Recent AI applications such as Collaborative Intelligence with neural networks involve transferring deep feature tensors between various computing devices. This necessitates tensor compression in order to optimize the usage of bandwidth-constrained channels between devices. In this paper we present a prediction scheme called Back-and-Forth (BaF) prediction, developed for deep feature tensors, which allows us to dramatically reduce tensor size and improve its compressibility. Our experiments with a state-of-the-art object detector demonstrate that the proposed method allows us to significantly reduce the number of bits needed for compressing feature tensors extracted from deep within the model, with negligible degradation of the detection performance and without requiring any retraining of the network weights. We achieve a 62% and 75% reduction in tensor size while keeping the loss in accuracy of the network to less than 1% and 2%, respectively.