Utilizing integrated circuits' manufacturing variations to produce responses unique for individual devises, physical unclonable functions (PUFs) are not reproducible even by PUF device manufacturers. However, many PUFs have been reported to be 'mathematically reproducible' by machine learning-based modeling methods. The feed-forward arbiter PUFs are among the PUFs which have showed strength ,  against machine learning modeling unless large computation time is used in machine learning process and the feed-forward loops are of a special type. In this paper, we develop a signal delay model for the feed-forward arbiter PUFs, through which efficient and accurate machine learning of the PUF's essential features is made possible. Experimental results show that the new model has led to high accuracy and high efficiency for the prediction of the responses of the PUFs with any type of feed-forward loops, and the high prediction accuracy was measured in terms of average prediction rate over all tested all cases. The high efficiency and high accuracy prediction of responses reported in this paper has revealed a weakness of the feed-forward arbiter PUFs that can be potentially utilized by response-prediction-based malicious software.