Related papers: Refining Integration-by-Parts Reduction of Feynman…
We posit that we can generate more robust and performant heuristics if we augment approaches using LLMs for heuristic design with tools that explain why heuristics underperform and suggestions about how to fix them. We find even simple…
Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…
In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be…
Genetic algorithms are heuristic optimization techniques inspired by Darwinian evolution, which are characterized by successfully finding robust solutions for optimization problems. Here, we propose a subroutine-based quantum genetic…
Machine learning methods usually depend on internal parameters -- so called hyperparameters -- that need to be optimized for best performance. Such optimization poses a burden on machine learning practitioners, requiring expert knowledge,…
Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that…
Computer vision based fine-grained recognition has received great attention in recent years. Existing works focus on discriminative part localization and feature learning. In this paper, to improve the performance of fine-grained…
Machine Learning algorithms based on Brain-inspired Hyperdimensional(HD) computing imitate cognition by exploiting statistical properties of high-dimensional vector spaces. It is a promising solution for achieving high energy efficiency in…
Deploying large language models (LLMs) encounters challenges due to intensive computational and memory requirements. Our research examines vocabulary trimming (VT) inspired by restricting embedding entries to the language of interest to…
Designing functional materials requires a deep search through multidimensional spaces for system parameters that yield desirable material properties. For cases where conventional parameter sweeps or trial-and-error sampling are impractical,…
The current trends in next-generation exascale systems go towards integrating a wide range of specialized (co-)processors into traditional supercomputers. Due to the efficiency of heterogeneous systems in terms of Watts and FLOPS per…
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…
Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…
When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…
We present a new implementation of the LLM-driven genetic algorithm {\it funsearch}, whose aim is to generate examples of interest to mathematicians and which has already had some success in problems in extremal combinatorics. Our…
In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification…
The Zippel algorithm performs a rational reconstruction of multivariate polynomials and aims specifically at the sparse case. It is applied in different fields of science, lately becoming an important step in Feynman integral reduction in…
The process of training feedforward neural networks (FFNNs) can benefit from an automated process where the best heuristic to train the network is sought out automatically by means of a high-level probabilistic-based heuristic. This…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…