Related papers: Local Computation Algorithms for Knapsack: impossi…

Stochastic search algorithms are among the most sucessful approaches for solving hard combinatorial problems. A large class of stochastic search approaches can be cast into the framework of Las Vegas Algorithms (LVAs). As the run-time…

Non-local quantum computation (NLQC) replaces a local interaction between two systems with a single round of communication and shared entanglement. Despite many partial results, it is known that a characterization of entanglement cost in at…

In this paper the approach to solving several combinatorial optimization problems using the local search and the genetic algorithm techniques is proposed. Initially this approach was developed in purpose to overcome some difficulties…

The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set…

Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…

Canonical Correlation Analysis (CCA) is a widely used spectral technique for finding correlation structures in multi-view datasets. In this paper, we tackle the problem of large scale CCA, where classical algorithms, usually requiring…

We introduce the notion of Local Computation Mechanism Design - designing game theoretic mechanisms which run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the…

We develop a novel mathematical programming approximation framework to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select…

Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods.…

Longest Common Subsequence ($LCS$) deals with the problem of measuring similarity of two strings. While this problem has been analyzed for decades, the recent interest stems from a practical observation that considering single characters is…

We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…

We present a significant advancement in the field of Langevin Monte Carlo (LMC) methods by introducing the Inexact Proximal Langevin Algorithm (IPLA). This novel algorithm broadens the scope of problems that LMC can effectively address…

Deep neural networks (DNNs) often produce overconfident out-of-distribution predictions, motivating Bayesian uncertainty quantification. The Linearized Laplace Approximation (LLA) achieves this by linearizing the DNN and applying Laplace…

Gaussian variational inference and the Laplace approximation are popular alternatives to Markov chain Monte Carlo that formulate Bayesian posterior inference as an optimization problem, enabling the use of simple and scalable stochastic…

The Canonical Correlation Analysis (CCA) family of methods is foundational in multiview learning. Regularised linear CCA methods can be seen to generalise Partial Least Squares (PLS) and be unified with a Generalized Eigenvalue Problem…

Large language models (LLMs) face significant challenges in processing long contexts due to the linear growth of the key-value (KV) cache and quadratic complexity of self-attention. Existing approaches address these bottlenecks separately:…

Hybrid quantum-classical algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such…

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA)…

We call matrix algorithms superfast if they use much fewer flops and memory cells than the input matrix has entries. Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one…

We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. Suppose that the CSP has $n$ variables with domain size at most q, each constraint contains at most k…