Related papers: Simplifying Polylogarithms with Machine Learning
Systems of integration-by-parts identities play an important role in simplifying the higher-loop Feynman integrals that arise in quantum field theory. Solving these systems is equivalent to reducing integrals containing numerator products…
We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FIs computation is conceptually changed to a linear algebraic problem. Examples up…
The prevalence of convolution in applications within signal processing, deep neural networks, and numerical solvers has motivated the development of numerous fast convolution algorithms. In many of these problems, convolution is performed…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Machine learning systems such as large scale recommendation systems or natural language processing systems are usually trained on billions of training points and are associated with hundreds of billions or trillions of parameters. Improving…
Meta-learning, or learning-to-learn, seeks to design algorithms that can utilize previous experience to rapidly learn new skills or adapt to new environments. Representation learning -- a key tool for performing meta-learning -- learns a…
We identify two families of ten-point Feynman diagrams that generalize the elliptic double box, and show that they can be expressed in terms of the same class of elliptic multiple polylogarithms to all loop orders. Interestingly, one of…
Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…
Chemical representations derived from deep learning are emerging as a powerful tool in areas such as drug discovery and materials innovation. Currently, this methodology has three major limitations - the cost of representation generation,…
As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, reinforcement learning techniques may be used for photorealistic image synthesis: Efficiency may be…
The polylogarithm function is one of the constellation of important mathematical functions. It has a long history, and many connections to other special functions and series, and many applications, for instance in statistical physics.…
Polylogarithmic time delineates a relevant notion of feasibility on several classical computational models such as Boolean circuits or parallel random access machines. As far as the quantum paradigm is concerned, this notion yields the…
Metalearning of deep neural network (DNN) architectures and hyperparameters has become an increasingly important area of research. Loss functions are a type of metaknowledge that is crucial to effective training of DNNs, however, their…
Analogical reasoning is a hallmark of human intelligence, enabling us to solve new problems by transferring knowledge from one situation to another. Yet, developing artificial intelligence systems capable of robust human-like analogical…
Multivariate goodness-of-fit and two-sample tests are important components of many nuclear and particle physics analyses. While a variety of powerful methods are available if the dimensionality of the feature space is small, such tests…
The purpose of this paper is to use reinforcement learning to model learning agents which can recognize formal languages. Agents are modeled as simple multi-head automaton, a new model of finite automaton that uses multiple heads, and six…
Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by…
Feynman integrals appropriately generalized are $\mathsf A$-hypergeometric functions. Among the properties of $\mathsf A$-hypergeometric functions are symmetries associated with the Newton polytope. In ordinary hypergeometric functions…
Divergence measures have a long association with statistical inference, machine learning and information theory. The density power divergence and related measures have produced many useful (and popular) statistical procedures, which provide…
We introduce dilogarithm identities through a beta integral-based technique that we apply to provide analytic proofs of previously conjectured dilogarithm relations, solving open problems given by both Bytsko and Campbell, and that we…