Related papers: Coppersmith's lattices and "focus groups": an atta…
Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the…
Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem.…
Graph coarsening aims to diminish the size of a graph to lighten its memory footprint, and has numerous applications in graph signal processing and machine learning. It is usually defined using a reduction matrix and a lifting matrix,…
Lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This…
We address the problem of few-shot pattern detection, which aims to detect all instances of a given pattern, typically represented by a few exemplars, from an input image. Although similar problems have been studied in few-shot object…
Analyzing the security of cryptosystems under attacks based on the malicious modification of memory registers is a research topic of high importance. This type of attacks may affect the randomness of the secret parameters by forcing a…
The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eight-point algorithm and two-view projective bundle adjustment. The eight-point algorithm first computes a simple linear least…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
The MinRank (MR) problem is a computational problem that arises in many cryptographic applications. In Verbel et al. (PQCrypto 2019), the authors introduced a new way to solve superdetermined instances of the MinRank problem, starting from…
Large language models (LLMs) have demonstrated remarkable performance across a wide range of tasks. However, the quadratic complexity of softmax attention remains a central bottleneck that limits their scalability. Alman and Song (NeurIPS…
Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
Let $k$ and $n$ be positive integers. Define $R(n,k)$ to be the minimum positive value of $$ | e_i \sqrt{s_1} + e_2 \sqrt{s_2} + ... + e_k \sqrt{s_k} -t | $$ where $ s_1, s_2, ..., s_k$ are positive integers no larger than $n$, $t$ is an…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…
Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…
Recently, Sharma et al. suggested a method called Layer-SElective-Rank reduction (LASER) which demonstrated that pruning high-order components of carefully chosen LLM's weight matrices can boost downstream accuracy -- without any…
Query rewriting, the process of transforming queries into semantically equivalent yet more efficient variants, is crucial for database optimization. Existing solutions predominantly rely on either rule-based heuristics or Large Language…
The Implicit Factorization Problem was first introduced by May and Ritzenhofen at PKC'09. This problem aims to factorize two RSA moduli $N_1=p_1q_1$ and $N_2=p_2q_2$ when their prime factors share a certain number of least significant bits…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…