相关论文: LLL & ABC
Large language models (LLMs) are increasingly used in statistical research and applications. However,they are also notorious for unreliable or biased information. Here, we explore whether LLMs can be used to improve the precision of…
The Lopsided Lovasz Local Lemma (LLLL) is a cornerstone probabilistic tool for showing that it is possible to avoid a collection of "bad" events as long as their probabilities and interdependencies are sufficiently small. The strongest…
Factors are a foundational component of legal analysis and computational models of legal reasoning. These factor-based representations enable lawyers, judges, and AI and Law researchers to reason about legal cases. In this paper, we…
Three publicly-available LLM specifically designed for legal tasks have been implemented and shown that classification accuracy can benefit from training over legal corpora, but why and how? Here we use two publicly-available legal…
The Casas-Alvero conjecture predicts that every univariate polynomial over a field of characteristic zero having a common factor with each of its derivatives $H_i(f)$ is a power of a linear polynomial. One approach to proving the conjecture…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
The probabilistic method is a technique for proving combinatorial existence results by means of showing that a randomly chosen object has the desired properties with positive probability. A particularly powerful probabilistic tool is the…
With recent advances, neural models can achieve human-level performance on various natural language tasks. However, there are no guarantees that any explanations from these models are faithful, i.e. that they reflect the inner workings of…
In this paper (propositional) probability logic ($PL$) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for $\sigma$-additive probability models, and subsequently when this class of…
We provide a simplified form of Primal Augmented Lagrange Multiplier algorithm. We intend to fill the gap in the steps involved in the mathematical derivations of the algorithm so that an insight into the algorithm is made. The experiment…
A comparison of Landin's form of lambda calculus with Church's shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the…
The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…
Some explanations to Kaldi's PLDA implementation to make formula derivation easier to catch.
Large Language Models (LLMs) are becoming very popular and are used for many different purposes, including creative tasks in the arts. However, these models sometimes have trouble with specific reasoning tasks, especially those that involve…
In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…
We apply recent ideas about complexity and randomness to the philosophy of laws and chances. We develop two ways to use algorithmic randomness to characterize probabilistic laws of nature. The first, a generative chance* law, employs a…
Various properties of relative entropy have led to its widespread use in information theory. These properties suggest that relative entropy has a role to play in systems that attempt to perform inference in terms of probability…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
The Lov\'{a}sz Local Lemma (LLL) is a keystone principle in probability theory, guaranteeing the existence of configurations which avoid a collection $\mathcal B$ of "bad" events which are mostly independent and have low probability. In its…
The Lovasz Local Lemma (LLL) is a probabilistic tool which has been used to show the existence of a variety of combinatorial structures with good "local" properties. The "LLL-distribution" can be used to show that the resulting structures…