Related papers: Uncovering Singularities in Feynman Integrals via …
Abstract reasoning is a cornerstone of human intelligence, and replicating it with artificial intelligence (AI) presents an ongoing challenge. This study focuses on efficiently solving Raven's progressive matrices (RPM), a visual test for…
The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
The study of Feynman integrals through the lens of intersection theory offers a unifying framework for their analysis, capturing both the linear and quadratic relations that arise among integrals. In doing so, it provides a powerful method…
Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning…
We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…
We propose a novel method to determine the structure of symbols for any family of polylogarithmic Feynman integrals. Using the d log-bases and simple formulas for the leading order and next-to-leading contributions to the intersection…
We present a Machine Learning approach based on Symbolic Regression to derive, from either numerically generated or experimentally measured spectral data, closed-form expressions that model the optical properties of biological materials. To…
Modern AI algorithms require labeled data. In real world, majority of data are unlabeled. Labeling the data are costly. this is particularly true for some areas requiring special skills, such as reading radiology images by physicians. To…
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…
Standard integration-by-parts (IBP) reduction methods typically yield Feynman integral bases where the reduction of some integrals gives rise to coefficients singular as the dimensional regulator $\epsilon\rightarrow 0$. These singular…
Ultrafast diffraction imaging is a powerful tool to retrieve the geometric structure of gas-phase molecules with combined picometre spatial and attosecond temporal resolution. However, structural retrieval becomes progressively difficult…
Symbolic regression, i.e. predicting a function from the observation of its values, is well-known to be a challenging task. In this paper, we train Transformers to infer the function or recurrence relation underlying sequences of integers…
We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent…
Neural sequence models trained with maximum likelihood estimation have led to breakthroughs in many tasks, where success is defined by the gap between training and test performance. However, their ability to achieve stronger forms of…
We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
Deep learning architectures based on convolutional neural networks tend to rely on continuous, smooth features. While this characteristics provides significant robustness and proves useful in many real-world tasks, it is strikingly…
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…