Related papers: BasisGen: automatic generation of operator bases

We present a unified approach to (bi-)orthogonal basis sets for gravitating systems. Central to our discussion is the notion of mutual gravitational energy, which gives rise to the self-energy inner product on mass densities. We consider a…

We present an algorithm using transformation groups and their irreducible representations to generate an orthogonal basis for a signal in the vector space of the signal. It is shown that multiresolution analysis can be done with amplitudes…

Behavioral models are incredibly useful for understanding and validating software. However, the automatic extraction of such models from actual industrial code remains a largely unsolved problem with current solutions often not scaling well…

The Barnes-Hut and Fast Multipole Methods are widely utilised methods applied in order to reduce the computational cost of evaluating long range forces in $N$-body simulations. Despite this, applying existing libraries to simple problems…

Synthetic data is essential for assessing clustering techniques, complementing and extending real data, and allowing for more complete coverage of a given problem's space. In turn, synthetic data generators have the potential of creating…

Manipulation policies deployed in uncontrolled real-world scenarios are faced with great in-category geometric diversity of everyday objects. In order to function robustly under such variations, policies need to work in a category-level…

Scientific computing requires handling large linear models, which are often composed of structured matrices. With increasing model size, dense representations quickly become infeasible to compute or store. Matrix-free implementations are…

The typical problem in Data Science is creating a structure that encodes the occurrence frequency of unique elements in rows and relations between different rows of a data frame. We present the probability tree abstract data structure, an…

Generative Adversarial Networks (GANs) advance face synthesis through learning the underlying distribution of observed data. Despite the high-quality generated faces, some minority groups can be rarely generated from the trained models due…

Large-scale and diverse datasets are vital for training robust robotic manipulation policies, yet existing data collection methods struggle to balance scale, diversity, and quality. Simulation offers scalability but suffers from sim-to-real…

Bayesian networks (BNs) are graphical \emph{first-order} probabilistic models that allow for a compact representation of large probability distributions, and for efficient inference, both exact and approximate. We introduce a…

Operator networks are designed to approximate nonlinear operators, which provide mappings between infinite-dimensional spaces such as function spaces. These networks are playing an increasingly important role in machine learning, with their…

In the era of deep learning, data is the critical determining factor in the performance of neural network models. Generating large datasets suffers from various difficulties such as scalability, cost efficiency and photorealism. To avoid…

We present MADLens a python package for producing non-Gaussian lensing convergence maps at arbitrary source redshifts with unprecedented precision. MADLens is designed to achieve high accuracy while keeping computational costs as low as…

MatchingTools is a Python library for doing symbolic calculations in effective field theory. It provides the tools to construct general models by defining their field content and their interaction Lagrangian. Once a model is given, the…

Operator learning trains a neural network to map functions to functions. An ideal operator learning framework should be mesh-free in the sense that the training does not require a particular choice of discretization for the input functions,…

In this paper we present a short overview of the new Wolfram Mathematica package intended for elementary "in-basis" tensor and differential-geometric calculations. In contrast to alternatives our package is designed to be easy-to-use,…

We introduce a systematic framework for counting and finding independent operators in effective field theories, taking into account the redundancies associated with use of the classical equations of motion and integration by parts. By…

Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the construction of symmetry--adapted polynomials in the symmetry…

Simulation plays a key role in scaling robot learning and validating policies, but constructing simulations remains a labor-intensive process. This paper introduces ReGen, a generative simulation framework that automates simulation design…