Real world images often have highly imbalanced content density. Some areas are very uniform, e.g., large patches of blue sky, while other areas are scattered with many small objects. Yet, the commonly used successive grid downsampling strategy in convolutional deep networks treats all areas equally. Hence, small objects are represented in very few spatial locations, leading to worse results in tasks such as segmentation. Intuitively, retaining more pixels representing small objects during downsampling helps to preserve important information. To achieve this, we propose AutoFocusFormer (AFF), a local-attention transformer image recognition backbone, which performs adaptive downsampling by learning to retain the most important pixels for the task. Since adaptive downsampling generates a set of pixels irregularly distributed on the image plane, we abandon the classic grid structure. Instead, we develop a novel point-based local attention block, facilitated by a balanced clustering module and a learnable neighborhood merging module, which yields representations for our point-based versions of state-of-the-art segmentation heads. Experiments show that our AutoFocusFormer (AFF) improves significantly over baseline models of similar sizes.