Related papers: Probabilistic Error Analysis of Limited-Precision …
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…
We study the potential of symbolic regression (SR) to derive compact and precise analytic expressions that can improve the accuracy and simplicity of phenomenological analyses at the Large Hadron Collider (LHC). As a benchmark, we apply SR…
Although mixed precision arithmetic has recently garnered interest for training dense neural networks, many other applications could benefit from the speed-ups and lower storage cost if applied appropriately. The growing interest in…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…
While the rapid progress of deep learning fuels end-to-end reinforcement learning (RL), direct application, especially in high-dimensional space like robotic scenarios still suffers from low sample efficiency. Therefore State Representation…
We propose a super-resolution (SR) simulation system that consists of a physics-based meteorological simulation and an SR method based on a deep convolutional neural network (CNN). The CNN is trained using pairs of high-resolution (HR) and…
Multistage Stochastic Programming (MSP) is a class of models for sequential decision-making under uncertainty. MSP problems are known for their computational intractability due to the sequential nature of the decision-making structure and…
Stochastic Approximation (SA) is a classical algorithm that has had since the early days a huge impact on signal processing, and nowadays on machine learning, due to the necessity to deal with a large amount of data observed with…
Symbolic regression (SR) searches for parametric models that accurately fit a dataset, prioritizing simplicity and interpretability. Despite this secondary objective, studies point out that the models are often overly complex due to…
Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…
Simplifying expressions is important to make numerical integration of large expressions from High Energy Physics tractable. To this end, Horner's method can be used. Finding suitable Horner schemes is assumed to be hard, due to the lack of…
Large language models (LLMs) have achieved impressive results on multi-step mathematical reasoning, yet at the cost of high computational overhead. This challenge is particularly acute for test-time scaling methods such as parallel…
Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of…
We heuristically show that Shor's algorithm for computing general discrete logarithms achieves an expected success probability of approximately 60% to 82% in a single run when modified to enable efficient implementation with the…
Progressive Hedging is a popular decomposition algorithm for solving multi-stage stochastic optimization problems. A computational bottleneck of this algorithm is that all scenario subproblems have to be solved at each iteration. In this…
Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap:…
Estimating the probability of rare failure events is an essential step in the reliability assessment of engineering systems. Computing this failure probability for complex non-linear systems is challenging, and has recently spurred the…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Training of large-scale deep neural networks is often constrained by the available computational resources. We study the effect of limited precision data representation and computation on neural network training. Within the context of…