Proposes a training-free transformer compression framework that sequentially optimizes cross-layer weight pairings and shared-dictionary factorizations instead of compressing layers in isolation or via heuristic grouping. The method identifies structurally compatible projections across layers and learns a shared representation that preserves each layer’s activation geometry, combined with structured sparsity for efficient weight decomposition. It achieves state-of-the-art compression results across diverse architectures, scales, and modalities without sacrificing functional fidelity.