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Weighted Reverse Convolution for Feature Upsampling

Pre-trained vision foundation models (VFMs) provide strong semantic representations, yet their patch-level features are inherently coarse, limiting their effectiveness on tasks requiring fine-grained localization, dense prediction, and point-wise correspondence. In this work, we revisit feature upsampling for VFMs from the perspective of \textbf{\textit{inverse problem}} and propose Weighted Reverse Convolution (WRC), a spatially adaptive inverse operator for densifying high-level visual descriptors. Specifically, we formulate feature upsampling as a weighted Tikhonov-regularized least-squares problem, where spatially varying weights modulate both data fidelity and prior strength at each spatial location. This allows WRC to adapt the reconstruction to spatially varying feature characteristics, thereby preserving critical structures while mitigating over-smoothing. Moreover, WRC retains an efficient, fully differentiable closed-form FFT solution, making it a practical drop-in upsampling operator. Integrated into a lightweight self-supervised densification framework, WRC consistently improves dense feature quality across various downstream benchmarks, including segmentation, depth estimation, video object segmentation, object discovery, and keypoint correspondence, while maintaining high computational efficiency.