Related papers: Analytic trajectory bootstrap for matrix models
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
Occupation of an interval by self-replicating initial pulses is studied numerically. Two different approximates in different categories are proposed for the numerical solutions of some initial-boundary value problems. The sinc differential…
Transformer models have achieved state-of-the-art results in a wide range of NLP tasks including summarization. Training and inference using large transformer models can be computationally expensive. Previous work has focused on one…
Lattices are an efficient and effective method to encode ambiguity of upstream systems in natural language processing tasks, for example to compactly capture multiple speech recognition hypotheses, or to represent multiple linguistic…
Consider a one dimensional simple random walk $X=(X_n)_{n\geq0}$. We form a new simple symmetric random walk $Y=(Y_n)_{n\geq0}$ by taking sums of products of the increments of $X$ and study the two-dimensional walk…
Recently, a growing body of research has focused on either optimizing CTR model architectures to better model feature interactions or refining training objectives to aid parameter learning, thereby achieving better predictive performance.…
Despite remarkable advances, large language models often fail at compositional reasoning tasks, a phenomenon exemplified by the ``curse of two-hop reasoning''. This paper introduces the Identity Bridge, a simple yet powerful mechanism that…
The estimation of various matrix integrals as the size of the matrices goes to infinity is motivated by theoretical physics, geometry and free probability questions. On a rigorous ground, only integrals of one matrix or of several matrices…
We study numerically the 6D (2,0) superconformal bootstrap using the soft-Actor-Critic (SAC) algorithm as a stochastic optimizer. We focus on the four-point functions of scalar superconformal primaries in the energy-momentum multiplet.…
We present a simple and robust technique to extract kinetic rate models and thermodynamic quantities from single molecule time traces. SMACKS (Single Molecule Analysis of Complex Kinetic Sequences) is a maximum likelihood approach that…
Learning the structure of dependencies among multiple random variables is a problem of considerable theoretical and practical interest. Within the context of Bayesian Networks, a practical and surprisingly successful solution to this…
Regge poles connect the analytic structure of scattering amplitudes, analytically continued in spin, to the high-energy limit in momentum space. Dual models are expected to have only Regge poles, and string theory suggests there should be…
We study an active Brownian run-and-tumble particle (ABRTP) model, that consists of an active Brownian run state during which the active velocity of the particle diffuses on the unit circle, and a tumble state during which the active…
We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity…
We model a set of point-to-point transports on a network as a system of polydisperse interacting self-avoiding walks (SAWs) over a finite square lattice. The ends of each SAW may be located both at random, uniformly distributed, positions…
This paper proposes a new model for extracting an interpretable sentence embedding by introducing self-attention. Instead of using a vector, we use a 2-D matrix to represent the embedding, with each row of the matrix attending on a…
We study two-point functions of single-trace half-BPS operators in the presence of a supersymmetric Wilson line in $\mathcal{N}=4$ SYM. We use inversion formula technology in order to reconstruct the CFT data starting from a single…
Long chain-of-thought (CoT) prompting helps Large Language Models (LLMs) solve difficult problems, but very long traces often slow or even degrade performance on fast, intuitive "System-1" tasks. We introduce Connector-Aware Compact CoT…
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…
We consider a stochastic process in which independent identically distributed random matrices are multiplied and where the Lyapunov exponent of the product is positive. We continue multiplying the random matrices as long as the norm,…