Related papers: ReLU-QP: A GPU-Accelerated Quadratic Programming S…
This paper presents the implementation of a HLLC finite volume solver using GPU technology for the solution of shallow water problems in two dimensions. It compares both CPU and GPU approaches for implementing all the solver's steps. The…
Planning long-horizon robot manipulation requires making discrete decisions about which objects to interact with and continuous decisions about how to interact with them. A robot planner must select grasps, placements, and motions that are…
To effectively control large-scale distributed systems online, model predictive control (MPC) has to swiftly solve the underlying high-dimensional optimization. There are multiple techniques applied to accelerate the solving process in the…
Robust trajectory optimization enables autonomous systems to operate safely under uncertainty by computing control policies that satisfy the constraints for all bounded disturbances. However, these problems often lead to large Second Order…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…
We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum,…
We introduce a novel approach for analyzing the training dynamics of ReLU networks by examining the characteristic activation boundaries of individual ReLU neurons. Our proposed analysis reveals a critical instability in common neural…
We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm…
Quantitative MRI (qMRI) offers tissue-specific biomarkers that can be tracked over time or compared across populations; however, its adoption in clinical research is hindered by significant computational demands of parameter estimation.…
The attention layer, a core component of Transformer-based LLMs, brings out inefficiencies in current GPU systems due to its low operational intensity and the substantial memory requirements of KV caches. We propose a High-bandwidth…
Emerging quantum computing technologies, such as Noisy Intermediate-Scale Quantum (NISQ) devices, offer potential advancements in solving mathematical optimization problems. However, limitations in qubit availability, noise, and errors pose…
We describe an algorithm that learns two-layer residual units using rectified linear unit (ReLU) activation: suppose the input $\mathbf{x}$ is from a distribution with support space $\mathbb{R}^d$ and the ground-truth generative model is a…
Convex quadratic programs (QPs) are fundamental to numerous applications, including finance, engineering, and energy systems. Among the various methods for solving them, the Douglas-Rachford (DR) splitting algorithm is notable for its…
Deep neural networks have emerged as a widely used and effective means for tackling complex, real-world problems. However, a major obstacle in applying them to safety-critical systems is the great difficulty in providing formal guarantees…
We present a versatile GPU-based parallel version of Logistic Regression (LR), aiming to address the increasing demand for faster algorithms in binary classification due to large data sets. Our implementation is a direct translation of the…
Quadratic Assignment Problem (QAP) is a practical combinatorial optimization problems that has been studied for several years. Since it is NP-hard, solving large problem instances of QAP is challenging. Although heuristics can find…
The quadratic assignment problem (QAP) is one of the most difficult combinatorial optimization problems. An effective heuristic for obtaining approximate solutions to the QAP is simulated annealing (SA). Here we describe an SA…
ReLU neural networks trained as surrogate models can be embedded exactly in mixed-integer linear programs (MILPs), enabling global optimization over the learned function. The tractability of the resulting MILP depends on structural…
Methods based on weight compensation, which iteratively apply quantization and weight compensation to minimize the output error, have recently demonstrated remarkable success in quantizing Large Language Models (LLMs). The representative…
In recent years, Quantum Machine Learning (QML) has increasingly captured the interest of researchers. Among the components in this domain, activation functions hold a fundamental and indispensable role. Our research focuses on the…