arXiv Machine Learning
Exact Convex Reformulations of Linear Neural Networks via Completely Positive Lifting
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arXiv Machine Learning
Oct 3
HUANet: Hard-Constrained Unrolled ADMM for Constrained Convex Optimization
HUANet is a deep neural network architecture that unrolls the Alternating Direction Method of Multipliers (ADMM) into a trainable model for accelerating parametric constrained convex optimization. It embeds a hard‑constrained neural network in each ADMM iteration, using a differentiable correction stage to enforce affine equalities of the primal subproblem. The method also incorporates first‑order optimality conditions into a self‑supervised training loss, and numerical experiments on benchmark problems and a control application demonstrate its effectiveness in speeding up constrained convex optimization.
arXiv Machine Learning
6d ago
Universal neural network approximation of symmetric polyconvex energies and envelopes
arXiv:2610.32598v1 Announce Type: cross Abstract: Symmetric polyconvexity provides a sufficient condition for weak lower semicontinuity in small-strain elasticity and a tractable lower bound for the...
arXiv Machine Learning
Aug 11
Input convex neural networks as surrogates in mathematical optimisation
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
arXiv Machine Learning
Sep 23
CAffNet: Hard Constraint-Affine Neural Networks
arXiv:2605.24437v2 Announce Type: replace Abstract: We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural net...
arXiv Machine Learning
Sep 21
Layerwise Decoupling for Stable Structured Sparsification of Fully Connected Layers
The paper introduces a layerwise, decoupled approach to structurally sparsify fully connected layers in pretrained neural networks. By extracting shallow two‑layer subnetworks, normalizing inner weights, and applying a structured group penalty to each block’s outer weight matrix, the method prunes neurons sequentially and reduces layer widths. The authors prove equivalence to a joint penalty for positively homogeneous activations, and demonstrate that this decoupled formulation is more robust, offering a broader regularization range and lower catastrophic over‑pruning while preserving accuracy in classification, sparse‑recovery, PINN, and OPT‑1.3B experiments.
arXiv Machine Learning
Aug 11
Generalized Convexity and Smoothness via Conjugate Duality: Optimization Theory for Deep Neural Networks
arXiv:2608. 09523v1 Announce Type: new Abstract: Deep neural network (DNN) training with stochastic gradient descent (SGD) and its variants achieves strong empirical performance, yet classical optimization theory does not fully explain this success.