Abstract
A method is presented for reducing the cost of representative token selection in transformer attention layers by exploiting the coherence of the representative set across depth. Activation Decorrelation Attention (ADA) selects r \ll T representative tokens at each layer via a Gram threshold and computes attention on the compressed r \times r problem, but the selection requires a T \times T Gram matrix at every layer. The cascade mechanism introduced here inherits the representative set from layer l to layer l+1, validates it via a (T - r) \times r cross-Gram computation, and updates it with a small number of additions and removals. The cost of the selection step drops from O(T^2 d) to O(T r d) per layer. Validation on three model families (GPT-2 124M, GPT-J 6B, OPT 6.7B) on AMD MI300X demonstrates Gram operation savings of 22\% to 63\% with mean Jaccard overlap of 0.83 to 0.94 between consecutive layers. The cascade reveals that the set of informative tokens is a structural property of the input that propagates coherently through the depth of the network: the same tokens carry the non-redundant information at layer l and at layer l+1.
