specifically for garden weeds.