arXiv subjects

Andres Algaba

Publications and source records attributed to Andres Algaba.

At least 19 recordsLinked to original sources

arXiv2026

Shorter Reasoning, Earlier Answers? An Evaluation of Reasoning Interfaces

Large language models often reason at length before answering, increasing cost and latency. Prompts and trained settings can shorten this reasoning, but a shorter trace may only show that the model stopped sooner. Here, we evaluate paired runs of the same question at matched reasoning horizons across 198 GPQA Diamond and 500 MMLU-Pro questions. We test a numeric/concision prompt that announces a token limit for Qwen3-14B and the trained effort settings of gpt-oss-20b and -120b. The Qwen prompt shortens reasoning traces by 12-17%, while accuracy changes at matched token limits are small and mixed. A concise/early-answer instruction raises MMLU-Pro accuracy by 3.8 percentage points at 512 tokens, including +2.7 points when both runs are unfinished. Its gain at 2,048 tokens is uncertain. For gpt-oss, candidate-logit answers from completed low- and medium-effort reasoning are 14.5-26.3 points more accurate than matched-horizon high-effort answers. Most of the 512-token advantage comes from lower effort finishing earlier, while differences among unfinished runs are smaller and mixed. Wrong early answers often concentrate probability on the chosen option, so earlier stopping does not uniformly improve probability quality. In these tests, a tight deadline can favor lower effort or a concise instruction, whereas allowing high effort to finish can recover higher final accuracy. Evaluations should report correct completion before a deadline, the answer obtained when a run is stopped, differences among unfinished runs, and probability assigned to the correct answer separately.

cs.LG↗

arXiv2026

How Much Does a Reasoning Summary Reveal? An Observability Ladder for Large Language Models

Large language models often show users a final response and a short reasoning summary while the full reasoning trace stays hidden. We introduce an observability ladder that holds each completed run fixed and varies only what a reader inspects to judge whether the answer is correct: the response, a self-summary the model writes from the trace, the trace itself, and internal signals, each with and without the prompt. Across three benchmarks and five open-weight Qwen3 and gpt-oss models, we train matched linear correctness predictors on each access level. Without the prompt, summaries carry most of the trace's ranking signal (mean AUROC 0.774 versus 0.813) and add +0.156 over the response alone. With the prompt visible, the summary's gain collapses to +0.019, while the trace still adds +0.041. Even at equal length, the trace's last words predict correctness as well as summaries, or slightly better, and carry denser and more discriminative uncertainty and self-correction cues. On MMLU-Pro questions with both correct and incorrect runs, linear summary readers are near chance and trace readers retain only modest signal, both with and without the prompt (prompt-withheld AUROC 0.503-0.545 versus 0.544-0.590). With the prompt withheld, a GPT-5-mini reader recovers substantially more signal from both summaries and traces on gpt-oss-20b, and even then the trace keeps a small +0.034 advantage. Much of the linear readers' trace signal is associated with length. In the common case where users already hold the prompt, summaries are less helpful than the full trace for monitoring correctness. Monitorability is thus a joint property of the display and the reader, so any monitorability claim, including for faithfulness, should specify both.

cs.LG↗

arXiv2026

Geometric Configurations of Perturbed Jailbreak Prompts

Perturbation techniques that turn unsuccessful jailbreak prompts into successful ones are continuously evolving, constituting a major security threat to LLM safety. In this paper, we investigate the internal representations of such string-level perturbed jailbreak inputs in the small weight models of the Qwen-2.5-1.5B/-3B/-7B-Instruct and Llama-3.2-1B/-3B/-3.1-8B-Instruct families. We select two representation spaces: the last-layer-last-token embedding space and the top-50 next-token probability space. The former space separates prompts based on their spelling and format, while the latter space is effectively one-dimensional but appears more complex to cluster. Within our refusal-dominated answer set we find no behavioral hyperplane in either space. Only the next token "Sure" in the 1.5B Qwen model, and both tokens "," and "\.C\.C" in the 1$ Llama model, display a significant association with a compliant-labeled answer.

