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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | https://arxiv.org/abs/2606.01227 |
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| _version_ | 1866911738286309376 |
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| author | Ferguson, James C. |
| author_facet | Ferguson, James C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01227 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | DAGGER: Gradient-Free Construction of Transiently Amplifying Networks under Hard Connectivity Constraints Ferguson, James C. Machine Learning Neurons and Cognition 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. |
| title | DAGGER: Gradient-Free Construction of Transiently Amplifying Networks under Hard Connectivity Constraints |
| topic | Machine Learning Neurons and Cognition |
| url | https://arxiv.org/abs/2606.01227 |