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Deep convolutional neural networks (CNNs) have achieved unprecedented success in single image super-resolution over the past few years. Meanwhile, there is an increasing demand for single image super-resolution with arbitrary scale factors in real-world scenarios. Many approaches adopt scale-specific multi-path learning to cope with multi-scale super-resolution with a single network. However, these methods require a large number of parameters. To achieve a better balance between the reconstruction quality and parameter amounts, we proposes a learnable interpolation method that leverages the advantages of neural networks and interpolation methods to tackle the scale-arbitrary super-resolution task. The scale factor is treated as a function parameter for generating the kernel weights for the learnable interpolation. We demonstrate that the learnable interpolation builds a bridge between neural networks and traditional interpolation methods. Experiments show that the proposed learnable interpolation requires much fewer parameters and outperforms state-of-the-art super-resolution methods.