Related papers: KNO scaling 30 years later
The accumulation point of the period-tripling bifurcation cascade in complex quadratic map was discovered by Golberg, Sinai, and Khanin (Russ.Math.Surv. 38:1, 1983, 187), and independently by Cvitanovic and Myrheim (Phys.Lett. A94:8, 1983,…
Starting from a short range expansion of the inelastic overlap function, capable of describing quite well the elastic pp and $\bar{p}p$ scattering data, we obtain extensions to the inelastic channel, through unitarity and an impact…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Using Mueller's dipole formalism for deep inelastic scattering in QCD, we formulate and solve the evolution for the generating function for the multiplicities of the produced particles, in hadronic processes at high energy. The solution for…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…
Output uncertainty indicates whether the probabilistic properties reflect objective characteristics of the model output. Unlike most loss functions and metrics in machine learning, uncertainty pertains to individual samples, but validating…
Neural scaling laws, which in some domains can predict the performance of large neural networks as a function of model, data, and compute scale, are the cornerstone of building foundation models in Natural Language Processing and Computer…
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
How quantum information is scrambled in the global degrees of freedom of non-equilibrium many-body systems is a key question to understand local thermalization. Here we propose that the scaling of the mutual information between two…
Unveiling universal non-equilibrium scaling laws has been a central theme in modern statistical physics, with recent attention increasingly directed toward non-equilibrium phases that exhibit rich dynamical phenomena. A striking example…
A scaling theory of replica symmetry breaking (RSB) in the SK-model is presented in the framework of critical phenomena for the scaling regime of small inverse RSB-orders, small temperatures, small magnetic fields, and near opposite…
The large $N_c$ nuclear potential puzzle arose because three- and higher-meson exchange contributions to the nucleon-nucleon potential did not automatically yield cancellations that make these contributions consistent with the general large…
A prominent self-supervised learning paradigm is to model the representations as clusters, or more generally as a mixture model. Learning to map the data samples to compact representations and fitting the mixture model simultaneously leads…
We compute the proton-proton multiplicity distributions at LHC energies in the framework of a multiple scattering model assuming a Poisson distribution for each inelastic collision. Multiple scattering is essential to broaden the…
Scaling laws are well studied for language models and first-stage retrieval, but not for reranking. We present the first systematic study of scaling laws for cross-encoder rerankers across pointwise, pairwise, and listwise objectives.…
The analogy between the intermittency and scaling in statistical physics is extended to the case of more variables. It is shown that the inclusive densities predicted by the perturbative QCD obey generalized homogeneity principle which…
Numerical simulations of massive neutrino cosmologies consistently find a spoon-like feature in the non-linear matter power spectrum ratios of cosmological models that differ only in the neutrino mass fraction f_N. Typically, the ratio…
Neural scaling laws have revolutionized the design and optimization of large-scale AI models by revealing predictable relationships between model size, dataset volume, and computational resources. Early research established power-law…
Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often…
General purpose optimization routines such as nlminb, optim (R) or nlmixed (SAS) are frequently used to estimate model parameters in nonstandard distributions. This paper presents Particle Swarm Optimization (PSO), as an alternative to many…