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Compared with traditional task-irrelevant downsampling methods, task-oriented neural networks have shown improved performance in point cloud downsampling range. Recently, Transformer family of networks has shown a more powerful learning capacity in visual tasks. However, Transformer-based architectures potentially consume too many resources which are usually worthless for low overhead task networks in downsampling range. This paper proposes a novel light-weight Transformer network (LighTN) for task-oriented point cloud downsampling, as an end-to-end and plug-and-play solution. In LighTN, a single-head self-correlation module is presented to extract refined global contextual features, where three projection matrices are simultaneously eliminated to save resource overhead, and the output of symmetric matrix satisfies the permutation invariant. Then, we design a novel downsampling loss function to guide LighTN focuses on critical point cloud regions with more uniform distribution and prominent points coverage. Furthermore, We introduce a feed-forward network scaling mechanism to enhance the learnable capacity of LighTN according to the expand-reduce strategy. The result of extensive experiments on classification and registration tasks demonstrates LighTN can achieve state-of-the-art performance with limited resource overhead.