A cost associated with "regularizing" the input distributions using a simple transformation is:

Regularizing the input distributions through transformation techniques, such as normalization or standardization, typically alters the scale and distribution of the data to meet certain criteria that can enhance model performance. However, one notable trade-off involves the complexity of interpreting the model results.

When data is transformed, the original relationships and patterns within the dataset might become obscured. This can make it challenging to explain the model outputs and understand the influence of input variables on predictions. For instance, if a logarithmic transformation is applied, interpreting the coefficients in terms of the original input units necessitates additional steps, which can complicate the model interpretation significantly.

Thus, while regularizing transformations can enhance the model's performance and generalizability, they often introduce additional hurdles when attempting to explain the model behavior, making it harder for stakeholders to draw insights or make decisions based on the model's findings.