Related papers: On the Power of Statistical Zero Knowledge
Recent advances in the study of voting classification algorithms have brought empirical and theoretical results clearly showing the discrimination power of ensemble classifiers. It has been previously argued that the search of this…
We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…
In the well-known complexity class NP are combinatorial problems, whose optimization counterparts are important for many practical settings. These problems typically consider full knowledge about the input. In practical settings, however,…
One-way functions are a very important notion in the field of classical cryptography. Most examples of such functions, including factoring, discrete log or the RSA function, can be, however, inverted with the help of a quantum computer. In…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called…
We study uniform computability properties of PAC learning using Weihrauch complexity. We focus on closed concept classes, which are either represented by positive, by negative or by full information. Among other results, we prove that…
We prove two sets of results concerning computational complexity classes. The first concerns a variation of the random oracle hypothesis posed by Bennett and Gill after they showed that relative to a randomly chosen oracle, P not equal NP…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a…
Learning scientific document representations can be substantially improved through contrastive learning objectives, where the challenge lies in creating positive and negative training samples that encode the desired similarity semantics.…
Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…
When users query proprietary LLM APIs, they receive outputs with no cryptographic assurance that the claimed model was actually used. Service providers could substitute cheaper models, apply aggressive quantization, or return cached…
We study the matrix completion problem that leverages hierarchical similarity graphs as side information in the context of recommender systems. Under a hierarchical stochastic block model that well respects practically-relevant social…
A proof is concurrent zero-knowledge if it remains zero-knowledge when many copies of the proof are run in an asynchronous environment, such as the Internet. It is known that zero-knowledge is not necessarily preserved in such an…
Zero-knowledge succinct non-interactive argument of knowledge (zkSNARK) allows a party, known as the prover, to convince another party, known as the verifier, that he knows a private value $v$, without revealing it, such that $F(u,v)=y$ for…
We introduce some classical complexity-theoretic techniques to Parameterized Complexity. First, we study relativization for the machine models that were used by Chen, Flum, and Grohe (2005) to characterize a number of parameterized…
The communication class $\mathbf{UPP}^{\text{cc}}$ is a communication analog of the Turing Machine complexity class $\mathbf{PP}$. It is characterized by a matrix-analytic complexity measure called sign-rank (also called dimension…
Our main results are in the following three sections: 1. We prove new relations between proof complexity conjectures that are discussed in \cite{pu18}. 2. We investigate the existence of p-optimal proof systems for $\mathsf{TAUT}$, assuming…
A classical result in descriptive complexity theory states that Datalog expresses exactly the class of polynomially computable queries on ordered databases. In this paper we extend this result to the case of higher-order Datalog. In…