Vincent Ginis

Marthe Ballon, Brecht Verbeken, Vincent Ginis et al.

Large language models (LLMs) increasingly solve difficult problems by producing "reasoning traces" before emitting a final response. However, it remains unclear how accuracy and decision commitment evolve along a reasoning trajectory, and whether intermediate trace segments provide answer-relevant information beyond generic length or stylistic effects. Here, we propose a protocol to systematically probe the trajectories of reasoning traces in LLMs by 1) generating a model's reasoning trace, 2) truncating it at fixed token-percentiles, and 3) injecting each partial trace back into the model (or a different model) to measure the induced distribution over answer choices via next-token probabilities. We apply this protocol to the open-source Qwen3-4B/-8B/-14B and gpt-oss-20b/-120b models across the multiple-choice GPQA Diamond and MMLU-Pro benchmarks. We find that accuracy and decision commitment consistently increase as the percentage of provided reasoning tokens grows. These gains are primarily driven by relevant content in the model generation rather than context length or generic "reasoning style" effects. Stronger models often backtrack successfully from incorrect partial traces, but immediate answers often remain anchored in the weaker model's incorrect response. More broadly, we show that trajectory probing provides diagnostics for efficient and safer deployment of reasoning models as the measurements can inform practical trace-handling and monitoring policies that improve reliability without assuming intermediate tokens are inherently faithful explanations.

Melika Mobini, Vincent Holst, Floriano Tori et al.

Large language models are increasingly used to curate bibliographies, raising the question: are their reference lists distinguishable from human ones? We build paired citation graphs, ground truth and GPT-4o-generated (from parametric knowledge), for 10,000 focal papers ($\approx$ 275k references) from SciSciNet, and added a field-matched random baseline that preserves out-degree and field distributions while breaking latent structure. We compare (i) structure-only node features (degree/closeness/eigenvector centrality, clustering, edge count) with (ii) 3072-D title/abstract embeddings, using an RF on graph-level aggregates and Graph Neural Networks with node features. Structure alone barely separates GPT from ground truth (RF accuracy $\approx$ 0.60) despite cleanly rejecting the random baseline ($\approx$ 0.89--0.92). By contrast, embeddings sharply increase separability: RF on aggregated embeddings reaches $\approx$ 0.83, and GNNs with embedding node features achieve 93\% test accuracy on GPT vs.\ ground truth. We show the robustness of our findings by replicating the pipeline with Claude Sonnet 4.5 and with multiple embedding models (OpenAI and SPECTER), with RF separability for ground truth vs.\ Claude $\approx 0.77$ and clean rejection of the random baseline. Thus, LLM bibliographies, generated purely from parametric knowledge, closely mimic human citation topology, but leave detectable semantic fingerprints; detection and debiasing should target content signals rather than global graph structure.

Marthe Ballon, Andres Algaba, Brecht Verbeken et al.

Benchmarks are important tools to track progress in the development of Large Language Models (LLMs), yet inaccuracies in datasets and evaluation methods consistently undermine their effectiveness. Here, we present Omni-MATH-2, a manually revised version of the Omni-MATH dataset comprising a clean, exact-answer subset ($n{=}4181$) and a tagged, non-standard subset ($n{=}247$). Each problem was audited to ensure LaTeX compilability, solvability and verifiability, which involved adding missing figures or information, labeling problems requiring a proof, estimation or image, and removing clutter. This process significantly reduces dataset-induced noise, thereby providing a more precise assessment of model performance. The annotated dataset also allows us to evaluate judge-induced noise by comparing GPT-5 mini with the original Omni-Judge, revealing substantial discrepancies between judges on both the clean and tagged problem subsets. Expert annotations reveal that Omni-Judge is wrong in $96.4\%$ of the judge disagreements, indicating its inability to differentiate between models' abilities, even well before saturation of the benchmark occurs. As problems become more challenging, we find that increasingly competent judges become essential in order to prevent judge errors from masking genuine differences between models. Finally, neither judge identifies the present failure modes for the subset of tagged problems, demonstrating that dataset quality and judge reliability are both critical to develop accurate benchmarks of model performance.

Floriano Tori, Lorenzo Bini, Marco Sorbi et al.

Curvature notions on graphs provide a theoretical description of graph topology, highlighting bottlenecks and denser connected regions. Artifacts of the message passing paradigm in Graph Neural Networks, such as oversmoothing and oversquashing, have been attributed to these regions. However, it remains unclear how the topology of a graph interacts with the learned preferences of GNNs. Through Massive Activations, which correspond to extreme edge activation values in Graph Transformers, we probe this correspondence. Our findings on synthetic graphs and molecular benchmarks reveal that MAs do not preferentially concentrate on curvature extremes, despite their theoretical link to information flow. On the Long Range Graph Benchmark, we identify a systemic \textit{curvature shift}: global attention mechanisms exacerbate topological bottlenecks, drastically increasing the prevalence of negative curvature. Our work reframes curvature as a diagnostic probe for understanding when and why graph learning fails.

Seorin Kim, Vincent Holst, Vincent Ginis

Scientific abstracts are increasingly used as primary data in computational metascience research, yet the quality of these abstracts in widely used bibliographic databases has not been systematically examined. We assess the integrity of 10,000 randomly sampled English-language journal abstracts from OpenAlex using a two-stage annotation protocol combining human expert review and large language model classification. We identify seven distinct failure modes and find that 12\% of abstracts have integrity issues, with insufficient content and misplaced metadata being the most prevalent. We discuss implications for downstream research and describe a forthcoming community portal to support collective annotation efforts.

Bert Verbruggen, Arne Vanhoyweghen, Vincent Ginis

Reinforcement Learning (RL) remains a central optimisation framework in machine learning. Although RL agents can converge to optimal solutions, the definition of ``optimality'' depends on the environment's statistical properties. The Bellman equation, central to most RL algorithms, is formulated in terms of expected values of future rewards. However, when ergodicity is broken, long-term outcomes depend on the specific trajectory rather than on the ensemble average. In such settings, the ensemble average diverges from the time-average growth experienced by individual agents, with expected-value formulations yielding systematically suboptimal policies. Prior studies demonstrated that traditional RL architectures fail to recover the true optimum in non-ergodic environments. We extend this analysis to deep RL implementations and show that these, too, produce suboptimal policies under non-ergodic dynamics. Introducing explicit time dependence into the learning process can correct this limitation. By allowing the network's function approximation to incorporate temporal information, the agent can estimate value functions consistent with the process's intrinsic growth rate. This improvement does not require altering the environmental feedback, such as reward transformations or modified objective functions, but arises naturally from the agent's exposure to temporal trajectories. Our results contribute to the growing body of research on reinforcement learning methods for non-ergodic systems.

Brecht Verbeken, Brando Vagenende, Marie-Anne Guerry et al.

Large Language Models (LLMs) are increasingly used as scientific copilots, but evidence on their role in research-level mathematics remains limited, especially for workflows accessible to individual researchers. We present early evidence for vibe-proving with a consumer subscription LLM through an auditable case study that resolves Conjecture 20 of Ran and Teng (2024) on the exact nonreal spectral region of a 4-cycle row-stochastic nonnegative matrix family. We analyze seven shareable ChatGPT-5.2 (Thinking) threads and four versioned proof drafts, documenting an iterative pipeline of generate, referee, and repair. The model is most useful for high-level proof search, while human experts remain essential for correctness-critical closure. The final theorem provides necessary and sufficient region conditions and explicit boundary attainment constructions. Beyond the mathematical result, we contribute a process-level characterization of where LLM assistance materially helps and where verification bottlenecks persist, with implications for evaluation of AI-assisted research workflows and for designing human-in-the-loop theorem proving systems.