In this paper, we propose a novel image retrieval network named Correlation Verification Network (CVNet) to replace the conventional geometric re-ranking with a 4D convolutional neural network that learns diverse geometric matching possibilities. To enable efficient cross-scale matching, we construct feature pyramids and establish cross-scale feature correlations in a single inference, thereby replacing the costly multi-scale inference. Additionally, we employ curriculum learning with the Hide-and-Seek strategy to handle challenging samples. Our proposed CVNet demonstrates state-of-the-art performance on several image retrieval benchmarks by a large margin. From an implementation perspective, however, CVNet has one drawback: it requires high memory usage because it needs to store dense features of all database images. This high memory requirement can be a significant limitation in practical applications. To address this issue, we introduce an extension of CVNet called Dense-to-Sparse CVNet (CVNet), which can significantly reduce memory usage by sparsifying the features of the database images. The sparsification module in CVNet learns to select the relevant parts of image features end-to-end using a Gumbel estimator. Since the sparsification is performed offline, CVNet does not increase online extraction and matching times. CVNet dramatically reduces the memory footprint while preserving performance levels nearly identical to CVNet.