相关论文: Quadratic Term Correction on Heaps' Law
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…
We show that the geometric relations between semantic features in large language models' hidden states closely mirror human psychological associations. We construct feature vectors corresponding to 360 words and project them on 32 semantic…
Even though quantum chromodynamics is a broken conformal theory, the AdS/CFT correspondence has led to important insights into the properties of QCD. For example, as shown by Polchinski and Strassler, dimensional counting rules for the…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
We propose and support the possibility that the shape of topological density 2-point function in pure-glue QCD is crucially, and possibly entirely, determined by the space-time folding (geometry) of the double-sheet sign-coherent structure…
Background: Zipf's law and Heaps' law are observed in disparate complex systems. Of particular interests, these two laws often appear together. Many theoretical models and analyses are performed to understand their co-occurrence in real…
In this paper, we study quadratic forms in spaces of holomorphic cusp forms. We show, conditionally, that when two quadratic forms in Hecke eigenforms share no common diagonal terms, their inner product is expected to converge to the sum of…
Identifying the statistical distribution that best fits citation data is important to allow robust and powerful quantitative analyses. Whilst previous studies have suggested that both the hooked power law and discretised lognormal…
Tokenization is a fundamental step in natural language processing (NLP) and other sequence modeling domains, where the choice of vocabulary size significantly impacts model performance. Despite its importance, selecting an optimal…
We examine the latest HERA experimental measurements of the $Q^2$ logarithmic derivative of the proton structure function. We analyze the characteristics of DGLAP with and without screening, as well as a Regge type model, and compare their…
Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a canonical nonlinear model: phase retrieval with anisotropic…
Semantic type mismatch between a noun and its context is central to coercion phenomena. This paper introduces a graph-based method to examine how lexical and contextual type information is reflected in word embeddings. We select nouns from…
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…
To any graph and smooth algebraic curve $C$ one may associate a "hypercurve" arrangement and one can study the rational homotopy theory of the complement $X$. In the rational case ($C=\mathbb{C}$), there is considerable literature on the…
The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the…
In the context of the Oppenheim-Horodecki paradigm of nonclassical correlation, a bipartite quantum state is (properly) classically correlated if and only if it is represented by a density matrix having a product eigenbasis. On the basis of…
Strongly correlated electron systems are generally described by tight binding lattice Hamiltonians with strong local (on site) interactions, the most popular being the Hubbard model. Although the half filled Hubbard model can be simulated…
Wall turbulence has a sublayer where one-point statistics, e.g., the mean velocity and the variances of some velocity fluctuations, vary logarithmically with the distance from the wall. This logarithmic scaling is found here for two-point…
Hierarchical vector field interpolation introduces a structured probabilistic framework for lexical representation, ensuring that word embeddings transition smoothly across a continuous manifold rather than being constrained to discrete…
A conclusive demonstration has been provided that the nature of the shear-thinning, that affects both film thickness and traction in EHL contacts, follows the ordinary power-law rule that has been described by many empirical models of which…