相关论文: Quadratic Term Correction on Heaps' Law

While the problem of computing the genus of a knot is now fairly well understood, no algorithm is known for its four-dimensional variants, both in the smooth and in the topological locally flat category. In this article, we investigate a…

Representation learning plays a central role in structuring internal embeddings to capture the statistical properties of language, influencing the coherence and contextual consistency of generated text. Statistical Coherence Alignment is…

For positive definite matrices $A$ and $B$, the Araki-Lieb-Thirring inequality amounts to an eigenvalue log-submajorisation relation for fractional powers $$\lambda(A^t B^t) \prec_{w(\log)} \lambda^t(AB), \quad 0<t\le 1,$$ while for…

In this paper we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with…

We show that an endpoint overlap model can explain the scaling laws observed in exclusive hadronic reactions at large momentum transfer. The model assumes one of the valence quarks carries most of the hadron momentum. Hadron form factors…

Hawkes processes were first introduced to obtain microscopic models for the rough volatility observed in asset prices. Scaling limits of such processes leads to the rough-Heston model that describes the macroscopic behavior. Blanc et al.…

The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $\alpha$ (the…

Brain representations of curvature may be formed on the basis of either vision or touch. Experimental and theoretical work by the author and her colleagues has shown that the processing underlying such representations directly depends on…

A scaling analysis is undertaken for the load balance in sliding friction in the hydrodynamic lubrication regime, with a particular emphasis on power-law shear-thinning typical of a structured liquid. It is argued that the shear-thinning…

While vector-based language representations from pretrained language models have set a new standard for many NLP tasks, there is not yet a complete accounting of their inner workings. In particular, it is not entirely clear what aspects of…

The asymptotic dynamical correlation functions in one-dimensional spin chains are described by power-laws. The corresponding exponents characterize different bulk and boundary critical behavior. We present novel results for the logarithmic…

Does text have an intrinsic curvature? Language is increasingly modeled in curved geometries - hyperbolic spaces for hierarchy, mixed-curvature manifolds for compositional structure - yet a basic scientific question remains unresolved: what…

By a conformal string in Euclidean space is meant a closed critical curve with non-constant conformal curvatures of the conformal arclength functional. We prove that (1) the set of conformal classes of conformal strings is in 1-1…

We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…

Recently a number of empirical "universal" scaling law papers have been published, most notably by OpenAI. `Scaling laws' refers to power-law decreases of training or test error w.r.t. more data, larger neural networks, and/or more compute.…

We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One…

This TASI lecture covers the material in hep-th/9205026. It reviewed the theory of effective strings, with particular emphasis on the manner in which Lorentz invariance is represented. The quantum properties of an example of an effective…

The theory of quadrature domains for harmonic functions and the Hele-Shaw problem of the fluid dynamics are related subjects of the complex variables and mathematical physics. We present results generalizing the above subjects for elliptic…

We give an atomic decomposition of closed forms on R n , the coefficients of which belong to some Hardy space of Musielak-Orlicz type. These spaces are natural generalizations of weighted Hardy-Orlicz spaces, when the Orlicz function…

We investigate the convexity property on $(0,1)$ of the function $$f_a(x)=\frac{{\cal K}{(\sqrt x)}}{a-(1/2)\log(1-x)}.$$ We show that $f_a$ is strictly convex on $(0,1)$ if and only if $a\geq a_c$ and $1/f_a$ is strictly convex on $(0,1)$…