相关论文: Analytic trajectory bootstrap for matrix models

The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter ($\Omega$) that determines the boundary conditions.…

Statistical inference of the dependence between objects often relies on covariance matrices. Unless the number of features (e.g. data points) is much larger than the number of objects, covariance matrix cleaning is necessary to reduce…

The integration of large language models (LLMs) with external tools has significantly expanded the capabilities of AI agents. However, as the diversity of both LLMs and tools increases, selecting the optimal model-tool combination becomes a…

This work analyzes singular-value spectra of weight matrices in pretrained transformer models to understand how information is stored at both ends of the spectrum. Using Random Matrix Theory (RMT) as a zero information hypothesis, we…

The (classical) truncated moment problem, extensively studied by Curto and Fialkow, asks to characterize when a finite sequence of real numbers indexes by words in commuting variables can be represented with moments of a positive Borel…

Given (orthonormal) approximations $\tilde{U}$ and $\tilde{V}$ to the left and right subspaces spanned by the leading singular vectors of a matrix $A$, we discuss methods to approximate the leading singular values of $A$ and study their…

The distances between words calculated in word units are studied and compared with the distributions of the Random Matrix Theory (RMT). It is found that the distribution of distance between the same words can be well described by the…

In this paper, we consider establishing a formal connection between two distinct tree-abstraction problems inspired by the information-bottleneck (IB) method. Specifically, we consider the hard- and soft-constrained formulations that have…

Exact formulas for the singularities of the dynamical structure factor, S^{zz}(q,omega), of the S=1/2 xxz spin chain at all q and any anisotropy and magnetic field in the critical regime are derived, expressing the exponents in terms of the…

We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework.…

Binary vulnerability analysis is increasingly performed by LLM-based agents in an iterative, multi-pass manner, with the model as the core decision-maker. However, how such systems organize exploration over hundreds of reasoning steps…

Conformal field theories that exhibit spontaneous breaking of conformal symmetry (a moduli space of vacua) must satisfy a set of bootstrap constraints, involving the usual data (scaling dimensions and OPE coefficients) as well as new data…

We study a model for nonperturbative unitarization of the four-point contact scalar amplitude in four dimensions. It is defined through an infinite sum of planar diagrams, constructed using two-particle unitarity and crossing symmetry. We…

The D0-brane/Banks-Fischler-Shenker-Susskind matrix theory is a strongly coupled quantum system with an interesting gravity dual. We develop a scheme to derive bootstrap bounds on simple correlators in the matrix theory at infinite $N$ at…

The S-matrix bootstrap is extended to a 1+1d theory with $O(N)$ symmetry and a boundary in what we call the R-matrix bootstrap since the quantity of interest is the reflection matrix (R-matrix). Given a bulk S-matrix, the space of allowed…

Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…

By the unitarity cut method, analytic expressions of one-loop coefficients have been given in spinor forms. In this paper, we present one-loop coefficients of various bases in Lorentz-invariant contraction forms of external momenta. Using…

This study presents the applicability of conventional deep recurrent neural networks (RNN) to predict path-dependent plasticity associated with material heterogeneity and anisotropy. Although the architecture of RNN possesses inductive…

The integrability-based solution of string theories related to AdS(n)/CFT(n-1) dualities relies on the worldsheet S matrix. Using generalized unitarity we construct the terms with logarithmic dependence on external momenta at one- and…

Recent advances in natural language processing highlight two key factors for improving reasoning in large language models (LLMs): (i) allocating more test-time compute tends to help on harder problems but often introduces redundancy in the…