Related papers: Higher-Order Corrections to BFKL Evolution from $t…
The generalization of the BFKL equation for the case of non-forward scattering is considered. The kernel of the generalized equation in the next-to-leading approximation is expressed in terms of the gluon Regge trajectory and the effective…
We develop a new systematic procedure for the Regge limit in perturbative QCD to arbitrary logarithmic order. The formalism relies on the IR structure and the gauge symmetry of the theory. We identify leading regions in loop momentum space…
Graph Neural Networks (GNNs) are widely used on a variety of graph-based machine learning tasks. For node-level tasks, GNNs have strong power to model the homophily property of graphs (i.e., connected nodes are more similar) while their…
We study the connection between complete representations of gauge invariant operators and their Moebius representations acting in a limited space of functions. The possibility to restore the complete representations from Moebius forms in…
We calculate the quark-anti-quark contribution to the next-to-leading logarithmic corrections to the BFKL kernel, retaining the dependence on the momenta of the produced particles. This allows us to study the details of the NLL corrections.…
We study the inclusion of running coupling corrections into the non-linear small-x JIMWLK and BK evolution equations by resumming all powers of alpha_s N_f in the evolution kernels. We demonstrate that the running coupling corrections are…
The renormalon calculus is used to calculate the terms of order $\beta_0^{n-1}\alpha_s^n$ in the perturbative expansions of the Wilson coefficients and hard-scattering kernels entering the QCD factorization formula for hadronic B-meson…
The ``non-Abelian'' part of the quark contribution to the BFKL kernel in the next-to-leading order (NLO) is found in the coordinate representation by direct transfer of the contribution from the momentum representation where it was…
We calculate the next-to-next-to-leading order ${\cal O}(\alpha_s^4)$ one-loop squared corrections to the production of heavy quark pairs in quark-antiquark annihilations. These are part of the next-to-next-to-leading order ${\cal…
We analyze feature learning in infinite-width neural networks trained with gradient flow through a self-consistent dynamical field theory. We construct a collection of deterministic dynamical order parameters which are inner-product kernels…
We study a family of fractional integral operators whose kernels satisfying an non-isotropic dilation have singularity on a coordinate subspace. A characterization is given for these operators bounded from the classical, atom decomposable…
Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular…
It is common practice to explain deviations between data and Standard-Model (SM) predictions by postulating new particles at the TeV scale ad-hoc. This approach becomes much more convincing, if one successfully embeds the postulated…
This paper introduces a diagonal adaptive kernel model that dynamically learns kernel eigenvalues and output coefficients simultaneously during training. Unlike fixed-kernel methods tied to the neural tangent kernel theory, the diagonal…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
Despite several algorithmic advances in the training of convolutional neural networks (CNNs) over the years, their generalization capabilities are still subpar across several pertinent domains, particularly within open-set tasks often found…
Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…
We consider applications of neural networks in nonlinear system identification and formulate a hypothesis that adjusting general network structure by incorporating frequency information or other known orthogonal transform, should result in…
Spectrum cartography reconstructs spatial radio fields from sparse and heterogeneous wireless measurements, underpinning many sensing and optimization tasks in wireless networks. Attention mechanisms have recently enabled adaptive…
We propose a modified version of the Balitsky-Kovchegov (B-K) evolution equation, which includes the main NLO corrections. We use the result that the main NLO corrections to the BFKL kernel are the LO DGLAP corrections. We present a…