cs.CR↗

arXiv2026

Rebuttals Move Peer-Review Scores, but Initial-Review Structure Bounds the Movement

Author rebuttals are the main post-submission window in peer review, but their effect on reviewer scores remains hard to measure because score updates mix rebuttal content with initial score position, paper-level consensus, reviewer confidence, and discussion dynamics. We study ICLR 2024-2025 using 73,000 reviewer trajectories with externally archived pre- and post-rebuttal scores, and use LLMs only as measurement instruments. Gemini Flash 3.0 predicts implied pre-rebuttal scores from score-stripped review text. The resulting text-score offset predicts later movement, with score-increase rates rising from 8.3% when text reads below the assigned score to 31.9% when it reads above. Claude Opus 4.6 induces, and outcome-blinded Gemini Flash 3.0 validates, a 44-feature taxonomy of resolved reviewer-author exchanges, where 23 features replicate across model and held-out year under Bonferroni correction. In the rebuttal-engaged benchmark (n=6,705), initial-review structure already predicts much score movement (AUC=0.747, minimal AUC=0.696), while adding the resolved exchange raises AUC to 0.804. Rebuttals can move scores, but measurable movement is bounded by initial-review structure, and robust exchange signals are mostly rebuttal failure modes.

cs.DL↗

arXiv2026

Thinking Like a Scientist? A Structural Study of LLM-Generated Research Methods

Large Language Models (LLMs) are increasingly used to guide research methodology, yet their default methodological tendencies under minimal prompting remain unclear. Here, we prompt GPT-5.1, Gemini 3 Pro, and DeepSeek-V3.2 with an LLM-extracted research question from each of 1,000 recent arXiv computer-science papers and compare the resulting methodology suggestions against a paper-derived experimental inventory. Since we provide only the research question, the differences we measure reflect initial suggestions and not how optimal those suggestions are. We extract structured method features from both sources, map them into a shared taxonomy, and quantify divergence across multiple taxonomy dimensions including model provider, dataset task type, and evaluation metric type. The strongest imbalance appears in provider choice, with Jensen-Shannon divergence about 3-5x larger than any other taxonomy dimension. Other/Academic single-occurrence models are underrepresented by 23-24 percentage points, while reused academic/community models are slightly overrepresented (4-6pp). LLMs also suggest a much narrower range of methods overall: the effective number of model entities contracts from 1,232 to 59-96, and inter-LLM rank correlations (0.55-0.68) generally exceed LLM-to-paper correlations (0.33-0.56), so the distortions are largely shared across models. Popularity baselines, BM25 retrieval calibration, and paper-level similarity tests confirm that the outputs are query-specific responses, but filtered through a narrower set of options. Researchers who rely on LLM suggestions without cross-checking therefore risk narrowing their methodological search space toward a more concentrated default.

cs.CL↗

arXiv2026

On the Spectral Region of 4-Cycle Stochastic Matrices

We study the spectrum of 4-cycle row-stochastic matrices. For real eigenvalues the spectral region is [-1,1]. For nonreal eigenvalues a+ib we derive necessary conditions in terms of the real and imaginary parts, including the inequality a+|b| <= 1 and the condition (b^2+a^2+a)^2+2a^2-b^2 >= 0. We also prove conversely that every point in the corresponding interior region occurs as an eigenvalue of a 4-cycle matrix. The proof is organized through a reformulation of the characteristic equation, an argument parametrization, a convex-analytic criterion, and explicit boundary constructions. Hence, the spectral region for the 4-cycle row-stochastic matrices is exactly and explicitly determined.

