arXiv subjects

Mateusz Koren

Publications and source records attributed to Mateusz Koren.

17 recordsLinked to original sources

arXiv2026

High-Frequency Pricing at Scale for E-Commerce

This paper presents the design, development, and implementation of a specialized forecast-then-optimize algorithmic pricing tool for sales campaigns in fashion e-commerce. Sales events present unique challenges for pricing including volatile demand patterns, rapid pricing decisions, and the need to balance short-term revenue with long-term profitability. We describe our approach combining daily-resolution demand forecasting using gradient-boosted trees with a multi-objective optimization framework that maximizes both long-term profit and net merchandise value for more than 5 million articles. Our solution addresses key limitations of existing weekly-granularity systems by implementing a forecast-then-optimize architecture that reduces pricing decision time from hours to minutes. We validate our approach through 23 A/B tests across 12 markets during 2023-2024 sales campaigns at Zalando, one of Europe's leading online fashion retailers. Experimental results demonstrate that the new pricing system achieves approximately 6% higher profit while maintaining equivalent performance on sales and revenue compared to the previous manual-algorithmic hybrid approach. Based on these results, the algorithm was successfully deployed to production and now handles the majority of algorithmic pricing decisions for sales campaigns at the company.

cs.LG↗

arXiv2023

Deep Learning based Forecasting: a case study from the online fashion industry

Demand forecasting in the online fashion industry is particularly amendable to global, data-driven forecasting models because of the industry's set of particular challenges. These include the volume of data, the irregularity, the high amount of turn-over in the catalog and the fixed inventory assumption. While standard deep learning forecasting approaches cater for many of these, the fixed inventory assumption requires a special treatment via controlling the relationship between price and demand closely. In this case study, we describe the data and our modelling approach for this forecasting problem in detail and present empirical results that highlight the effectiveness of our approach.

cs.LG↗

arXiv2021

Probabilistic Time Series Forecasting with Implicit Quantile Networks

Here, we propose a general method for probabilistic time series forecasting. We combine an autoregressive recurrent neural network to model temporal dynamics with Implicit Quantile Networks to learn a large class of distributions over a time-series target. When compared to other probabilistic neural forecasting models on real- and simulated data, our approach is favorable in terms of point-wise prediction accuracy as well as on estimating the underlying temporal distribution.

cs.LG↗

arXiv2019

Extraction of bare Form Factors for $\mathrm B_\mathrm s \to \mathrm K \ell ν$ Decays in non-perturbative HQET

We discuss the extraction of the ground state $\langle \mathrm{K} ({\bf p})|V_μ(0)|\mathrm{B} ({\bf 0})\rangle$ matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings $0.075, \; 0.05$ fm and pion masses $330,\;270$ MeV are used from the O($a$)- improved CLS 2-flavour simulations and the final state momentum is $|{\bf p}|=0.5\,{\rm GeV}$. The b-quark is treated in HQET including the $1/m_\mathrm{b}$ corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is $not$ limited by the $1/m_\mathrm{b}$ corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

hep-lat↗

arXiv2018

The spectrum of 2+1 dimensional Yang-Mills theory on a twisted spatial torus

We compute and analyse the low-lying spectrum of 2+1 dimensional $SU(N)$ Yang-Mills theory on a spatial torus of size $l\times l$ with twisted boundary conditions. This paper extends our previous work \cite{Perez:2013dra}. In that paper we studied the sector with non-vanishing electric flux and concluded that the energies only depend on the parameters through two combinations: $x=λN l /(4π)$ (with $λ$ the 't Hooft coupling) and the twist angle $\tilde θ$ defined in terms of the magnetic flux piercing the two-dimensional box. Here we made a more complete study and we are able to condense our results, obtained by non-perturbative lattice methods, into a simple expression which has important implications for the absence of tachyonic instabilities, volume independence and non-commutative field theory. Then we extend our study to the sector of vanishing electric flux. We conclude that the onset of the would-be large-volume glueball states occurs at an approximately fixed value of $x$, much before the stringy torelon states have become very massive.

hep-th↗

arXiv2017

HQET form factors for $B_s\to K\ellν$ decays beyond leading order

We compute semi-leptonic $B_s$ decay form factors using Heavy Quark Effective Theory on the lattice. To obtain good control of the $1/m_b$ expansion, one has to take into account not only the leading static order but also the terms arising at $O(1/m_b)$: kinetic, spin and current insertions. We show results for these terms calculated through the ratio method, using our prior results for the static order. After combining them with non-perturbative HQET parameters they can be continuum-extrapolated to give the QCD form factor correct up to $O(1/m_b^2)$ corrections and without $O(α_s(m_b)^n)$ corrections.

