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Deep neural networks (DNNs) have delivered a remarkable performance in many tasks of computer vision. However, over-parameterized representations of popular architectures dramatically increase their computational complexity and storage costs, and hinder their availability in edge devices with constrained resources. Regardless of many tensor decomposition (TD) methods that have been well-studied for compressing DNNs to learn compact representations, they suffer from non-negligible performance degradation in practice. In this paper, we propose Scalable Tensorizing Networks (STN), which dynamically and adaptively adjust the model size and decomposition structure without retraining. First, we account for compression during training by adding a low-rank regularizer to guarantee networks' desired low-rank characteristics in full tensor format. Then, considering network layers exhibit various low-rank structures, STN is obtained by a data-driven adaptive TD approach, for which the topological structure of decomposition per layer is learned from the pre-trained model, and the ranks are selected appropriately under specified storage constraints. As a result, STN is compatible with arbitrary network architectures and achieves higher compression performance and flexibility over other tensorizing versions. Comprehensive experiments on several popular architectures and benchmarks substantiate the superiority of our model towards improving parameter efficiency.