DAGGER: Gradient-Free Construction of Transiently Amplifying Networks under Hard Connectivity Constraints

Many networks not only support but also rely on transient non-normal amplification, an orders-of-magnitude increase in the activity of an otherwise stable system. Constructing such networks under hard sign/sparsity/diagonal constraints -- the regime relevant for biological connectomes and structured RNN initializations -- has so far required either gradient-based local search with thousands of inner-loop eigendecompositions or Schur-form direct construction in an abstract basis that breaks the constraints under projection. Here we introduce DAGGER (Directed Acyclic Graph Guided Edge Reweighting), a gradient-free single-pass algorithm. Given a stable signed sparse matrix, DAGGER produces an output with the same sign, sparsity, and diagonal. A single scalar $β$ controls a Wasserstein-2 budget that smoothly trades exact multiset preservation ($β= 0$) for amplification; peak amplification grows essentially without bound with $β$, empirically reaching $10^{10}$ before numerical overflow. DAGGER matches or exceeds gradient-based methods at multiset preservation in a single forward pass -- 30-100$\times$ fewer eigendecompositions than a typical gradient inner loop -- and at moderate $β$ beats them by orders of magnitude with connectivity exactly preserved. We develop the algorithm, compare it to the existing methods and on a downstream signal-detection task, and examine the diagnostics that show why DAGGER is structurally different from other amplifying networks.