hep-lat↗

arXiv2017

SU(3) Yang Mills theory at small distances and fine lattices

We investigate the SU(3) Yang Mills theory at small gradient flow time and at short distances. Lattice spacings down to $a=0.015$ fm are simulated with open boundary conditions to allow topology to flow in and out. We study the behaviour of the action density $E(t)$ close to the boundaries, the feasibility of the small flow-time expansion and the extraction of the $Λ$-parameter from the static force at small distances. For the latter, significant deviations from the 4-loop perturbative $β$-function are visible at $α\approx 0.2\,$. We still can extrapolate to extract $r_0Λ$.

hep-lat↗

arXiv2016

Continuum limit of the leading order HQET form factor in $B_s \to K\ellν$ decays

We discuss the computation of form factors for semi-leptonic decays of $\rm B$-, $\rm B_s$- mesons in lattice QCD. Considering in particular the example of the static $\rm B_s$ form factors we demonstrate that after non-perturbative renormalization the continuum limit can be taken with confidence. The resulting precision is of interest for extractions of $V_{\rm ub}$. The size of the corrections of order $1/m_{\rm b}$ is just estimated at present but it is expected that their inclusion does not pose significant difficulties.

hep-lat↗

arXiv2014

Glueball masses in 2+1 dimensional SU(N) gauge theories with twisted boundary conditions

We analyze 2+1 dimensional Yang-Mills theory regularized on a lattice with twisted boundary conditions in the spatial directions. In previous work it was shown that the observables in the non-zero electric flux sectors obey the so-called $x$-scaling, i.e. depend only on the dimensionless variable $x\propto NL/b$ and the angle $\tildeθ$ given by the parameters of the twist ($L$ being the length of the spatial torus and $b$ the inverse 't Hooft coupling). It is conjectured that this scaling is obeyed by all physical quantities. In this work we extend the previous analyses to the zero electric flux (glueball) sector. We study the mass of the lightest scalar glueball in two theories with different $N$ but matching $x$ and $\tildeθ$ in a wide range of couplings from the perturbative small-volume regime to the non-perturbative one. We find that the results are consistent with the $x$-scaling hypothesis.

hep-lat↗

arXiv2014

Wilson loops with arbitrary charges

We discuss how to implement, in lattice gauge theories, external charges which are not commensurate with an elementary gauge coupling. It is shown that an arbitrary, real power of a standard Wilson loop (or Polyakov line) can be defined and consistently computed in lattice formulation of non-abelian, two dimensional gauge theories. However, such an observable can excite quantum states with integer fluxes only. Since the non-integer fluxes are not in the spectrum of the theory they cannot be created, no matter which observable is chosen. Also the continuum limit of above averages does not exist unless the powers in question are in fact integer. On the other hand, a new continuum limit exists, which is rather intuitive, and where above observables make perfect sense and lead to the string tension proportional to the square of arbitrary (non necessary commensurate with gauge coupling) charge.

hep-lat↗

arXiv2013

Volume reduction in large-N lattice gauge theories [with adjoint fermions]

This work covers volume reduction in quantum field theories on a lattice at large $N$ (number of colors), as first described by Eguchi and Kawai in 1982. The volume reduction (or volume independence) means that the theory defined on an arbitrarily small lattice is equivalent in the large-$N$ limit to the theory on an infinite lattice with the same bare parameters. We analyze the volume reduction by means of Monte Carlo simulations using the lattice model on a single site (or a small fixed number of sites) with Wilson fermions in the adjoint representation, using $N$ up to 60. Most of the results focus on two flavours of Dirac fermions and the single fermionic flavour is also discussed where there is a significant difference of behaviour. We find that the $(Z_N)^4$ center symmetry, necessary for the realization of volume reduction, is unbroken in the reduced model for a large range of parameters and, in particular, that the maximum admissible value of the adjoint fermion mass is non-zero in the large-$N$ limit. We calculate physical quantities, such as the plaquette, the static quark potential and the eigenvalues of the Dirac operator. We analyze the finite-$N$ corrections and consider the practicality of volume-reduced models in supplementing the large-volume calculations.

