# Choice of objective function for log transformed data for feedforward NN

I am processing some data using a feedforward neural network in Keras. I have noticed that if I log transform the data, the model trains better, however the error metric on the transformed data doesn't necessarily reflect very well what's going on with the original dataset.

At the moment I am using Mean Average Percentage Error metric (mape), and a CV error of 3.8% on log transformed data set corresponds to about 25% when I reverse-transform the predictions and check against the original outputs.

Is there a better choice of cost/objective function for situations like this?

$$log error = \frac{1}{n} \sum_{t=1}^{n} abs( \frac{log(y_{t})-model(X_{t})}{log(y_{t})})$$
$$error = \frac{1}{n} \sum_{t=1}^{n} abs(\frac{y_{t}- exp(model(X_{t}))}{y_{t}})$$