REOrdering Patches Improves Vision Models
Declan Kutscher, David Chan, Yutong Bai, Trevor Darrell, Ritwik Gupta
Transformers require inputs to be represented as one-dimensional sequences, and in vision, this typically involves flattening images using a fixed row-major (raster-scan) order. While full self-attention is permutation-equivariant, modern long-sequence transformers increasingly rely on architectural approximations that break this invariance and introduce sensitivity to patch ordering. We show that patch order significantly affects model performance in such settings, with simple alternatives like column-major or Hilbert curves yielding notable accuracy shifts. Motivated by this, we propose _REOrder_, a two-stage framework for discovering task-optimal patch orderings. First, we derive an information-theoretic prior by evaluating the compressibility of various patch sequences. Then, we learn a policy over permutations by optimizing a Plackett-Luce policy using REINFORCE. This approach enables efficient learning in a combinatorial permutation space. _REOrder_ improves top-1 accuracy over row-major ordering on ImageNet-1K by up to $3.01\%$ and Functional Map of the World by $13.35\%$. Code is available at [this link](https://anonymous.4open.science/r/patch-order-8C3D/).