Turn the Bottleneck Knob: Token-Valve Path Explanations for Vision Transformers

Turn the Bottleneck Knob (TBK) is a post-hoc explanation method for frozen Vision Transformers. It combines shared token gates on selected pre-attention branches, finite-step target cross-entropy optimization, and integration of absolute gate sensitivities along a linear opening path. The resulting scores measure unsigned sensitivity per unit gate coordinate; they do not identify minimal or necessary tokens. We give a shared-parameter derivative and a loss-change upper bound, distinguish these properties from causal faithfulness, and clarify why a finite-noise information-bottleneck motivation does not establish deterministic information compression. Existing ImageNet-1K results on ViT-B/16 and DeiT-B/16 show a competitive but mixed proxy-metric profile. A separate ViT-Base follow-up supports an Insertion gain over CoIBA with a paired confidence interval excluding zero; its ROAD, Deletion, and Infidelity intervals include zero. Smoothing materially affects the Insertion comparison. The evidence supports this particular attribution pipeline in the evaluated setting, with unresolved implementation and protocol details stated explicitly.