Related papers: On the Power of Statistical Zero Knowledge
Determinantal Point Processes (DPPs) are a widely used probabilistic model for negatively correlated sets. DPPs have been successfully employed in Machine Learning applications to select a diverse, yet representative subset of data. In…
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…
In this paper, we examine the impact of lexicalization on Question Answering over Linked Data (QALD). It is well known that one of the key challenges in interpreting natural language questions with respect to SPARQL lies in bridging the…
This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…
Humans use introspection to evaluate their understanding through private internal states inaccessible to external observers. We investigate whether large language models possess similar privileged knowledge about answer correctness,…
When formalizing proofs with interactive theorem provers, it often happens that extra background knowledge (declarative or procedural) about mathematical concepts is employed without the formalizer explicitly invoking it, to help the…
The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
In this paper,we consider a high-dimensional statistical estimation problem in which the the number of parameters is comparable or larger than the sample size. We present a unified analysis of the performance guarantees of exponential…
This paper introduces quantum analogues of non-interactive perfect and statistical zero-knowledge proof systems. Similar to the classical cases, it is shown that sharing randomness or entanglement is necessary for non-trivial protocols of…
This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
Extreme Classification (XC) aims to map a query to the most relevant documents from a very large document set. XC algorithms used in real-world applications learn this mapping from datasets curated from implicit feedback, such as user…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
While large language models (LLMs) excel at factual recall, the real challenge lies in knowledge application. A gap persists between their ability to answer complex questions and their effectiveness in performing tasks that require that…
The Sliding Window Lempel-Ziv (SWLZ) algorithm that makes use of recurrence times and match lengths has been studied from various perspectives in information theory literature. In this paper, we undertake a finer study of these quantities…
Random constraint satisfaction problems (CSPs) are known to exhibit threshold phenomena: given a uniformly random instance of a CSP with $n$ variables and $m$ clauses, there is a value of $m = \Omega(n)$ beyond which the CSP will be…
One of the most challenging question types in VQA is when answering the question requires outside knowledge not present in the image. In this work we study open-domain knowledge, the setting when the knowledge required to answer a question…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
Numerical Question Answering is the task of answering questions that require numerical capabilities. Previous works introduce general adversarial attacks to Numerical Question Answering, while not systematically exploring numerical…
The complexity class $\exists\mathbb R$, standing for the complexity of deciding the existential first order theory of the reals as real closed field in the Turing model, has raised considerable interest in recent years. It is well known…