Related papers: A Closed-form Solution for Weight Optimization in …

The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted…

This paper provides a least squares formulation for the training of a 2-layer convolutional neural network using quadratic activation functions, a 2-norm loss function, and no regularization term. Using this method, an analytic expression…

When training deep learning models, the performance depends largely on the selected hyperparameters. However, hyperparameter optimization (HPO) is often one of the most expensive parts of model design. Classical HPO methods treat this as a…

Linear transformation of the inputs alters the training performance of feed-forward networks that are otherwise equivalent. However, most linear transforms are viewed as a pre-processing operation separate from the actual training. Starting…

An Undirected Weighted Network (UWN) is commonly found in big data-related applications. Note that such a network's information connected with its nodes, and edges can be expressed as a Symmetric, High-Dimensional and Incomplete (SHDI)…

This paper considers coordinated linear precoding for rate optimization in downlink multicell, multiuser orthogonal frequency- division multiple access networks. We focus on two different design criteria. In the first, the weighted sum-rate…

Recent work has shown that purely quadratic functions can replace MLPs in transformers with no significant loss in performance, while enabling new methods of interpretability based on linear algebra. In this work, we theoretically derive…

In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…

In this paper, we propose a novel approach for implicit data representation to evaluate similarity of input data using a trained neural network. In contrast to the previous approach, which uses gradients for representation, we utilize only…

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…

The Best-Worst Method (BWM) has emerged as a prominent multi-criteria decision-making method for determining the weights of the decision criteria. Among various BWM models, this research focuses on the linear model of the BWM. This model…

We describe a novel family of models of multi- layer feedforward neural networks in which the activation functions are encoded via penalties in the training problem. Our approach is based on representing a non-decreasing activation function…

Least-squares (LS) forms of the transport equation can circumvent the void problems of other second order forms, but are almost always non-conservative. Additionally, the standard LS form is not compatible with discrete ordinates method…

We analyze the performance of a linear-equality-constrained least-squares (CLS) algorithm and its relaxed version, called rCLS, that is obtained via the method of weighting. The rCLS algorithm solves an unconstrained least-squares problem…

Training neural networks with reinforcement learning (RL) typically relies on backpropagation (BP), necessitating storage of activations from the forward pass for subsequent backward updates. Furthermore, backpropagating error signals…

In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…

We introduce a new class of inverse optimization problems in which an input solution is given together with $k$ linear weight functions, and the goal is to modify the weights by the same deviation vector $p$ so that the input solution…

We propose a new optimization method for training feed-forward neural networks. By rewriting the activation function as an equivalent proximal operator, we approximate a feed-forward neural network by adding the proximal operators to the…

Autonomous navigation often requires the simultaneous optimization of multiple objectives. The most common approach scalarizes these into a single cost function using a weighted sum, but this method is unable to find all possible trade-offs…