A huge fraction of the signals that could in principle be hiding in LHC data is still unexplored. The difficulty in extracting them is related to a long-standing statistical problem: how to perform a goodness-of-fit test in high-dimensional spaces. I will discuss two new ideas based on a geometric interpretation of collider data. They are completely orthogonal (in a colloquial sense) to existing approaches and scale exponentially better in p-value when the number of input dimensions (collider observables) is increased.