English
Related papers

Related papers: General Hardness Amplification of Predicates and P…

200 papers

Tight and efficient neural network bounding is crucial to the scaling of neural network verification systems. Many efficient bounding algorithms have been presented recently, but they are often too loose to verify more challenging…

Machine Learning · Computer Science 2024-02-27 Alessandro De Palma , Harkirat Singh Behl , Rudy Bunel , Philip H. S. Torr , M. Pawan Kumar

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…

Data Structures and Algorithms · Computer Science 2019-09-04 Peyman Afshani , Rolf Fagerberg , David Hammer , Riko Jacob , Irina Kostitsyna , Ulrich Meyer , Manuel Penschuck , Nodari Sitchinava

We establish and fully characterize the multidimensional extension of the Stronger Central Sets Theorem. Additionally, we develop a polynomial generalization of this result. Our approach utilizes tools from the Algebra of the Stone-\v{C}ech…

Combinatorics · Mathematics 2025-10-31 Sayan Goswami , Sourav Kanti Patra

The goal of this paper is to introduce ideas and methodology of the generic case complexity to cryptography community. This relatively new approach allows one to analyze the behavior of an algorithm on ''most'' inputs in a simple and…

Computational Complexity · Computer Science 2008-02-27 Alex D. Myasnikov

In this paper, we consider a new type of urn scheme, where the selection probabilities are proportional to a weight function, which is linear but decreasing in the proportion of existing colours. We refer to it as the \emph{negatively…

Probability · Mathematics 2018-01-09 Antar Bandyopadhyay , Gursharn Kaur

Can a committee of weak reasoning-model calls reach the performance of much stronger models? We study verifier-backed committee search as inference-time boosting for reasoning language models. The mechanism is not simply that ``more agents…

Artificial Intelligence · Computer Science 2026-05-15 Varun Sunkaraneni , Pierfrancesco Beneventano , Riccardo Neumarker , Tomaso Poggio , Tomer Galanti

We prove the strong converse for the $N$-source Gaussian multiple access channel (MAC). In particular, we show that any rate tuple that can be supported by a sequence of codes with asymptotic average error probability less than one must lie…

Information Theory · Computer Science 2016-10-19 Silas L. Fong , Vincent Y. F. Tan

We derive novel sufficient conditions for convergence of Loopy Belief Propagation (also known as the Sum-Product algorithm) to a unique fixed point. Our results improve upon previously known conditions. For binary variables with…

Artificial Intelligence · Computer Science 2012-07-09 Joris Mooij , Hilbert Kappen

A recent sequence of works, initially motivated by the study of the nonlocal properties of entanglement, demonstrate that a source of information-theoretically certified randomness can be constructed based only on two simple assumptions:…

Quantum Physics · Physics 2013-06-25 Matthew Coudron , Thomas Vidick , Henry Yuen

There are several public key establishment protocols as well as complete public key cryptosystems based on allegedly hard problems from combinatorial (semi)group theory known by now. Most of these problems are search problems, i.e., they…

Group Theory · Mathematics 2007-05-23 Vladimir Shpilrain , Gabriel Zapata

We discuss the recently introduced concept of non-deterministic noiseless linear amplification, demonstrating that such an operation can only be performed perfectly with vanishing probability of success. We show that a weak measurement,…

Quantum Physics · Physics 2009-03-26 David Menzies , Sarah Croke

We present an algorithm, called Predict, for updating beliefs in causal networks quantified with order-of-magnitude probabilities. The algorithm takes advantage of both the structure and the quantification of the network and presents a…

Artificial Intelligence · Computer Science 2013-02-21 Moises Goldszmidt

As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify…

Computational Complexity · Computer Science 2024-09-11 Tal Herman , Guy Rothblum

Neural networks are often susceptible to minor perturbations in input that cause them to misclassify. A recent solution to this problem is the use of globally-robust neural networks, which employ a function to certify that the…

Programming Languages · Computer Science 2025-05-13 James Tobler , Hira Taqdees Syeda , Toby Murray

Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…

Information Theory · Computer Science 2010-06-03 Siu-Wai Ho

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…

Machine Learning · Computer Science 2016-05-30 Sanjeev Arora , Rong Ge , Frederic Koehler , Tengyu Ma , Ankur Moitra

We revisit known constructions of efficient learning algorithms from various notions of constructive circuit lower bounds such as distinguishers breaking pseudorandom generators or efficient witnessing algorithms which find errors of small…

Computational Complexity · Computer Science 2020-12-29 Ján Pich

In this paper, we prove a general hardness amplification scheme for optimization problems based on the technique of direct products. We say that an optimization problem $\Pi$ is direct product feasible if it is possible to efficiently…

Computational Complexity · Computer Science 2019-08-28 Elazar Goldenberg , Karthik C. S.

Strong converse theorems refer to the study of impossibility results in information theory. In particular, Mosonyi and Ogawa established a one-shot strong converse bound for quantum hypothesis testing [Comm. Math. Phys, 334(3), 2014], which…

Quantum Physics · Physics 2024-03-21 Hao-Chung Cheng , Li Gao

We provide two proofs of the compactness theorem for extensions of first-order logic based on team semantics. First, we build upon L\"uck's ultraproduct construction for team semantics and prove a suitable version of {\L}o\'s' Theorem.…

Logic · Mathematics 2025-01-24 Joni Puljujärvi , Davide Emilio Quadrellaro