Since I first started training last year with PIM (Power in Motion) I've heard over and over from PIM coaches and others to aim for a negative split on training runs and races. Of course, a negative split is defined as running the second half of a course faster than the first half. From the little I have read about training, in particular aerobic base building (what every beginner should be doing, IMHO exclusively), negative splits would not be in order for training runs.
If I am maintaining a consistent effort over the course of a run (e.g. 70% maxHR), then my pace would most certainly decrease over the last half of the run as I fatigue. At the very best, it stays the same. I believe it is best to keep a consistent effort through a training run, not a consistent or increasingly faster pace. That being the case, you should see your mile split slow as you get closer to finishing. Otherwise, if you are trying to maintain your pace or run a faster pace you effort is certainly increasing and may begin to go more anaerobic which builds up LA and brings on fatigue even faster.
To me, the purpose of negative splits in racing is not necessarily to ensure you go faster over the 2nd half of the race. Rather it is to ensure you do not go too fast over the 1st half of the race.
I'm really curious about this. Why do negative splits in a training run? This post may be better suited for the forum so that there can be some discussion on this. Feel free to comment here or go on over to the forum. I'll post the question there, too.