arXiv subjects

Brecht Verbeken

Publications and source records attributed to Brecht Verbeken.

24 records · Page 2Linked to original sources

arXiv2025

Eigenvalue regions and realising monotone stochastic matrices

Eigenvalues of stochastic matrices have been studied from two complementary perspectives. The individual eigenvalues are characterised through the well-established Karpelevich regions. The spectrum as a whole has also been analysed, yielding powerful results such as the Johnson-Loewy-London (JLL) inequalities. Current research now turns toward particular subsets of stochastic matrices, among others the doubly stochastic matrices. This paper studies spectral properties of monotone stochastic matrices which are characterised by the fact that each row stochastically dominates the preceding one, and which arise in contexts such as intergenerational mobility, equal-input models, and credit-rating systems. This paper analyses the dominance matrix associated with a monotone matrix, which is a non-negative matrix that preserves the non-trivial eigenvalues. Properties are established and the conditions are given under which a non-negative matrix can be regarded as a dominance matrix. In analogy with the stochastic matrices, this study examines for the monotone stochastic matrices both the individual eigenvalues as the spectrum as a whole. Individually, the eigenvalue region for all monotone matrices up till order 3 is completely determined, and realising matrices are provided. Collectively, the set of possible pairs of non-trivial eigenvalues arising from 3x3 monotone matrices is characterised, accompanied by realising matrices. In both perspectives, the resulting regions are substantially smaller than those for general stochastic matrices. Finally, this paper proves a reduction theorem stating that, for all n from 4 on, the eigenvalue region of n x n monotone matrices is contained within that of (n-1) x (n-1) stochastic matrices.

math.SP↗

arXiv2025

Estimating problem difficulty without ground truth using Large Language Model comparisons

Recent advances in the finetuning of large language models (LLMs) have significantly improved their performance on established benchmarks, emphasizing the need for increasingly difficult, synthetic data. A key step in this data generation pipeline is a method for estimating problem difficulty. Current approaches, such as human calibration or performance-based scoring, fail to generalize to out-of-distribution problems, i.e. problems currently unsolvable by humans and LLMs, because they are not scalable, time-consuming, and ground truth dependent. Therefore, we propose a new method for estimating problem difficulty, LLM compare, that addresses these limitations. An LLM performs pairwise difficulty comparisons, and then Bradley-Terry scores are computed based on the outcomes. To validate our method, we first propose a conceptual framework that positions existing approaches on three orthogonal planes--construction, scale and dependence--identifying which quadrants a measure needs to occupy to score out-of-distribution problems. LLM compare naturally occupies all desirable quadrants as the first measure that is continuous and dynamic, model-agnostic and independent of ground truth information. As a second validation, we show that LLM compare demonstrates strong alignment with human annotations: Pearson $r \geq 0.80$ for $n=1876$. Thirdly, we show that LLM compare is robust to hallucinations, with less than $6\%$ degradation in Pearson correlation for $10\%$ noise injection. Our work represents a significant step towards replacing time-consuming human annotations and synthetic data generation, and will be an important driver for curriculum design, model evaluation, and AI-assisted research ideation.

cs.LG↗

arXiv2025

Metro 3 in Brussels under uncertainty: scenario-based public transport accessibility analysis

Metro Line 3 in Brussels is one of Europe's most debated infrastructure projects, marked by escalating costs, delays, and uncertainty over completion. Yet no public accessibility appraisal exists to inform this policy debate. This paper provides a scenario-based assessment of the spatial and distributional accessibility impacts of Metro 3 using schedule-based public transport data. Official GTFS feeds from all regional operators were combined and adapted to represent three scenarios: (i) the current network, (ii) partial implementation of Metro 3 (conversion of the southern premetro section), and (iii) full implementation to Bordet. Accessibility was measured as public transport travel time between 647 evenly spaced 500 m points covering the Brussels-Capital Region. Simulations were conducted for morning, evening, and weekend midday periods, each with three departure times (t-10, t, t+10), capturing robustness to short-term timetable variation. Results show substantial but uneven accessibility gains, with the largest improvements occurring in neighborhoods with below-average incomes. Temporal robustness analysis highlights variability in accessibility outcomes, underscoring the need to account for uncertainty in departure timing. These findings suggest that Metro 3 has the potential to reduce socio-spatial inequalities in accessibility, providing transparent evidence for a project where public debate is dominated by cost concerns.

