Related papers: Scaling laws for nonlinear dynamical models of art…
The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so…
How do neural language models acquire a language's structure when trained for next-token prediction? We address this question by deriving theoretical scaling laws for neural network performance on synthetic datasets generated by the Random…
In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For…
Large Language Models (LLMs) have benefited enormously from scaling, yet these gains are bounded by five fundamental limitations: (1) hallucination, (2) context compression, (3) reasoning degradation, (4) retrieval fragility, and (5)…
Implementation is a common problem with feedback laws with distributed delays. This paper focuses on a specific aspect of the implementation problem for predictor-based feedback laws: the problem of the approximation of the predictor…
Understanding procedural language requires anticipating the causal effects of actions, even when they are not explicitly stated. In this work, we introduce Neural Process Networks to understand procedural text through (neural) simulation of…
Recent breakthroughs in large language model-driven autonomous agents have revealed that multi-agent collaboration often surpasses each individual through collective reasoning. Inspired by the neural scaling law--increasing neurons enhances…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
Large language models can now generate political messages as persuasive as those written by humans, raising concerns about how far this persuasiveness may continue to increase with model size. Here, we generate 720 persuasive messages on 10…
We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute…
In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fronts in a new genre of nonlinear sonic vacua with strongly non-local effects. Indeed, it is surprising that such models naturally arise in…
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a…
One's ability to learn a generative model of the world without supervision depends on the extent to which one can construct abstract knowledge representations that generalize across experiences. To this end, capturing an accurate…
Nonlinear control allocation is an important part of modern nonlinear dynamic inversion based flight control systems which require highly accurate model of aircraft aerodynamics. Generally, an accurately implemented onboard model determines…
Methods for constructing causal linear models from nonlinear dynamical systems through lifting linearization underpinned by Koopman operator and physical system modeling theory are presented. Outputs of a nonlinear control system, called…
We study analytically and numerically the problem of a nonlinear mechanical oscillator with additive noise in the absence of damping. We show that the amplitude, the velocity and the energy of the oscillator grow algebraically with time.…
Rhythmic fluctuations in acoustic energy and accompanying neuronal excitations in cortical oscillations are characteristic of human speech, yet whether a corresponding rhythmicity inheres in the articulatory movements that generate speech…
Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…
We examine a variety of numerical methods that arise when considering dynamical systems in the context of physics-based simulations of deformable objects. Such problems arise in various applications, including animation, robotics, control…
While language progresses through a sequence of semantic states, the underlying dynamics of this progression remain elusive. Here, we treat the semantic progression of written text as a stochastic trajectory in a high-dimensional state…