Abstract: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 $\beta$ controls a Wasserstein-2 budget that smoothly trades exact multiset preservation ($\beta = 0$) for amplification; peak amplification grows essentially without bound with $\beta$, 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 $\beta$ 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.
From: James Ferguson [view email]
[v1]
Sun, 31 May 2026 13:20:26 UTC (254 KB)
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