Factorization Machine - prevent over fitting
Here are some excerpts from the original paper that I think are key to understanding the question:



  Instead of using an own model parameter for each interaction,
  the FM models the interaction by factorizing it. We will see later on,
  that this is the key point which allows high quality parameter
  estimates of higher-order interactions under sparsity.


  Factorization machines can estimate interactions even in these
  settings (sparse data) well because they break the independence of the interaction
  parameters by factorizing them. In general this means that the data
  for one interaction helps also to estimate the parameters for related
  interactions.



In other words, instead of fitting an independent parameter for every second order interaction, it factorizes the parameters which reduces the parameter space and the model complexity, and thus making the model less prone to over fitting.

Hope this helps understand some aspects of the question.