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Nonlinear string vibration, in particular the case of nonplanar motion, has been an area of intense study for many years. Numerical simulation methods, essential for the comparison between measured data and theory, have received somewhat…

Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…

Scaling laws for large language models (LLMs) have provided useful guidance in training ever larger models for predictable performance gains. Time series forecasting shares a similar sequential structure to language, and is amenable to…

Scaling laws predict the loss of a target machine learning model by extrapolating from easier-to-train models with fewer parameters or smaller training sets. This provides an efficient way for practitioners and researchers alike to compare…

Bio-inspired flapping wings have been extensively studied for their remarkable aerodynamic performance. Recently, their noise emission has attracted growing interest, but a careful analysis of scaling laws for their sound generation is…

Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…

The requirement for identifying accurate system representations has not only been a challenge to fulfill, but it has compromised the scalability of formal methods, as the resulting models are often too complex for effective decision making…

Many mathematical models of synaptic plasticity have been proposed to explain the diversity of plasticity phenomena observed in biological organisms. These models range from simple interpretations of Hebb's postulate, which suggests that…

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…

One of the most important branches of nonlinear control theory is the so-called sliding-mode. Its aim is the design of a (nonlinear) feedback law that brings and maintains the state trajectory of a dynamic system on a given sliding surface.…

Scaling laws for language model training traditionally characterize how performance scales with model size and dataset volume. Prior work has explored architecture variants and data treatments such as dataset filtering and noise injection…

Low-precision training is critical for optimizing the trade-off between model quality and training costs, necessitating the joint allocation of model size, dataset size, and numerical precision. While empirical scaling laws suggest that…

Control of nonlinear uncertain systems is a common challenge in the robotics field. Nonlinear latent force models, which incorporate latent uncertainty characterized as Gaussian processes, carry the promise of representing such systems…

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

Steady-state models which have been learned from historical operational data may be unfit for model-based optimization unless correlations in the training data which are introduced by control are accounted for. Using recent results from…

Scaling up neural models has yielded significant advancements in a wide array of tasks, particularly in language generation. Previous studies have found that the performance of neural models frequently adheres to predictable scaling laws,…

Modern large language models (LLMs) represent a paradigm shift in what can plausibly be expected of machine learning models. The fact that LLMs can effectively generate sensible answers to a diverse range of queries suggests that they would…

It is increasingly considered that human speech perception and production both rely on articulatory representations. In this paper, we investigate whether this type of representation could improve the performances of a deep generative model…

We show that a scaling law exists for the near resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasi-classical phase-space representation of the quantum system with noise…

Empirically, large-scale deep learning models often satisfy a neural scaling law: the test error of the trained model improves polynomially as the model size and data size grow. However, conventional wisdom suggests the test error consists…