Related papers: BasisGen: automatic generation of operator bases

We present an easy-to-use, Python-based framework that allows a researcher to automate their computational simulations. In particular the framework facilitates assembling several long-running computations and producing various plots from…

Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large…

Gr\"obner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field…

We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular these functions include all the homogeneous polynomials…

AxialGen is a research prototype for automatically generating the axial map, which consists of the least number of the longest visibility lines (or axial lines) for representing individual linearly stretched parts of open space of an urban…

Executing complex terminal tasks remains a significant challenge for open-weight LLMs, constrained by two fundamental limitations. First, high-fidelity, executable training environments are scarce: environments synthesized from real-world…

We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra $\mathfrak{g}$. The Lie algebra generators are represented…

Young's orthogonal basis is a classical basis for an irreducible representation of a symmetric group. This basis happens to be a Gelfand-Tsetlin basis for the chain of symmetric groups. It is well-known that the chain of alternating groups,…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

Bridging physics and deep learning is a topical challenge. While deep learning frameworks open avenues in physical science, the design of physically-consistent deep neural network architectures is an open issue. In the spirit of…

Deep neural networks can form high-level hierarchical representations of input data. Various researchers have demonstrated that these representations can be used to enable a variety of useful applications. However, such representations are…

The impressive success of Generative Adversarial Networks (GANs) is often overshadowed by the difficulties in their training. Despite the continuous efforts and improvements, there are still open issues regarding their convergence…

Generative adversarial networks (GANs) have been shown to provide an effective way to model complex distributions and have obtained impressive results on various challenging tasks. However, typical GANs require fully-observed data during…

We introduce DatasetGAN: an automatic procedure to generate massive datasets of high-quality semantically segmented images requiring minimal human effort. Current deep networks are extremely data-hungry, benefiting from training on…

A weight basis for each finite-dimensional irreducible representation of the orthogonal Lie algebra o(2n) is constructed. The basis vectors are parametrized by the D-type Gelfand--Tsetlin patterns. Explicit formulas for the matrix elements…

Generation of photo-realistic images, semantic editing and representation learning are a few of many potential applications of high resolution generative models. Recent progress in GANs have established them as an excellent choice for such…

In this work, we present BasisNet which combines recent advancements in efficient neural network architectures, conditional computation, and early termination in a simple new form. Our approach incorporates a lightweight model to preview…

Generative models such as the variational autoencoder (VAE) and the generative adversarial networks (GAN) have proven to be incredibly powerful for the generation of synthetic data that preserves statistical properties and utility of…

Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we…

In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…