Related papers: A physical study of the LLL algorithm

Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D…

Since the invention of the famous LLL algorithm, lattice reduction has been an extremely useful tool in computational number theory. By construction, the LLL algorithm deals with lattices living in a vector space endowed with a positive…

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…

Unlearning in large language models (LLMs) aims to remove specified data, but its efficacy is typically assessed with task-level metrics like accuracy and perplexity. We show that these metrics can be misleading, as models can appear to…

The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is the most practical lattice reduction algorithm in digital communications. In this paper, several variants of the LLL algorithm with either lower theoretic complexity or fixed-complexity…

Supervised fine-tuning (SFT) is a critical step in aligning large language models (LLMs) with human instructions and values, yet many aspects of SFT remain poorly understood. We trained a wide range of base models on a variety of datasets…

We develop a framework for the rigorous analysis of focused stochastic local search algorithms. These are algorithms that search a state space by repeatedly selecting some constraint that is violated in the current state and moving to a…

Large Language Models (LLMs) display strikingly different generalization behaviors: supervised fine-tuning (SFT) often narrows capability, whereas reinforcement-learning (RL) tuning tends to preserve it. The reasons behind this divergence…

We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the…

We consider the stochastic sandpile model with uniform toppling rule on the integer line. During a uniform toppling, with probability $1/3$ one particle is sent to the right of the toppled vertex, with probability $1/3$ one particle is sent…

Although it is widely accepted that every system should be robust, in the sense that "small" violations of environment assumptions should lead to "small" violations of system guarantees, it is less clear how to make this intuitive notion of…

We study stochastic sandpile models with a height restriction in one and two dimensions. A site can topple if it has a height of two, as in Manna's model, but, in contrast to previously studied sandpiles, here the height (or number of…

Recently, Brandt, Maus and Uitto [PODC'19] showed that, in a restricted setting, the dependency of the complexity of the distributed Lov\'asz Local Lemma (LLL) on the chosen LLL criterion exhibits a sharp threshold phenomenon: They proved…

We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate $1$, sending two of its particles to neighbouring…

The Lopsided Lov\'{a}sz Local Lemma (LLLL) is a powerful probabilistic principle which has been used in a variety of combinatorial constructions. While originally a general statement about probability spaces, it has recently been…

We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can hypothesis test between high-dimensional probability measures. These functions are a…

As large language models (LLMs) are overwhelmingly more and more integrated into various applications, ensuring they generate safe responses is a pressing need. Previous studies on alignment have largely focused on general…

Locality-sensitive hashing (LSH) is a fundamental technique for similarity search and similarity estimation in high-dimensional spaces. The basic idea is that similar objects should produce hash collisions with probability significantly…

There is an overwhelmingly large literature and algorithms already available on `large scale inference problems' based on different modeling techniques and cultures. Our primary goal in this paper is \emph{not to add one more new…

Federated learning (FL) has shown promising potential in safeguarding data privacy in healthcare collaborations. While the term "FL" was originally coined by the engineering community, the statistical field has also explored similar…