Related papers: Multiple-rank Modification of Symmetric Eigenvalue…
We propose a Riemannian optimization approach for computing low-rank solutions of the algebraic Riccati equation. The scheme alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is on the set of…
Algorithm configurators are automated methods to optimise the parameters of an algorithm for a class of problems. We evaluate the performance of a simple random local search configurator (ParamRLS) for tuning the neighbourhood size $k$ of…
We give a randomized $1+\frac{5.06}{\sqrt{k}}$-approximation algorithm for the minimum $k$-edge connected spanning multi-subgraph problem, $k$-ECSM.
Reinforcement Learning (RL) algorithms sample multiple n>1 solution attempts for each problem and reward them independently. This optimizes for pass@1 performance and prioritizes the strength of isolated samples at the expense of the…
Compression has emerged as one of the essential deep learning research topics, especially for the edge devices that have limited computation power and storage capacity. Among the main compression techniques, low-rank compression via matrix…
We present a dynamic algorithm for maintaining $(1+\epsilon)$-approximate maximum eigenvector and eigenvalue of a positive semi-definite matrix $A$ undergoing \emph{decreasing} updates, i.e., updates which may only decrease eigenvalues.…
Many testing problems are readily amenable to randomised tests such as those employing data splitting. However despite their usefulness in principle, randomised tests have obvious drawbacks. Firstly, two analyses of the same dataset may…
In this paper we present the first known deterministic algorithm for the construction of multiple rank-1 lattices for the approximation of periodic functions of many variables. The algorithm works by converting a potentially large…
We present a new algorithm for solving an eigenvalue problem for a real symmetric arrowhead matrix. The algorithm computes all eigenvalues and all components of the corresponding eigenvectors with high relative accuracy in $O(n^{2})$…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
This paper revisits the 2-approximation algorithm for $k$-MST presented by Garg in light of a recent paper of Paul et al.. In the $k$-MST problem, the goal is to return a tree spanning $k$ vertices of minimum total edge cost. Paul et al.…
Large Language Models have shown remarkable capabilities in the NLP domain. Their effectiveness can mainly be attributed to their ability to adapt to an array of downstream tasks. However, generally, full fine-tuning is a computationally…
A fast implicit QR algorithm for eigenvalue computation of low rank corrections of unitary matrices is adjusted to work with matrix pencils arising from polynomial zerofinding problems . The modified QZ algorithm computes the generalized…
This paper describes an efficient reduction of the learning problem of ranking to binary classification. The reduction guarantees an average pairwise misranking regret of at most that of the binary classifier regret, improving a recent…
Hyperparameter tuning is a common technique for improving the performance of neural networks. Most techniques for hyperparameter search involve an iterated process where the model is retrained at every iteration. However, the expected…
The quantum rate-distortion function plays a fundamental role in quantum information theory, however there is currently no practical algorithm which can efficiently compute this function to high accuracy for moderate channel dimensions. In…
The Subset Sum Ratio problem (SSR) asks, given a multiset $A$ of positive integers, to find two disjoint subsets of $A$ such that the largest-to-smallest ratio of their sums is minimized. In this paper we study the $k$-version of SSR,…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the…
We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O(log…