arXiv subjects

Piotr Bialas

Publications and source records attributed to Piotr Bialas.

14 recordsLinked to original sources

arXiv2025

NeuMC -- a package for neural sampling for lattice field theories

We present the \texttt{NeuMC} software package, based on \pytorch, aimed at facilitating the research on neural samplers in lattice field theories. Neural samplers based on normalizing flows are becoming increasingly popular in the context of Monte-Carlo simulations as they can effectively approximate target probability distributions, possibly alleviating some shortcomings of the Markov chain Monte-Carlo methods. Our package provides tools to create such samplers for two-dimensional field theories.

hep-lat↗

arXiv2024

Training normalizing flows with computationally intensive target probability distributions

Machine learning techniques, in particular the so-called normalizing flows, are becoming increasingly popular in the context of Monte Carlo simulations as they can effectively approximate target probability distributions. In the case of lattice field theories (LFT) the target distribution is given by the exponential of the action. The common loss function's gradient estimator based on the "reparametrization trick" requires the calculation of the derivative of the action with respect to the fields. This can present a significant computational cost for complicated, non-local actions like e.g. fermionic action in QCD. In this contribution, we propose an estimator for normalizing flows based on the REINFORCE algorithm that avoids this issue. We apply it to two dimensional Schwinger model with Wilson fermions at criticality and show that it is up to ten times faster in terms of the wall-clock time as well as requiring up to $30\%$ less memory than the reparameterization trick estimator. It is also more numerically stable allowing for single precision calculations and the use of half-float tensor cores. We present an in-depth analysis of the origins of those improvements. We believe that these benefits will appear also outside the realm of the LFT, in each case where the target probability distribution is computationally intensive.

cs.LG↗

arXiv2023

On Random Allocation Models in the Thermodynamic Limit

We discuss the phase transition and critical exponents in the random allocation model (urn model) for different statistical ensembles. We provide a unified presentation of the statistical properties of the model in the thermodynamic limit, uncover new relationships between the thermodynamic potentials and fill some lacunae in previous results on the singularities of these potentials at the critical point and behaviour in the thermodynamic limit. The presentation is intended to be self-contained, so we carefully derive all formulae step by step throughout. Additionally, we comment on a quasi-probabilistic normalisation of configuration weights which has been considered in some recent studies

cond-mat.stat-mech↗

arXiv2023

Rényi Entropy of Zeta-Urns

We calculate analytically the Renyi entropy for the zeta-urn model with a Gibbs measure definition of the micro-state probabilities. This allows us to obtain the singularities in the Rényi entropy from those of the thermodynamic potential, which is directly related to the free energy density of the model. We enumerate the various possible behaviours of the Rényi entropy and its singularities, which depend on both the value of the power law in the zeta-urn and the order of the Rényi entropy under consideration

cond-mat.stat-mech↗

arXiv2022

Gradient estimators for normalising flows

Recently a machine learning approach to Monte-Carlo simulations called Neural Markov Chain Monte-Carlo (NMCMC) is gaining traction. In its most popular form it uses neural networks to construct normalizing flows which are then trained to approximate the desired target distribution. In this contribution we present new gradient estimator for Stochastic Gradient Descent algorithm (and the corresponding \texttt{PyTorch} implementation) and show that it leads to better training results for $ϕ^4$ model. For this model our estimator achieves the same precision in approximately half of the time needed in standard approach and ultimately provides better estimates of the free energy. We attribute this effect to the lower variance of the new estimator. In contrary to the standard learning algorithm our approach does not require estimation of the action gradient with respect to the fields, thus has potential of further speeding up the training for models with more complicated actions.

stat.ML↗

arXiv2015

Benchmarking the cost of thread divergence in CUDA

All modern processors include a set of vector instructions. While this gives a tremendous boost to the performance, it requires a vectorized code that can take advantage of such instructions. As an ideal vectorization is hard to achieve in practice, one has to decide when different instructions may be applied to different elements of the vector operand. This is especially important in implicit vectorization as in NVIDIA CUDA Single Instruction Multiple Threads (SIMT) model, where the vectorization details are hidden from the programmer. In order to assess the costs incurred by incompletely vectorized code, we have developed a micro-benchmark that measures the characteristics of the CUDA thread divergence model on different architectures focusing on the loops performance.

cs.DC↗

arXiv2013

Three dimensional finite temperature SU(3) gauge theory near the phase transition

We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent νhas the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu-Goto string model in spite of the different critical behaviour.

hep-lat↗

arXiv2011

Correlation functions of Ising spins on thin graphs

We investigate analytically and numerically an Ising spin model with ferromagnetic coupling defined on random graphs corresponding to Feynman diagrams of a $ϕ^q$ field theory, which exhibits a mean field phase transition. We explicitly calculate the correlation functions both in the symmetric and in the broken symmetry phase in the large volume limit. They agree with the results for finite size systems obtained from Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2010

Correlations in connected random graphs

We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated and derive analytic formulas for the joint nearest-neighbor degree probability distribution. Using those results we describe the correlations in maximal entropy connected random graphs. We show that connected graphs are disassortative and that correlations are strongly related to the presence of one-degree nodes (leaves). We propose an efficient algorithm for generating connected random graphs. We illustrate our results with several examples.

cond-mat.stat-mech↗

arXiv2010

Long-range disassortative correlations in generic random trees

We explicitly calculate the distance dependent correlation functions in a maximal entropy ensemble of random trees. We show that correlations remain disassortative at all distances and vanish only as a second inverse power of the distance. We discuss in detail the example of scale-free trees where the diverging second moment of the degree distribution leads to some interesting phenomena.

cond-mat.stat-mech↗

arXiv2000

Percolation and Magnetization in the Continuous Spin Ising Model

In the strong coupling limit the partition function of SU(2) gauge theory can be reduced to that of the continuous spin Ising model with nearest neighbour pair-interactions. The random cluster representation of the continuous spin Ising model in two dimensions is derived through a Fortuin-Kasteleyn transformation, and the properties of the corresponding cluster distribution are analyzed. It is shown that for this model, the magnetic transition is equivalent to the percolation transition of Fortuin-Kasteleyn clusters, using local bond weights. These results are also illustrated by means of numerical simulations.

hep-lat↗

arXiv2000

Matter Correlations in Branched Polymers

We analyze correlation functions in a toy model of a random geometry interacting with matter. We show that in general the connected correlator will contain a long--range scaling part. This result supports the previously conjectured general form of correlation functions on random geometries. We discuss the interplay between matter and geometry and the role of the symmetry in the matter sector.

cond-mat.stat-mech↗

arXiv1996

RG flow in an exactly solvable model with fluctuating geometry

A recently proposed renormalization group technique, based on the hierarchical structures present in theories with fluctuating geometry, is implemented in the model of branched polymers. The renormalization group equations can be solved analytically, and the flow in coupling constant space can be determined.

hep-lat↗

arXiv1995

Long range correlations in branched polymers

We study the correlation functions in the branched polymer model. Although there are no correlations in the grand canonical ensemble, when looking at the canonical ensemble we find negative long range power like correlations. We propose that a similar mechanism explains the shape of recently measured correlation functions in the elongated phase of 4d simplicial gravity.

hep-lat↗