Related papers: Refining Integration-by-Parts Reduction of Feynman…
Heuristic algorithms play a vital role in solving combinatorial optimization (CO) problems, yet traditional designs depend heavily on manual expertise and struggle to generalize across diverse instances. We introduce \textbf{HeurAgenix}, a…
There are two common approaches for optimizing the performance of a machine: genetic algorithms and machine learning. A genetic algorithm is applied over many generations whereas machine learning works by applying feedback until the system…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for theevaluation of Feynman diagrams. We describe the operational rules and illustrate the method…
Hebbian meta-learning has recently shown promise to solve hard reinforcement learning problems, allowing agents to adapt to some degree to changes in the environment. However, because each synapse in these approaches can learn a very…
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…
Fine-grained visual categorization is a classification task for distinguishing categories with high intra-class and small inter-class variance. While global approaches aim at using the whole image for performing the classification,…
We describe how Groebner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some…
One of the most critical issues in machine learning is the selection of appropriate hyper parameters for training models. Machine learning models may be able to reach the best training performance and may increase the ability to generalize…
This paper introduces a technique to enhance the efficiency of quadratic machine learning models, particularly Field-Aware Factorization Machines (FFMs) handling binary data. Our approach strategically reduces model size through optimized…
We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a…
The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases algorithm, region-bases and integrating…
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…
Partitioning a set of elements into an unknown number of mutually exclusive subsets is essential in many machine learning problems. However, assigning elements, such as samples in a dataset or neurons in a network layer, to an unknown and…
Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master…
The classical method of determining the atomic structure of complex molecules by analyzing diffraction patterns is currently undergoing drastic developments. Modern techniques for producing extremely bright and coherent X-ray lasers allow a…
Machine learning algorithms often take inspiration from established results and knowledge from statistical physics. A prototypical example is the Boltzmann machine algorithm for supervised learning, which utilizes knowledge of classical…
This paper presents preliminary work on using deep neural networks to guide general-purpose heuristic algorithms for performing utilitarian combinatorial assignment. In more detail, we use deep learning in an attempt to produce heuristics…