Related papers: The Liouville Generator for Producing Integrable E…
For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a result of the canonical quantization of the integrable…
The large success of deep learning based methods in Visual Question Answering (VQA) has concurrently increased the demand for explainable methods. Most methods in Explainable Artificial Intelligence (XAI) focus on generating post-hoc…
The usage of Large Language Models (LLMs) for software and test development has continued to increase since LLMs were first introduced, but only recently have the expectations of LLMs become more realistic. Verifying the correctness of code…
In this paper, we introduce ILLUME, a unified multimodal large language model (MLLM) that seamlessly integrates multimodal understanding and generation capabilities within a single large language model through a unified next-token…
Generative Artificial Intelligence (GenAI) has demonstrated its capabilities in the present world that reduce human effort significantly. It utilizes deep learning techniques to create original and realistic content in terms of text,…
Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They…
Visual generation models have achieved remarkable progress in computer graphics applications but still face significant challenges in real-world deployment. Current assessment approaches for visual generation tasks typically follow an…
Consider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the integral curve in reduced form provided that the previous one is…
Under mild assumptions, we establish a Liouville theorem for the "Laplace" equation $Au=0$ associated with the infinitesimal generator $A$ of a L\'evy process: If $u$ is a weak solution to $Au=0$ which is at most of (suitable) polynomial…
Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates…
When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…
A symplectic theory approach is devised for solving the problem of algebraic-analytical construction of integral submanifold imbeddings for integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on canonically…
A method is given that "inverts" a logic grammar and displays it from the point of view of the logical form, rather than from that of the word string. LR-compiling techniques are used to allow a recursive-descent generation algorithm to…
We present VAEL, a neuro-symbolic generative model integrating variational autoencoders (VAE) with the reasoning capabilities of probabilistic logic (L) programming. Besides standard latent subsymbolic variables, our model exploits a…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
Disentangled representations can be useful in many downstream tasks, help to make deep learning models more interpretable, and allow for control over features of synthetically generated images that can be useful in training other models…
In this study we work on a novel Hamiltonian system which is Liouville integrable. In the integrable Hamiltonian model, conserved currents can be represented as Binomial polynomials in which each order corresponds to the integral of motion…
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…
Training on verifiable symbolic data is a promising way to expand the reasoning frontier of language models beyond what standard pre-training corpora provide. Yet existing procedural generators often rely on fixed puzzles or templates and…
According to Kirillov's theory, the construction of a unitary irreducible representation of a nilpotent Lie group requires a precise computation of some polarizing subalgebra subordinated to a linear functional in the linear dual of the…