econ.GN↗

arXiv2025

Lexical Hints of Accuracy in LLM Reasoning Chains

Fine-tuning Large Language Models (LLMs) with reinforcement learning to produce an explicit Chain-of-Thought (CoT) before answering produces models that consistently raise overall performance on code, math, and general-knowledge benchmarks. However, on benchmarks where LLMs currently achieve low accuracy, such as Humanity's Last Exam (HLE), they often report high self-confidence, reflecting poor calibration. Here, we test whether measurable properties of the CoT provide reliable signals of an LLM's internal confidence in its answers. We analyze three feature classes: (i) CoT length, (ii) intra-CoT sentiment volatility, and (iii) lexicographic hints, including hedging words. Using DeepSeek-R1 and Claude 3.7 Sonnet on both Humanity's Last Exam (HLE), a frontier benchmark with very low accuracy, and Omni-MATH, a saturated benchmark of moderate difficulty, we find that lexical markers of uncertainty (e.g., $\textit{guess}$, $\textit{stuck}$, $\textit{hard}$) in the CoT are the strongest indicators of an incorrect response, while shifts in the CoT sentiment provide a weaker but complementary signal. CoT length is informative only on Omni-MATH, where accuracy is already high ($\approx 70\%$), and carries no signal on the harder HLE ($\approx 9\%$), indicating that CoT length predicts correctness only in the intermediate-difficulty benchmarks, i.e., inside the model's demonstrated capability, but still below saturation. Finally, we find that uncertainty indicators in the CoT are consistently more salient than high-confidence markers, making errors easier to predict than correct responses. Our findings support a lightweight post-hoc calibration signal that complements unreliable self-reported probabilities and supports safer deployment of LLMs.

cs.CL↗

arXiv2025

How Deep Do Large Language Models Internalize Scientific Literature and Citation Practices?

The spread of scientific knowledge depends on how researchers discover and cite previous work. The adoption of large language models (LLMs) in the scientific research process introduces a new layer to these citation practices. However, it remains unclear to what extent LLMs align with human citation practices, how they perform across domains, and may influence citation dynamics. Here, we show that LLMs systematically reinforce the Matthew effect in citations by consistently favoring highly cited papers when generating references. This pattern persists across scientific domains despite significant field-specific variations in existence rates, which refer to the proportion of generated references that match existing records in external bibliometric databases. Analyzing 274,951 references generated by GPT-4o for 10,000 papers, we find that LLM recommendations diverge from traditional citation patterns by preferring more recent references with shorter titles and fewer authors. Emphasizing their content-level relevance, the generated references are semantically aligned with the content of each paper at levels comparable to the ground truth references and display similar network effects while reducing author self-citations. These findings illustrate how LLMs may reshape citation practices and influence the trajectory of scientific discovery by reflecting and amplifying established trends. As LLMs become more integrated into the scientific research process, it is important to understand their role in shaping how scientific communities discover and build upon prior work.

cs.DL↗

arXiv2024

State Re-union Maintainability for Semi-Markov Models in Manpower Planning

In previous research the importance of both Markov and semi-Markov models in manpower planning is highlighted. Maintainability of population structures for different types of personnel strategies (i.e. under control by promotion and control by recruitment) were extensively investigated for various types of Markov models (homogeneous as well as non-homogeneous) (Bartholomew, 1967; Vassiliou and Tsantas, 1984a). Semi-Markov models are extensions of Markov models that account for duration of stay in the states. Less attention is paid to the study of maintainability for semi-Markov models. Although, some interesting maintainability results were obtained for non-homogeneous semi-Markov models (Vassiliou and Papadopoulou, 1992). The current paper focuses on discrete-time homogeneous semi-Markov models, and explores the concept of maintainable population structures in this setting for a system with constant total size or one with a growth factor. In particular, a new concept of maintainability is introduced, the so called State Re-union maintainability (SR-maintainability). Moreover, we show that, under certain conditions, the seniority-based paths associated with the SR-maintainable structures converge. This allows to characterize the convex set of SR-maintainable structures.

math.PR↗