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Photo exposure correction is widely investigated, but fewer studies focus on correcting under and over-exposed images simultaneously. Three issues remain open to handle and correct under and over-exposed images in a unified way. First, a locally-adaptive exposure adjustment may be more flexible instead of learning a global mapping. Second, it is an ill-posed problem to determine the suitable exposure values locally. Third, photos with the same content but different exposures may not reach consistent adjustment results. To this end, we proposed a novel exposure correction network, ExReg, to address the challenges by formulating exposure correction as a multi-dimensional regression process. Given an input image, a compact multi-exposure generation network is introduced to generate images with different exposure conditions for multi-dimensional regression and exposure correction in the next stage. An auxiliary module is designed to predict the region-wise exposure values, guiding the mainly proposed Encoder-Decoder ANP (Attentive Neural Processes) to regress the final corrected image. The experimental results show that ExReg can generate well-exposed results and outperform the SOTA method by 1.3dB in PSNR for extensive exposure problems. In addition, given the same image but under various exposure for testing, the corrected results are more visually consistent and physically accurate.