I am/was a computational neuroscientist. There's way more papers published in neuroscience than any one person has a hope of reading.

The best way for me to keep up was to use an rss reader. The big publishers and publication portals (such as arxiv) all have rss feeds, usually per keyword, and you follow the ones that might interest you.

Then you use the filtering available in your feed reader to get rid of any item you obviously don't care about. I was typically left with ~100 papers every morning, with about 4-5 that I'd actually download.