Related papers: Constructive Lyapunov Functions via Topology-Prese…

The advancement of autonomous robotic systems has led to impressive capabilities in perception, localization, mapping, and control. Yet, a fundamental gap remains: existing frameworks excel at geometric reasoning and dynamic stability but…

In this paper, a mechanistic data-driven approach is proposed to accelerate structural topology optimization, employing an in-house developed finite element convolutional neural network (FE-CNN). Our approach can be divided into two stages:…

This study provides a foundational theoretical investigation into the mathematical existence and asymptotic properties of Ulanowicz's structural resilience. While ecological evidence suggests that sustainable systems gravitate toward an…

Machine learning assisted optimal power flow (OPF) aims to reduce the computational complexity of these non-linear and non-convex constrained optimization problems by consigning expensive (online) optimization to offline training. The…

This paper proposes a new topology optimization method that applies a convolutional neural network (CNN), which is one deep learning technique for topology optimization problems. Using this method, we acquire a structure with a little…

Optical neural network (ONN) is emerging as an attractive proposal for machine-learning applications, enabling high-speed computation with low-energy consumption. However, there are several challenges in applying ONN for industrial…

We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…

Recently, there are increasing efforts on advancing optical neural networks (ONNs), which bring significant advantages for machine learning (ML) in terms of power efficiency, parallelism, and computational speed. With the considerable…

In this paper, we approach the problem of cost (loss) minimization in underparametrized shallow ReLU networks through the explicit construction of upper bounds which appeal to the structure of classification data, without use of gradient…

We study reinforcement learning for partially observed Markov decision processes (POMDPs) with infinite observation and state spaces, which remains less investigated theoretically. To this end, we make the first attempt at bridging partial…

Motivated by the fact that the gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs), here we derive an ODE representation of the accelerated triple momentum (TM)…

The rapid growth in computing demands, particularly driven by artificial intelligence applications, has begun to exceed the capabilities of traditional electronic hardware. Optical computing offers a promising alternative due to its…

We present the Condensate Theorem: attention sparsity is a learned topological property, not an architectural constraint. Through empirical analysis of trained language models, we find that attention mass concentrates on a distinct…

We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…

This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…

We propose neural network operator inference (NN-OpInf): a structure-preserving, composable, and minimally restrictive operator inference framework for the non-intrusive reduced-order modeling of dynamical systems. The approach learns…

Discriminative learning based on convolutional neural networks (CNNs) aims to perform image restoration by learning from training examples of noisy-clean image pairs. It has become the go-to methodology for tackling image restoration and…

Convolutional Neural Networks (CNNs) dominate various computer vision tasks since Alex Krizhevsky showed that they can be trained effectively and reduced the top-5 error from 26.2 % to 15.3 % on the ImageNet large scale visual recognition…

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…