Very large-scale Deep Neural Networks (DNNs) have achieved remarkable successes in a large variety of computer vision tasks. However, the high computation intensity of DNNs makes it challenging to deploy these models on resource-limited systems. Some studies used low-rank approaches that approximate the filters by low-rank basis to accelerate the testing. Those works directly decomposed the pre-trained DNNs by Low-Rank Approximations (LRA). How to train DNNs toward lower-rank space for more efficient DNNs, however, remains as an open area. To solve the issue, in this work, we propose Force Regularization, which uses attractive forces to enforce filters so as to coordinate more weight information into lower-rank space. We mathematically and empirically prove that after applying our technique, standard LRA methods can reconstruct filters using much lower basis and thus result in faster DNNs. The effectiveness of our approach is comprehensively evaluated in ResNets, AlexNet, and GoogLeNet. In AlexNet, for example, Force Regularization gains 2x speedup on modern GPU without accuracy loss and 4.05x speedup on CPU by paying small accuracy degradation. Moreover, Force Regularization better initializes the low-rank DNNs such that the fine-tuning can converge faster toward higher accuracy. The obtained lower-rank DNNs can be further sparsified, proving that Force Regularization can be integrated with state-of-the-art sparsity-based acceleration methods.