Related papers: Scaling laws for nonlinear dynamical models of art…

In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body,…

Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…

This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of {\em…

Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale…

Scaling laws have been used to describe how large language model (LLM) performance scales with model size, training data size, or amount of computational resources. Motivated by the fact that neural quantum states (NQS) has increasingly…

Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language…

Many machine learning models based on neural networks exhibit scaling laws: their performance scales as power laws with respect to the sizes of the model and training data set. We use large-N field theory methods to solve a model recently…

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…

Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…

We present new scaling laws for the thrust production and power consumption of three-dimensional combined heaving and pitching hydrofoils by extending the three-dimensional pitching scaling laws introduced by Ayancik et al. (2019). New…

Scaling laws describe how model performance grows with data, parameters and compute. While large datasets can usually be collected at relatively low cost in domains such as language or vision, scientific machine learning is often limited by…

Neural scaling laws offer valuable insights for designing robust sequence processing architectures. While these laws have been extensively characterized in other modalities, their behavior in speech remains comparatively underexplored. In…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Causal inference and model interpretability research are gaining increasing attention, especially in the domains of healthcare and bioinformatics. Despite recent successes in this field, decorrelating features under nonlinear environments…

A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…

A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…

In the last few years there has been a growing interest in the use of symbolic models for the formal verification and control design of purely continuous or hybrid systems. Symbolic models are abstract descriptions of continuous systems…

In this review, we examine computational models that explore the role of neural oscillations in speech perception, spanning from early auditory processing to higher cognitive stages. We focus on models that use rhythmic brain activities,…

Large foundation models are typically trained on data from multiple domains, with the data mixture--the proportion of each domain used--playing a critical role in model performance. The standard approach to selecting this mixture relies on…

Scaling laws aim to accurately predict model performance across different scales. Existing scaling-law studies almost exclusively rely on cross-entropy as the evaluation metric. However, cross-entropy provides only a partial view of…