Related papers: Getting in the Zone for Successful Scalability
This paper derives "scaling laws"--empirical relationships between the training compute of Large Language Models (LLMs) and their performance--for economic outcomes. In a preregistered online experiment, 300 professional translators…
The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the…
In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with…
Causal Graph Dynamics generalize Cellular Automata, extending them to bounded degree, time varying graphs. The dynamics rewrite the graph at each time step with respect to two physics-like symmetries: causality (bounded speed of…
The Unified Modeling Language (UML) is a widely used general purpose modeling language. Together with the Object Constraint Language (OCL), formal models can be described by defining the structure and behavior with UML and additional OCL…
Stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear…
This paper reinterprets Amdahl's law in terms of execution time and applies this simple model to supercomputing. The systematic discussion results in practical formulas enabling to calculate expected running time using large number of…
In homogenization theory and multiscale modeling, typical functions satisfy the scaling law $f^{\epsilon}(x) = f(x,x/\epsilon)$, where $f$ is periodic in the second variable and $\epsilon$ is the smallest relevant wavelength,…
Generalized linear statistics are an unifying class that contains U-statistics, U-quantiles, L-statistics as well as trimmed and winsorized U-statistics. For example, many commonly used estimators of scale fall into this class.…
The multiprocessor effect refers to the loss of computing cycles due to processing overhead. Amdahl's law and the Multiprocessing Factor (MPF) are two scaling models used in industry and academia for estimating multiprocessor capacity in…
Cities play a pivotal role in human development and sustainability, yet studying them presents significant challenges due to the vast scale and complexity of spatial-temporal data. One such challenge is the need to uncover universal urban…
Scaling theory predicts complete localization in $d=2$ in quantum systems belonging to orthogonal class (i.e. with time-reversal symmetry and spin-rotation symmetry). The conductance $g$ behaves as $g \sim exp(-L/l)$ with system size $L$…
Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the…
Auto-scalability has become an evident feature for cloud software systems including but not limited to big data and IoT applications. Cloud application providers now are in full control over their applications' microservices and…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
Neural scaling laws have driven significant advancements in machine learning, particularly in domains like language modeling and computer vision. However, the exploration of neural scaling laws within robotics has remained relatively…
Ultrasonic motors (USMs) are commonly used in aerospace, robotics, and medical devices, where fast and precise motion is needed. Remarkably, sliding mode controller (SMC) is an effective controller to achieve precision motion control of the…
Dynamical universality plays a fundamental role in understanding the scaling properties of critical dynamics, including absorbing phase transitions and physical aging. Although individual universality classes have been extensively studied,…
Code Large Language Models (LLMs) are revolutionizing software engineering. However, scaling laws that guide the efficient training are predominantly analyzed on Natural Language (NL). Given the fundamental differences like strict syntax…
The universal scaling behavior is studied for nonequilibrium transport through a quantum dot. To describe the dot we use the standard Anderson impurity model and use the non-equilibrium non-crossing approximation in the limit of infinite…