4
Attribute the prediction to region, time, and modality
For every layer \(\ell\), head \(h\), and token, PRISMt multiplies the residual-aware rollout coefficient \(\rho\) (how much the token is routed to CLS) by the token’s signed value message projected onto the direction of the target logit \(\zeta_n\).
Layer–head pairs are then weighted by how strongly their attribution differs between classes, removing the transformer-specific axes while keeping sample, region, time, and modality.
Token attribution\[ G_n^{(\ell,h)}(r,t,m) = \rho^{(\ell,h)}_{n,i}\; u_n^{\top} W_O^{(\ell,h)} v^{(\ell,h)}_{n,i}, \qquad u_n = \frac{\nabla_{h_{n,\mathrm{CLS}}}\zeta_n}{\lVert \nabla_{h_{n,\mathrm{CLS}}}\zeta_n \rVert_2} \]
Layer–head reduction\[ w_{\ell h} = \frac{D_{\ell h}}{\sum_{\ell',h'} D_{\ell' h'}}, \qquad \tilde G_n(r,t,m) = \sum_{\ell,h} w_{\ell h}\, G_n^{(\ell,h)}(r,t,m) \]