hep-lat↗

arXiv2013

On non-trivial spectra of trivial gauge theories

In this Letter we point out that the analytic solution of the two dimensional U(1) gauge theory, on a finite lattice, reveals in the continuum limit the renowned Manton's spectrum of topological electric fluxes together with their effective hamiltonian and wave functions. We extend this result for the system with strings and external charges providing also a novel interpretation of the theta parameter. Some further generalizations are also outlined.

hep-th↗

arXiv2012

Large-N reduction with adjoint Wilson fermions

We analyze the large-N behavior of SU(N) lattice gauge theories with adjoint fermions by studying volume-reduced models, as pioneered by Eguchi and Kawai. We perform simulations on a single-site lattice for Nf = 1 and Nf = 2 Wilson Dirac fermions with values of N up to 53. We show for both values of Nf that in the large-N limit there is a finite region, containing both light and heavy fermions, of unbroken center symmetry where the theory exhibits volume independence. Using large-N reduction we attempt to calculate physical quantities such as the string tension and meson masses.

hep-lat↗

arXiv2012

Screening in two-dimensional gauge theories

We analyze the problem of screening in 1+1 dimensional gauge theories. Using QED2 as a warm-up for the non-abelian models we show the mechanism of the string breaking, in particular the vanishing overlap of the Wilson loops to the broken-string ground state that has been conjectured in higher-dimensional analyses. We attempt to extend our analysis to non-integer charges in the quenched and unquenched cases, in pursuit of the numerical check of a renowned result for the string tension between arbitrarily-charged fermions in the massive Schwinger model.

hep-lat↗

arXiv2012

Large-N reduction in QCD with two adjoint Dirac fermions

We use lattice simulations to study the single-site version of SU(N) lattice gauge theory with two flavors of Wilson-Dirac fermions in the adjoint representation, a theory whose large volume correspondent is expected to be conformal or nearly conformal. Working with N as large as 53, we map out the phase diagram in the plane of bare `t Hooft coupling, g^2 N, and of the lattice quark mass, a*m, and look for the region where the Z_N^4 center symmetry of the theory is intact. In this region one expects the large-N equivalence of the single site and infinite volume theories to be valid. As for the N_f=1 case (see Phys. Rev. D80: 065031), we find that the center-symmetric region is large and includes both light fermion masses and masses at the cutoff scale. We study the N-dependence of the width of this region and find strong evidence that it remains of finite width as N goes to infinity. Simulating with couplings as small as g^2 N = 0.005, we find that the width shrinks slowly with decreasing g^2 N, at a rate consistent with analytic arguments. Within the center-symmetric region our results for the phase structure, when extrapolated to infinite N, apply also for the large volume theory, which is minimal walking technicolor with N=infinity. We find a first-order transition as a function of a*m for all values of b, which we argue favors that the theory is confining in the infrared. Finally, we measure the eigenvalue densities of the Wilson-Dirac operator and its hermitian version, and use large Wilson loops to study the utility of reduction for extracting physical observables.

hep-lat↗

arXiv2011

Preliminary study of two-dimensional SU(N) Yang-Mills theory with adjoint matter by Hybrid Monte Carlo approach

Two-dimensional non-abelian quantum field models provide a useful laboratory for analytic and numerical investigations of quantum theories with gauge symmetry. They can exhibit various features, such as charge confinement, which are known from D=4 theories like QCD. Several analytic predictions concerning the spectra of two-dimensional systems with adjoint matter were postulated and numerical results were obtained using Discrete Light Cone Quantization techniques, however none of them has been checked via Monte Carlo simulations. In this Letter we present two such models which are particularly interesting from the physical point of view and discuss first numerical results.

hep-lat↗

arXiv2011

Large-N reduction with two adjoint Dirac fermions

We study the single site SU(N) lattice gauge theory with N_f=2 adjoint Wilson fermions for values of N up to 53. We determine the phase diagram of the theory as a function of the hopping parameter kappa and the inverse 't Hooft coupling b, searching for the region in which the Z_N^4 center symmetry is unbroken. In this region the theory is equivalent to the infinite volume theory when N goes to infinity. We find a region of values of kappa on both sides of kappa_c for which the symmetry is unbroken, including both light physical quarks and masses ~O(1/a). This is surrounded by a region with a complicated sequence of partially broken phases. We calculate Wilson loop expectation values and find that using N <= 53 it is possible to extract the heavy-quark potential at small distances (1-3 links) but not at longer distances. For this, larger values of N, or lattices with more sites, are needed.

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