To my knowledge, R2 is basically a comparison of your model fit, to the
model that is fit by simply drawing a line through the mean of your output
variable. To that extent, if your fit model does worse than the "mean fit",
then R2 will be negative. E.g., check out:

http://randomanalyses.blogspot.com/2011/11/coefficient-of-determination-r2.html
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