How many published papers should you have when applying to PhD programs? I'm thinking about applying to PhD programs focused on Deep Learning and Theoretical Neuroscience this fall, and quite frankly I feel like I'm not good enough.

I just started doing research in the past 6 months, and I feel like I'm so far behind my peers its not even funny. I have a paper accepted for a small conference in the fall, but after talking to some folks at Phd programs at places like Stanford or MIT, I hear that students often come in with multiple first author publications. Is this true? I don't know how I can compete with that :/

I want to do research, I love it and have been working 80 hour weeks juggling two RAships and a research internship at a startup this summer, but I just feel like I won't be able to get into a solid background because of my non traditional background. 

I'm finishing two Master's degrees, one in Biology and one in Computer science, from Harvard and Georgia Tech respectively. I previously did my undergraduate studies in Cognitive Science from UCSD. My GPA in my masters is a 4.0. I'll have theses written for each program as well. 

My undergrad was non technical and weak (some family issues, I finished in 2.5 years without a strong focus on doing particularly well), and my research record is short, if a little intense. I've worked in Industry and have started a small, semi successful ML startup. 

Do you have any advice for a nervous kid?
You should be fine.  Realize that there are other kids coming out of liberal arts schools and going into top Ph.D. programs with almost no research experience.  And they do fine, getting into R1 grad programs, and producing work during Ph.D.  All of the kerflutter about undergrad research will fade into the background when you are in a real Ph.D. where there is sooo much more time to spend on research than undergrads (for whom it is a collateral duty...even if they manage to collect a few cap feathers).

Your application will consist of grades, test scores, letters, and other things.  Probably the importance is in that order.  We get kids all the time here who ask about overcoming the opposite worry (subpar grades and standardized test scores) by research.

Just do a decent job and apply to a few places.  You sound like quite a catch, really.  Also, realize that getting into good grad schools in the sciences is quite a bit easier than the whole hothouse environment of high school kids targeting Harvard.  Odds are much more in your favor.  The bigger question to consider is if you should spend more time in school or get a job.  But just put the whole ardent high schooler wanting to go to Brown mindset out of your mind.  It's a different thing, now.