math.SP↗

arXiv2026

Human-in-the-Loop LLM Grading for Handwritten Mathematics Assessments

Providing timely and individualised feedback on handwritten student work is highly beneficial for learning but difficult to achieve at scale. This challenge has become more pressing as generative AI undermines the reliability of take-home assessments, shifting emphasis toward supervised, in-class evaluation. We present a scalable, end-to-end workflow for LLM-assisted grading of short, pen-and-paper assessments. The workflow spans (1) constructing solution keys, (2) developing detailed rubric-style grading keys used to guide the LLM, and (3) a grading procedure that combines automated scanning and anonymisation, multi-pass LLM scoring, automated consistency checks, and mandatory human verification. We deploy the system in two undergraduate mathematics courses using six low-stakes in-class tests. Empirically, LLM assistance reduces grading time by approximately 23% while achieving agreement comparable to, and in several cases tighter than, fully manual grading. Occasional model errors occur but are effectively contained by the hybrid design. Overall, our results show that carefully embedded human-in-the-loop LLM grading can substantially reduce workload while maintaining fairness and accuracy.

cs.CY↗

arXiv2026

Scalable Classification of Course Information Sheets Using Large Language Models: A Reusable Institutional Method for Academic Quality Assurance

Purpose: Higher education institutions face increasing pressure to audit course designs for generative AI (GenAI) integration. This paper presents an end-to-end method for using large language models (LLMs) to scan course information sheets at scale, identify where assessments may be vulnerable to student use of GenAI tools, validate system performance through iterative refinement, and operationalise results through direct stakeholder communication and effort. Method: We developed a four-phase pipeline: (0) manual pilot sampling, (1) iterative prompt engineering with multi-model comparison, (2) full production scan of 4,684 Bachelor and Master course information sheets (Academic Year 2024-2025) from the Vrije Universiteit Brussel (VUB) with automated report generation and email distribution to teaching teams (91.4% address-matched) using a three-tier risk taxonomy (Clear risk, Potential risk, Low risk), and (3) longitudinal re-scan of 4,675 sheets after the next catalogue release. Results: Five iterations of prompt refinement achieved 87% agreement with expert labels. GPT-4o was selected for production based on superior handling of ambiguous cases involving internships and practical components. The Year 1 scan classified 60.3% of courses as Clear risk, 15.2% as Potential risk, and 24.5% as Low risk. Year 2 comparison revealed substantial shifts in risk distributions, with improvements most pronounced in practice-oriented programmes. Implications: The method enables institutions to rapidly transform heterogeneous catalogue data into structured and actionable intelligence. The approach is transferable to other audit domains (sustainability, accessibility, pedagogical alignment) and provides a template for responsible LLM deployment in higher education governance.

cs.LG↗

arXiv2026

Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)

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.

cs.AI↗

arXiv2026

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.

cs.LG↗

arXiv2026

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.

cs.LG↗

arXiv2026

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.

cs.AI↗

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

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

Decision-centric fairness: Evaluation and optimization for resource allocation problems

Data-driven decision support tools play an increasingly central role in decision-making across various domains. In this work, we focus on binary classification models for predicting positive-outcome scores and deciding on resource allocation, e.g., credit scores for granting loans or churn propensity scores for targeting customers with a retention campaign. Such models may exhibit discriminatory behavior toward specific demographic groups through their predicted scores, potentially leading to unfair resource allocation. We focus on demographic parity as a fairness metric to compare the proportions of instances that are selected based on their positive outcome scores across groups. In this work, we propose a decision-centric fairness methodology that induces fairness only within the decision-making region -- the range of relevant decision thresholds on the score that may be used to decide on resource allocation -- as an alternative to a global fairness approach that seeks to enforce parity across the entire score distribution. By restricting the induction of fairness to the decision-making region, the proposed decision-centric approach avoids imposing overly restrictive constraints on the model, which may unnecessarily degrade the quality of the predicted scores. We empirically compare our approach to a global fairness approach on multiple (semi-synthetic) datasets to identify scenarios in which focusing on fairness where it truly matters, i.e., decision-centric fairness, proves beneficial.

cs.LG↗

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↗

arXiv2025

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.

cs.LG↗

arXiv2025

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 reinforcement learning. 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 reasoning chain 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.

cs.LG↗