Related papers: KNO scaling 30 years later
We have derived explicit expressions in the 1-d Ising model for multiplicity distributions $P_{\del\xi}(n)$ and factorial moments $F_q(\del\xi)$. We identify the salient features of $P_{\del\xi}(n)$ that lead to scaling,…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
When data is plentiful, the loss achieved by well-trained neural networks scales as a power-law $L \propto N^{-\alpha}$ in the number of network parameters $N$. This empirical scaling law holds for a wide variety of data modalities, and may…
We numerically study the scaling behavior of period doublings at the zero-coupling critical point in a four-dimensional volume-preserving map consisting of two coupled area-preserving maps. In order to see the fine structure of period…
Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws…
It is experimentally observed that the width of the KNO multiplicity distribution --or the negative binomial parameter 1/k-- for pp collisions, in the energy region 10 to 1800 GeV, is an increasing function of the energy. We argue that in…
Data-collapse is a way of establishing scaling and extracting associated exponents in problems showing self-similar or self-affine characteristics as e.g. in equilibrium or non-equilibrium phase transitions, in critical phases, in dynamics…
We demonstrate that the output of a cosmological N-body simulation can, to remarkable accuracy, be scaled to represent the growth of large-scale structure in a cosmology with parameters similar to but different from those originally…
In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time,…
Scaling laws arise and are eulogized across disciplines from natural to social sciences for providing pithy, quantitative, `scale-free', and `universal' power law relationships between two variables. On a log-log plot, the power laws…
Neural scaling laws and double-descent phenomena suggest that deep-network training obeys a simple macroscopic structure despite highly nonlinear optimization dynamics. We derive such structure directly from gradient descent in function…
Between the linear and nonlinear regimes, we identify a universal transition range centered on a characteristic halo mass $m_h^*\propto t$, within which gravitational dynamics self-organize the matter field toward an effective spectral…
The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…
Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly concerned by the…
This paper continue earlier investigations on the decay of Burgers turbulence in one dimension from Gaussian random initial conditions of the power-law spectral type $E_0(k)\sim|k|^n$. Depending on the power $n$, different characteristic…
Using the negative binomial distribution (NBD) and the generalized Glauber-Lachs (GGL) formula, we analyze the data on charged multiplicity distributions in the several pseudorapidity intervals |\eta| < \eta_c at 0.2 - 7 TeV by UA5 and…
This review is intended to give a pedagogical and unified view on the subject of the statistics and scaling of physical quantities in disordered electron systems at very low temperatures. Quantum coherence at low temperatures and randomness…
In an early paper (Horowitz and Albano, Phys. Rev. E.,{\bf 73} 031111 (2006)) we studied growing models, generically called $X/RD$, such that a particle is attached to the aggregate with probability $p$ following the mechanisms of a generic…
Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…
Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems has been reported. Inspired by these results, we explore the KPZ scaling in…