Related papers: Fast semidefinite programming with feedforward neu…

In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel…

Quantifying the robustness of neural networks or verifying their safety properties against input uncertainties or adversarial attacks have become an important research area in learning-enabled systems. Most results concentrate around the…

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…

In training neural networks, it is common practice to use partial gradients computed over batches, mostly very small subsets of the training set. This approach is motivated by the argument that such a partial gradient is close to the true…

In this paper, we investigate a special class of quadratic-constrained quadratic programming (QCQP) with semi-definite constraints. Traditionally, since such a problem is non-convex and N-hard, the neural network (NN) is regarded as a…

Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…

The performance of a neural network for a given task is largely determined by the initial calibration of the network parameters. Yet, it has been shown that the calibration, also referred to as training, is generally NP-complete. This…

This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…

We introduce the SaaS Algorithm for semi-supervised learning, which uses learning speed during stochastic gradient descent in a deep neural network to measure the quality of an iterative estimate of the posterior probability of unknown…

Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…

The calibration and training of a neural network is a complex and time-consuming procedure that requires significant computational resources to achieve satisfactory results. Key obstacles are a large number of hyperparameters to select and…

A semi-supervised learning framework using the feedforward-designed convolutional neural networks (FF-CNNs) is proposed for image classification in this work. One unique property of FF-CNNs is that no backpropagation is used in model…

In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…

Artificial neural networks are algorithms which have been developed to tackle a range of computational problems. These range from modelling brain function to making predictions of time-dependent phenomena to solving hard (NP-complete)…

A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously…

We propose several deep-learning accelerated optimization solvers with convergence guarantees. We use ideas from the analysis of accelerated forward-backward schemes like FISTA, but instead of the classical approach of proving convergence…

The optimization problem behind neural networks is highly non-convex. Training with stochastic gradient descent and variants requires careful parameter tuning and provides no guarantee to achieve the global optimum. In contrast we show…

We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

We develop a machine-learning framework to learn hyperparameter sequences for accelerated first-order methods (e.g., the step size and momentum sequences in accelerated gradient descent) to quickly solve parametric convex optimization…