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

• URL: http://arxiv.org/abs/2606.01227v1
• Date: Sun, 31 May 2026 13:20:26 GMT
• Title: DAGGER: Gradient-Free Construction of Transiently Amplifying Networks under Hard Connectivity Constraints
• Abstract summary: DAGGER is a gradient-free single-pass algorithm for transient non-normal amplification.<n>It matches or exceeds gradient-based methods at multiset preservation in a single forward pass.<n>We show why DAGGER is structurally different from other amplifying networks.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $β$ 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.

Related papers

• Dead-Direction Signatures: A Cheap Spectral Reading of Singular Complexity [5.67642958049511]
  Singular learning theory characterises the complexity of a deep network through the geometry of its loss singularities.<n>We introduce DeadDirection Signatures (DDS), a family of cheap closed-form spectral readings of singular structure.<n>Each reads a network's activation matrix or per-sample-gradient FisherGram at a chosen layer, replacing the posterior chain spectral linear algebra.
  arXiv  Detail & Related papers  (2026-06-19T06:49:09Z)
• Closed-Form Spectral Regularization for Multi-Task Model Merging [96.82449201305234]
  Model merging combines several independently fine-tuned experts into a single multi-task model without any training data.<n>State-of-the-art merging methods formulate merging as a layer-wise interference problem.<n>We propose SWUDI, a closed-form method that combines a soft exponential filter, which matches the gradient-flow trajectory of iterative descent.
  arXiv  Detail & Related papers  (2026-06-05T14:00:47Z)
• Neural Autoregressive Control Variates for the Quantum Monte Carlo Sign Problem [2.3717692810269586]
  We train a pair of autoregressive models to mitigate the sign problem in quantum Monte Carlo simulations.<n>The two autoregressive networks are confined to the positive- and negative-sign sectors with strictly disjoint support.<n>Their difference is structurally zero-mean, providing an auxiliary observable whose correlation with the sign estimator controls the variance reduction.
  arXiv  Detail & Related papers  (2026-05-26T10:30:44Z)
• Metric--Phase Fields: Decoupling Distance and Sign for Thin-Structure Reconstruction from Unoriented Point Clouds [67.30236447078187]
  We introduce Metric-Phase Fields (MPFs), a decoupled implicit representation that separates metric proximity from topological phase.<n>Experiments on both synthetic and scanned thin-shell and thin-plate shapes demonstrate that MPFs preserve thin and layered structures more faithfully than recent SDF-based methods.
  arXiv  Detail & Related papers  (2026-05-25T07:08:57Z)
• Dimensional Criticality at Grokking Across MLPs and Transformers [2.652953665748039]
  Abrupt transitions between distinct dynamical regimes are a hallmark of complex systems.<n>We introduce textbfTDU--OFC (Thresholded Diffusion Update--Olami-Feder-Christensen), an offline avalanche probe.<n>Across Transformers trained on modular addition and generalizations trained on XOR, we discover a localized crossing of the diffusion baseline $D=1$.
  arXiv  Detail & Related papers  (2026-04-06T13:43:20Z)
• Variational Bayesian Flow Network for Graph Generation [54.94088904387278]
  We propose Variational Bayesian Flow Network (VBFN) for graph generation.<n>VBFN performs variational lifting to a tractable joint Gaussian variational belief family governed by structured precisions.<n>On synthetic and molecular graph datasets, VBFN improves fidelity and diversity, and surpasses baseline methods.
  arXiv  Detail & Related papers  (2026-01-30T03:59:38Z)
• Universal Hirschberg for Width Bounded Dynamic Programs [0.0]
  Hirschberg's algorithm reduces the space complexity for the longest common subsequence problem from $O(N2)$ to $O(N)$ via a midpoint bisection on a grid dynamic program (DP)<n>We show that the underlying idea generalizes to a broad class of dynamic programs with local dependencies on directed acyclic graphs (DP DAGs)<n>We show that an $()$ space term is unavoidable in forward single-pass models and discuss conjectured $sqrtT$-type barriers in streaming settings.
  arXiv  Detail & Related papers  (2025-12-10T22:26:22Z)
• Continual Release of Densest Subgraphs: Privacy Amplification & Sublinear Space via Subsampling [2.0607844057825324]
  We study the sublinear space continual release model for edge-differentially private (DP) graph algorithms.<n>Our main result is the first continual release DSG algorithm that matches the additive error of the best static DP algorithms.<n>We introduce graph densification in the graph DP setting, adding edges to trigger earlier subsampling, which removes the extra logarithmic factors in error and space incurred by prior work.
  arXiv  Detail & Related papers  (2025-10-13T17:20:13Z)
• FedSVD: Adaptive Orthogonalization for Private Federated Learning with LoRA [68.44043212834204]
  Low-Rank Adaptation (LoRA) is widely used for efficient fine-tuning of language models in learning (FL)<n>Low-Rank Adaptation (LoRA) is widely used for efficient fine-tuning of language models in learning (FL)
  arXiv  Detail & Related papers  (2025-05-19T07:32:56Z)
• Sharper Guarantees for Learning Neural Network Classifiers with Gradient Methods [43.32546195968771]
  We study the data-dependent convergence and generalization behavior of gradient methods for neural networks with smooth activation.<n>Our results improve upon the shortcomings of the well-established Rademacher complexity-based bounds.<n>We show that a large step-size significantly improves upon the NTK regime's results in classifying the XOR distribution.
  arXiv  Detail & Related papers  (2024-10-13T21:49:29Z)
• Rethinking PGD Attack: Is Sign Function Necessary? [131.6894310945647]
  We present a theoretical analysis of how such sign-based update algorithm influences step-wise attack performance. We propose a new raw gradient descent (RGD) algorithm that eliminates the use of sign. The effectiveness of the proposed RGD algorithm has been demonstrated extensively in experiments.
  arXiv  Detail & Related papers  (2023-12-03T02:26:58Z)
• On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems [75.58134963501094]
  This paper analyzes the trajectories of gradient descent (SGD) We show that SGD avoids saddle points/manifolds with $1$ for strict step-size policies.
  arXiv  Detail & Related papers  (2020-06-19T14:11:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.