#1
I'm trying to learn this song and for months now i've practiced the intro but i can't get up to speed. It's at 110 tempo and i can't get past 80 tempo without mistakes.

My alternate picking sucks and it isn't improving even with practice. (I've been doing a few "speed" exercises like moving up the neck in 4-3-2-1, 5-4-3-2, 6-5-4-3, 5-4-3-2 style pattern from that "speed guitar" book but i don't think its helping
#2
I don't know if you're already doing this, but try to focus just on one aspect of playing guitar, and practice it for like an hour in a row. So if you're practicing that song, just do that picking, nothing else, like some power chords or so.
Hope it helps, if you weren't doing this already.
#3
Make sure your right hand (if you're right handed) technique is correct. I had the same problem, couldn't alternate pick even at moderate tempos, but then changed the way I hold the pick and just in a month I could play much faster.
#4
If you want to play this riff at 110bpm.
First, try and play it at 110bpm. Watch yourself play it in front of a mirror.
What exactly is preventing you from playing cleanly at this speed?
Is your hand not swift enough? Are you tiring your hand out? Or your muting fails and notes bleed into each other?
Now slow it down as slow as possible (20-30bpm) and correct whatever is limiting your speed.
-If your arm or wrist is tiring out, you need to watch that your arm doesn't tense, or if it moves when you change strings, if it's not, fix it.
-If your hands not fast enough then keep reading.

Practice it at 25 bpm, make sure your technique remains disciplined, but DON'T tense.
Then move onto 30bpm. Then go back to 27bpm. Set yourself an achievable goal speed, aka. 40bpm.
That might not seem like much, but you can play at 40bpm flawlessly.
After that, stop playing and move onto something else; maybe economy picking or riffing.

The next day start at 40bpm, and continue the cycle, going up in small increments, occasionally moving above your comfortable tempo, then back down.
and then until you get to your goal tempo.
This can take weeks, for a single riff.
BUT
your technique will be absolutely perfect, every note you pluck will be 100% crystal clear, and you'll find in future, that it will be worth it.

I may have gone overboard, but in conclusion:
-Don't spend 3 hours practicing alternate picking. You get distracted, and you ignore technique and start 'noodling'
-The slower you practice something the more attention you can pay to every little movement you're making and change it into an effortless motion.
- Record and watch yourself play, or get an experienced player to watch you.
If you spot anything wrong with your playing, fix it.
- Don't let others tell you your technique is 'wrong' do what is most comfortable for you.
#5
I'd agree with EsotericSurgery, the best way to practice anything is simply to slow it down and eventually build up to the speed you want. Ironically, I had the same issue with downpicking, since I spent most of my time with guitar alternate picking. I just started out with slow downpicking, now I can do it pretty damn fast (not sure on the exact bpm, I don't use a metronome). Despite my natural proclivity I still struggle with some aspects of alternate picking though, mostly pushing it higher than 120bpm (or thereabouts, again, not sure) whilst palm muting, though I find the more I practice high tempo and precision without palm muting the better I become whilst using it.

In conclusion; a useful mantra in life in general - Make sure you can walk before you try to run.
#6
when you're practicing slowly like the others have suggested, do it correctly. it should still be the same tiny, fast flicks of the picking wrist you'd do if you were playing faster, except you're giving yourself more time in between each picking.
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#7
One thing you need to realize is that, as long as you're practicing, you ARE improving. What helped me a LOT on speed was a little video by Allen Van Wert. I doubt you can find it on YouTube, but it's on JamPlay.com.

Anyways, the gist of it is to slow WAYY down and alternate pick through the riff very close to the bridge and with the pick as close to parallel to the strings as possible all while stopping your picking hand right as it crosses the string so that you cross the string, but it doesn't ring out hardly at all. This will do two things:

1: It will help your picking hand strength. This was my problem. I was using economy of motion, but without the strength to carry through the string, it was virtually useless.

2: It will help your economy of motion which, as we all know, is one of the biggest keys to speed.

It should be noted that, while you do need to do some strength training to your picking hand, a large amount of such exercises will NOT turn you into John Petrucci. There are many more points to realize when you're practicing your alternate picking and I'm not, in any way, trying to tell you to focus on your strength. What I think you need is the economy of motion part of it. However, a little added firmness/strength in your wrist isn't going to hurt you along the way. Just be careful with how you interpret "strength." I DO NOT mean to lock your wrist. I mean to build the small muscles that move your wrist in the directions needed for alternate picking.

It's very hard to understand without the video, but I tried my best to explain it. Let me know if it helps or if you don't understand something. I'll do my best to help you out, and any feedback is appreciated.