Prompt tuning adapts CLIP-based vision-language models with few trainable parameters, yet its predictions remain sensitive to the spatial sampling imposed by a frozen vision transformer. In particular, non-overlapping patch tokenization makes predictions depend on the alignment (phase) between image and the patch lattice. To reduce prediction sensitivity to patch-grid alignment, we introduce Patch-Phase Orbit Marginalization (PPOM), a training-free inference operator that treats phase shift as a nuisance variable. Given a patch stride, PPOM evaluates the identity view and reflection-padded translations, pairs opposite shifts into horizontal, vertical, and diagonal antithetic families, and assigns equal mass to these families and the identity prediction to avoid view-count bias during phase integration. In summary, PPOM provides a deterministic interface between prompt adaptation and patch-grid sensitivity. Across multiple prompt-learning hosts, PPOM improves host performance without re-training.
Vision Transformers operate on fixed patch grids, which can introduce phase-dependent instability for dense prediction: changing the patch partition can change the token evidence available to a pixel, especially near boundaries. We formalize patch-grid phase as a nuisance variable and propose Phase Marginalization, a post-hoc marginalization method that evaluates structured patch-grid phases, inverse-aligns dense outputs, and aggregates them in the original image coordinate system. The central variant, Uniform Phase Marginalization with K = 4, is training-free and improves over the canonical K = 1 baseline across measured segmentation, depth, and local matching settings. In a controlled Cityscapes experiment, Uniform Phase Marginalization provides a modest compute-matched advantage over generic shift-based four-forward test-time augmentation (TTA) (+0.31 mean Intersection-over-Union over the strongest tested generic row). A scaling study further shows that K = 4 is a practical cost-accuracy trade-off: K = 8 is essentially unchanged and K = 16 adds little accuracy at much higher latency. These results position patch-grid phase as a measurable nuisance variable and Phase Marginalization as a simple diagnostic and post-hoc marginalization baseline for dense ViT prediction.