Related papers: The Liouville Generator for Producing Integrable E…

Integrating symbolic knowledge and data-driven learning algorithms is a longstanding challenge in Artificial Intelligence. Despite the recognized importance of this task, a notable gap exists due to the discreteness of symbolic…

Quantum simulators and processors are rapidly improving nowadays, but they are still not able to solve complex and multidimensional tasks of practical value. However, certain numerical algorithms inspired by the physics of real quantum…

There are many problems in physics, biology, and other natural sciences in which symbolic regression can provide valuable insights and discover new laws of nature. A widespread Deep Neural Networks do not provide interpretable solutions.…

Generative models for image generation are now commonly used for a wide variety of applications, ranging from guided image generation for entertainment to solving inverse problems. Nonetheless, training a generator is a non-trivial feat…

We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a…

The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…

We propose a novel multi-dimensional integration algorithm using a machine learning (ML) technique. After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral.…

We propose a novel exact multi-parameter persistent homology method for analyzing time-series data utilizing the Liouville torus. In the field of topological data analysis (TDA), the conventional approach to analyzing time-series data often…

As financial applications of large language models (LLMs) gain attention, accurate Information Retrieval (IR) remains crucial for reliable AI services. However, existing benchmarks fail to capture the complex and domain-specific information…

We provide a detailed analysis of the disk path integral of timelike Liouville theory, conceived as a tractable and precise toy-model quantum cosmology in two dimensions. Disk path integrals with the insertion of matter field operators,…

Conditional image generation has gained significant attention for its ability to personalize content. However, the field faces challenges in developing task-agnostic, reliable, and explainable evaluation metrics. This paper introduces…

LLMs are vulnerable to hallucinations, and thus their outputs generally require laborious human verification for high-stakes applications. To this end, we propose symbolically grounded generation (SymGen) as a simple approach for enabling…

We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR…

We present a novel integrator based on normalizing flows which can be used to improve the unweighting efficiency of Monte-Carlo event generators for collider physics simulations. In contrast to machine learning approaches based on surrogate…

Learning disentangled and interpretable representations is an important step towards accomplishing comprehensive data representations on the manifold. In this paper, we propose a novel representation learning algorithm which combines the…

This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using…

Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…

We propose a novel architecture for integrating large language models (LLMs) with a persistent, interactive Lisp environment. This setup enables LLMs to define, invoke, and evolve their own tools through programmatic interaction with a live…

Scalable Vector Graphics (SVG) is a code-based representation for 2D visuals. Leveraging recent advances in large language models (LLMs), we study text-to-SVG generation and address two persistent gaps: weak generalization and poor…

Large Language Models (LLMs) have become increasingly popular for generating RTL code. However, producing error-free RTL code in a zero-shot setting remains highly challenging for even state-of-the-art LLMs, often leading to issues that…