# How to explain ANN can predict much larger output values (e.g., y>2.5) when it was only trained with small output values (y>=2.5)

I have trained models with both ANN and XGBoost. I am wondering that whether ANN has the ability to predict much larger output values (e.g., $$y>2.5)$$ when it was only trained with small output values $$(y\le2.5$$). Actually, my experiment confirms this but I do not have theoretical evidence to support it (I am not very familiar with computing science).

I trained both ANN and XGBoost models and the experiment shows that XGBoost outperforms ANN at both validation and test data sets (y values are all less than 2.5). But when I apply the models to other cases without true y labels (expected larger y values), ANN seems to be able to give more reliable results while XGBoost can only give y values less than 2.5.

One point should be mentioned is a prior knowledge is that the cases of both small and large y values obey the same physical function (e.g. $$y=e^x+lnx$$, the real function is much more complex than this), can I argue that ANN has the ability to predict extended y values while XGBoost does not?