Related papers: Mapping Uncharted Symmetries: Machine Discovery in…

An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…

We propose a method to facilitate exploration and analysis of new large data sets. In particular, we give an unsupervised deep learning approach to learning a latent representation that captures semantic similarity in the data set. The core…

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data…

In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regulariza- tion…

Machine learning has recently emerged as a promising approach for studying complex phenomena characterized by rich datasets. In particular, data-centric approaches lend to the possibility of automatically discovering structures in…

Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some…

The ``black-box'' nature of deep learning models presents a significant barrier to their adoption for scientific discovery, where interpretability is paramount. This challenge is especially pronounced in discovering the governing equations…

Robot navigation is a task where reinforcement learning approaches are still unable to compete with traditional path planning. State-of-the-art methods differ in small ways, and do not all provide reproducible, openly available…

Unsupervised Skill Discovery (USD) allows agents to autonomously learn diverse behaviors without task-specific rewards. While recent USD methods have shown promise, their application to real-world robotics remains underexplored. In this…

In this paper, we study the MapReduce framework from an algorithmic standpoint and demonstrate the usefulness of our approach by designing and analyzing efficient MapReduce algorithms for fundamental sorting, searching, and simulation…

In machine learning datasets with symmetries, the paradigm for backward compatibility with symmetry-breaking has been to relax equivariant architectural constraints, engineering extra weights to differentiate symmetries of interest.…

Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…

The authors have been using a largely algebraic form of ``computational discovery'' in various undergraduate classes at their respective institutions for some decades now to teach pure mathematics, applied mathematics, and computational…

Our results can be viewed as applications of algebraic combinatorics in random matrix theory. These applications are motivated by the predictive power of random matrix theory for the statistical behavior of the celebrated Riemann…

We use a semi-supervised, neural-network based machine learning technique, the confusion method, to investigate structural transitions in magnetic polymers, which we model as chains of magnetic colloidal nanoparticles characterized by…

Matrix preconditioning is a critical technique to accelerate the solution of linear systems, where performance heavily depends on the selection of preconditioning parameters. Traditional parameter selection approaches often define fixed…

Unsupervised learning is the most challenging problem in machine learning and especially in deep learning. Among many scenarios, we study an unsupervised learning problem of high economic value --- learning to predict without costly pairing…

This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…

Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…

In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which…