相关论文: Coppersmith's lattices and "focus groups": an atta…
Instruction tuning has underscored the significant potential of large language models (LLMs) in producing more human controllable and effective outputs in various domains. In this work, we focus on the data selection problem for…
We give a deterministic algorithm for solving the (1+eps)-approximate Closest Vector Problem (CVP) on any n dimensional lattice and any norm in 2^{O(n)}(1+1/eps)^n time and 2^n poly(n) space. Our algorithm builds on the lattice point…
Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However,…
This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a…
Optimization over low rank matrices has broad applications in machine learning. For large scale problems, an attractive heuristic is to factorize the low rank matrix to a product of two much smaller matrices. In this paper, we study the…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
Efficiently estimating energy expectation values of quantum lattice systems on quantum computers is a crucial subroutine for various quantum algorithms, which can lead to significant overhead due to the high measurement shot numbers…
Complex bases, along with direct-sums defined by rings of imaginary quadratic integers, induce algebraic lattices. In this work, we study such lattices and their reduction algorithms. Firstly, when the lattice is spanned over a two…
Key Encapsulation Mechanisms (KEMs) are a set of cryptographic techniques that are designed to provide symmetric encryption key using asymmetric mechanism (public key). In the current study, we concentrate on design and analysis of key…
We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the…
Failure-Directed Search (FDS) is a significant complete generic search algorithm used in Constraint Programming (CP) to efficiently explore the search space, proven particularly effective on scheduling problems. This paper analyzes FDS's…
Backdoor and data-poisoning attacks can flip predictions with tiny training corruptions, yet a sharp theory linking poisoning strength, overparameterization, and regularization is lacking. We analyze ridge least squares with an unpenalized…
In this note, we investigate how well we can reconstruct the best rank-$r$ approximation of a large matrix from a small number of its entries. We show that even if a data matrix is of full rank and cannot be approximated well by a low-rank…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
Physical attacks are serious threats to cryptosystems deployed in the real world. In this work, we propose a microarchitectural end-to-end attack methodology on generic lattice-based post-quantum key encapsulation mechanisms to recover the…
We study the Minimum Latency Submodular Cover problem (MLSC), which consists of a metric $(V,d)$ with source $r\in V$ and $m$ monotone submodular functions $f_1, f_2, ..., f_m: 2^V \rightarrow [0,1]$. The goal is to find a path originating…
Lokshtanov et al.~[STOC 2017] introduced \emph{lossy kernelization} as a mathematical framework for quantifying the effectiveness of preprocessing algorithms in preserving approximation ratios. \emph{$\alpha$-approximate reduction rules}…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…