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Lukas Gehring

Publications and source records attributed to Lukas Gehring.

9 recordsLinked to original sources

Assessing LLM Text Detection in Educational Contexts: Does Human Contribution Affect Detection?

Recent advancements in Large Language Models (LLMs) and their increased accessibility have made it easier than ever for students to automatically generate texts, posing new challenges for educational institutions. To enforce norms of academic integrity and ensure students' learning, learning analytics methods to automatically detect LLM-generated text appear increasingly appealing. This paper benchmarks the performance of different state-of-the-art detectors in educational contexts, introducing a novel dataset, called Generative Essay Detection in Education (GEDE), containing over 900 student-written essays and over 12,500 LLM-generated essays from various domains. To capture the diversity of LLM usage practices in generating text, we propose the concept of contribution levels, representing students' contribution to a given assignment. These levels range from purely human-written texts, to slightly LLM-improved versions, to fully LLM-generated texts, and finally to active attacks on the detector by "humanizing" generated texts. We show that most detectors struggle to accurately classify texts of intermediate student contribution levels, like LLM-improved human-written texts. Detectors are particularly likely to produce false positives, which is problematic in educational settings where false suspicions can severely impact students' lives. Our dataset, code, and additional supplementary materials are publicly available at https://github.com/lukasgehring/Assessing-LLM-Text-Detection-in-Educational-Contexts.

cs.CL

PermRust: A Token-based Permission System for Rust

Permission systems which restrict access to system resources are a well-established technology in operating systems, especially for smartphones. However, as such systems are implemented in the operating system they can at most manage access on the process-level. Since moderns software often (re)uses code from third-parties libraries, a permission system for libraries can be desirable to enhance security. In this short-paper, we adapt concepts from capability systems building a novel theoretical foundation for permission system at the level of the programming language. This leads to PermRust, a token-based permission system for the Rust programming language as a zero cost abstraction on top of its type-system. With it access to system resources can be managed per library.

cs.PL

PrivTru: A Privacy-by-Design Data Trustee Minimizing Information Leakage

Data trustees serve as intermediaries that facilitate secure data sharing between independent parties. This paper offers a technical perspective on Data trustees, guided by privacy-by-design principles. We introduce PrivTru, an instantiation of a data trustee that provably achieves optimal privacy properties. Therefore, PrivTru calculates the minimal amount of information the data trustee needs to request from data sources to respond to a given query. Our analysis shows that PrivTru minimizes information leakage to the data trustee, regardless of the trustee's prior knowledge, while preserving the utility of the data.

cs.CR

Adaptive Mesh Refinement for arbitrary initial Triangulations

We introduce a simple initialization of the Maubach bisection routine for adaptive mesh refinement which applies to any conforming initial triangulation and terminates in linear time with respect to the number of initial vertices. We show that Maubach's routine with this initialization generates meshes that preserve shape regularity and satisfy the closure estimate needed for optimal convergence of adaptive schemes. Our ansatz allows for the intrinsic use of existing implementations.

math.NA

The Constant in the Theorem of Binev-Dahmen-DeVore-Stevenson and a Generalisation of it

A triangulation of a polytope into simplices is refined recursively. In every refinement round, some simplices which have been marked by an external algorithm are bisected and some others around also must be bisected to retain regularity of the triangulation. The ratio of the total number of marked simplices and the total number of bisected simplices is bounded from above. Binev, Dahmen and DeVore proved under a certain initial condition a bound that depends only on the initial triangulation. This thesis proposes a new way to obtain a better bound in any dimension. Furthermore, the result is proven for a weaker initial condition, invented by Alkämper, Gaspoz and Klöfkorn, who also found an algorithm to realise this condition for any regular initial triangulation. Supposably, it is the first proof for a Binev-Dahmen-DeVore theorem in any dimension with always practically realiseable initial conditions without an initial refinement. Additionally, the initialisation refinement proposed by Kossaczký and Stevenson is generalised, and the number of recursive bisections of one single simplex in one refinement round is bounded from above by twice the dimension, sharpening a result of Gallistl, Schedensack and Stevenson.

math.NA

PyExperimenter: Easily distribute experiments and track results

PyExperimenter is a tool to facilitate the setup, documentation, execution, and subsequent evaluation of results from an empirical study of algorithms and in particular is designed to reduce the involved manual effort significantly. It is intended to be used by researchers in the field of artificial intelligence, but is not limited to those.

cs.DC

A Strengthened Alexandrov Maximum Principle or Uniform Hölder Continuity for Solutions of the Monge--Ampère Equation with Bounded Right-Hand Side

This article is about the convex solution $u$ of the Monge--Ampère equation on an at least 2-dimensional open bounded convex domain with Dirichlet boundary data and nonnegative bounded right-hand side. For convex functions with zero boundary data, an Alexandrov maximum principle $|u(x)| \leq C \operatorname{dist}(x,\partialΩ)^α$ is equivalent to (uniform) Hölder continuity with the same constant and exponent. Convex $α$-Hölder continuous functions are $W^{1,p}$ for $p < 1/(1{-}α)$. We prove Hölder continuity with the exponent $α=2/n$ for $n \geq 3$ and any $α\in (0,1)$ for $n=2$, provided that the boundary data satisfy this Hölder continuity, and show that these bounds for the exponent are sharp. The only means is to bound the Hessian determinant of a certain explicit function on an $n$-dimensional cylinder and to use the comparison princple.

math.AP

Algorithm Selection on a Meta Level

The problem of selecting an algorithm that appears most suitable for a specific instance of an algorithmic problem class, such as the Boolean satisfiability problem, is called instance-specific algorithm selection. Over the past decade, the problem has received considerable attention, resulting in a number of different methods for algorithm selection. Although most of these methods are based on machine learning, surprisingly little work has been done on meta learning, that is, on taking advantage of the complementarity of existing algorithm selection methods in order to combine them into a single superior algorithm selector. In this paper, we introduce the problem of meta algorithm selection, which essentially asks for the best way to combine a given set of algorithm selectors. We present a general methodological framework for meta algorithm selection as well as several concrete learning methods as instantiations of this framework, essentially combining ideas of meta learning and ensemble learning. In an extensive experimental evaluation, we demonstrate that ensembles of algorithm selectors can significantly outperform single algorithm selectors and have the potential to form the new state of the art in algorithm selection.

cs.LG

Estimating the density of a set of primes with applications to group theory

We estimate the asymptotic density of the set $\bar{A}$ of primes $p$ satisfying the constraint that $p+1$ and $p-1$ have only one prime divisor larger than $3$. We also estimate the density of a maximal subset $\bar{B} \subset \bar{A}$ such that for $p_1, p_2 \in \bar{B}$ no common prime divisor of $p_1(p_1 + 1)(p_1 - 1)$ and $p_2 (p_2 + 1)(p_2 - 1)$ is larger than $3$. Assuming a generalized Hardy--Littlewood conjecture, we prove that for both $\bar{A}$ and $\bar{B}$ the number of elements lesser than $x$ is asymptotically equal to a constant times $ x / (\log x)^3$.

math.NT