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

Abstract: Transient non-normal amplification—a phenomenon where the activity of an otherwise stable system increases by several orders of magnitude—is not only supported but often essential for many networks. However, generating such networks while adhering to strict sign, sparsity, and diagonal constraints (a scenario pertinent to biological connectomes and specific recurrent neural network initializations) has historically been challenging. Previous approaches necessitated either gradient-based local searches involving thousands of inner-loop eigendecompositions or Schur-form direct construction methods in abstract bases that fail to preserve constraints upon projection.

To address this, we present DAGGER (Directed Acyclic Graph Guided Edge Reweighting), a novel gradient-free algorithm that operates in a single pass. Starting with a stable, signed, and sparse matrix, DAGGER generates an output matrix that strictly maintains the original sign, sparsity, and diagonal properties. The algorithm utilizes a single scalar parameter, $\beta$, to manage a Wasserstein-2 budget. This parameter allows for a smooth trade-off between preserving the exact eigenvalue multiset (when $\beta = 0$) and maximizing amplification. Empirical results indicate that peak amplification can grow nearly without limit as $\beta$ increases, reaching values as high as $10^{10}$ prior to numerical overflow.

In terms of efficiency and performance, DAGGER matches or outperforms gradient-based techniques in multiset preservation during a single forward pass, requiring 30 to 100 times fewer eigendecompositions than typical gradient inner loops. Furthermore, at moderate $\beta$ values, it surpasses these methods by orders of magnitude while ensuring exact connectivity preservation. This study details the development of the algorithm, compares it against existing methodologies, evaluates its performance on a downstream signal-detection task, and analyzes diagnostic metrics that reveal the structural distinctions between DAGGER-generated networks and other amplifying architectures.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC