Probing the Trajectories of Reasoning Traces in Large Language Models

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.

Structurally Human, Semantically Biased: Detecting LLM-Generated References with Embeddings and GNNs

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.

Benchmarks Saturate When The Model Gets Smarter Than The Judge

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.

Model-Agnostic Solutions for Deep Reinforcement Learning in Non-Ergodic Contexts

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.

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.

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.

Flexible Counterfactual Explanations with Generative Models

Counterfactual explanations provide actionable insights to achieve desired outcomes by suggesting minimal changes to input features. However, existing methods rely on fixed sets of mutable features, which makes counterfactual explanations inflexible for users with heterogeneous real-world constraints. Here, we introduce Flexible Counterfactual Explanations, a framework incorporating counterfactual templates, which allows users to dynamically specify mutable features at inference time. In our implementation, we use Generative Adversarial Networks (FCEGAN), which align explanations with user-defined constraints without requiring model retraining or additional optimization. Furthermore, FCEGAN is designed for black-box scenarios, leveraging historical prediction datasets to generate explanations without direct access to model internals. Experiments across economic and healthcare datasets demonstrate that FCEGAN significantly improves counterfactual explanations' validity compared to traditional benchmark methods. By integrating user-driven flexibility and black-box compatibility, counterfactual templates support personalized explanations tailored to user constraints.

The Relationship Between Reasoning and Performance in Large Language Models -- o3 (mini) Thinks Harder, Not Longer

Large language models have demonstrated remarkable progress in mathematical reasoning, leveraging chain-of-thought and test-time compute scaling. However, many open questions remain regarding the interplay between reasoning token usage and accuracy gains. In particular, when comparing models across generations, it is unclear whether improved performance results from longer reasoning chains or more efficient reasoning. We systematically analyze chain-of-thought length across o1-mini and o3-mini variants on the Omni-MATH benchmark, finding that o3-mini (m) achieves superior accuracy without requiring longer reasoning chains than o1-mini. Moreover, we show that accuracy generally declines as reasoning chains grow across all models and compute settings, even when controlling for difficulty of the questions. This accuracy drop is significantly smaller in more proficient models, suggesting that new generations of reasoning models use test-time compute more effectively. Finally, we highlight that while o3-mini (h) achieves a marginal accuracy gain over o3-mini (m), it does so by allocating substantially more reasoning tokens across all problems, even the ones that o3-mini (m) can already solve. These findings provide new insights into the relationship between model capability and reasoning length, with implications for efficiency, scaling, and evaluation methodologies.

Humanity's Last Exam

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 3,000 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Early evidence of how LLMs outperform traditional systems on OCR/HTR tasks for historical records

We explore the ability of two LLMs -- GPT-4o and Claude Sonnet 3.5 -- to transcribe historical handwritten documents in a tabular format and compare their performance to traditional OCR/HTR systems: EasyOCR, Keras, Pytesseract, and TrOCR. Considering the tabular form of the data, two types of experiments are executed: one where the images are split line by line and the other where the entire scan is used as input. Based on CER and BLEU, we demonstrate that LLMs outperform the conventional OCR/HTR methods. Moreover, we also compare the evaluated CER and BLEU scores to human evaluations to better judge the outputs of whole-scan experiments and understand influential factors for CER and BLEU. Combining judgments from all the evaluation metrics, we conclude that two-shot GPT-4o for line-by-line images and two-shot Claude Sonnet 3.5 for whole-scan images yield the transcriptions of the historical records most similar to the ground truth.