相关论文: Domain size asymptotics for Markov logic networks
Knowledge Bases (KBs) are easy to query, verifiable, and interpretable. They however scale with man-hours and high-quality data. Masked Language Models (MLMs), such as BERT, scale with computing power as well as unstructured raw text data.…
We analyze the asymptotic properties of a Euclidean optimization problem on the plane. Specifically, we consider a network with three bins and $n$ objects spatially uniformly distributed, each object being allocated to a bin at a cost…
We consider continuous relational structures with finite domain $[n] := \{1, \ldots, n\}$ and a many valued logic, $CLA$, with values in the unit interval and which uses continuous connectives and continuous aggregation functions. $CLA$…
The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to…
Large language models generate text through probabilistic sampling from high-dimensional distributions, yet how this process reshapes the structural statistical organization of language remains incompletely characterized. Here we show that…
Let $\boldsymbol W=\{\boldsymbol W_n:n\in\mathbb N\}$ be a sequence of random vectors in $\mathbb R^d$, $d\ge 1$. This paper considers the logarithmic asymptotics of the extremes of $\boldsymbol W$, that is, for any vector $\boldsymbol…
This article initiates the semantic study of distribution-free normal modal logic systems, laying the semantic foundations and anticipating further research in the area. The article explores roughly the same area, though taking a different…
Research on mental state reasoning in language models (LMs) has the potential to inform theories of human social cognition--such as the theory that mental state reasoning emerges in part from language exposure--and our understanding of LMs…
With the rapid advancement of large language models (LLMs) for handling complex language tasks, an increasing number of studies are employing LLMs as agents to emulate the sequential decision-making processes of humans often represented as…
This paper introduces the Quantified Boolean Bayesian Network (QBBN), which provides a unified view of logical and probabilistic reasoning. The QBBN is meant to address a central problem with the Large Language Model (LLM), which has become…
While Large Language Models (LLMs) are widely documented to be sensitive to minor prompt perturbations and prone to sycophantic alignment, their robustness in consequential, rule-bound decision-making remains under-explored. We uncover a…
Markov networks (MNs) are a powerful way to compactly represent a joint probability distribution, but most MN structure learning methods are very slow, due to the high cost of evaluating candidates structures. Dependency networks (DNs)…
Penalized $M-$estimators for logistic regression models have been previously study for fixed dimension in order to obtain sparse statistical models and automatic variable selection. In this paper, we derive asymptotic results for penalized…
It is becoming increasingly common to see large collections of network data objects -- that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based…
We investigate the asymptotic risk of a general class of overparameterized likelihood models, including deep models. The recent empirical success of large-scale models has motivated several theoretical studies to investigate a scenario…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
The "large p, small n" paradigm arises in microarray studies, where expression levels of thousands of genes are monitored for a small number of subjects. There has been an increasing demand for study of asymptotics for the various…
A generative probabilistic model for relational data consists of a family of probability distributions for relational structures over domains of different sizes. In most existing statistical relational learning (SRL) frameworks, these…
Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables…
The advancement of large language models (LLMs) for real-world applications hinges critically on enhancing their reasoning capabilities. In this work, we explore the reasoning abilities of large language models (LLMs) through their…