Is Mathematical Problem-Solving Expertise in Large Language Models Associated with Assessment Performance?

Large Language Models (LLMs) are increasingly used in math education not only as problem solvers but also as assessors of learners' reasoning. However, it remains unclear whether stronger math problem-solving ability is associated with stronger step-level assessment performance. This study examines that relationship using the GSM8K and MATH subsets of PROCESSBENCH, a human-annotated benchmark for identifying the earliest erroneous step in mathematical reasoning. We evaluate two LLM-based math tutor agent settings, instantiated with GPT-4 and GPT-5, in two independent tasks on the same math problems: solving the original problem and assessing a benchmark-provided solution by predicting the earliest erroneous step. Results show a consistent within-model pattern: assessment accuracy is substantially higher on math problem items the same model solved correctly than on items it solved incorrectly, with statistically significant associations across both models and datasets. At the same time, assessment remains more difficult than direct problem solving, especially on error-present solutions. These findings suggest that math problem-solving expertise supports stronger assessment performance, but reliable step-level diagnosis also requires additional capabilities such as step tracking, monitoring, and precise error localization. The results have implications for the design and evaluation of AI-supported Adaptive Instructional Systems (AISs) for formative assessment in math education.

NeuroVLM-Bench: Evaluation of Vision-Enabled Large Language Models for Clinical Reasoning in Neurological Disorders

Recent advances in multimodal large language models enable new possibilities for image-based decision support. However, their reliability and operational trade-offs in neuroimaging remain insufficiently understood. We present a comprehensive benchmarking study of vision-enabled large language models for 2D neuroimaging using curated MRI and CT datasets covering multiple sclerosis, stroke, brain tumors, other abnormalities, and normal controls. Models are required to generate multiple outputs simultaneously, including diagnosis, diagnosis subtype, imaging modality, specialized sequence, and anatomical plane. Performance is evaluated across four directions: discriminative classification with abstention, calibration, structured-output validity, and computational efficiency. A multi-phase framework ensures fair comparison while controlling for selection bias. Across twenty frontier multimodal models, the results show that technical imaging attributes such as modality and plane are nearly solved, whereas diagnostic reasoning, especially subtype prediction, remains challenging. Tumor classification emerges as the most reliable task, stroke is moderately solvable, while multiple sclerosis and rare abnormalities remain difficult. Few-shot prompting improves performance for several models but increases token usage, latency, and cost. Gemini-2.5-Pro and GPT-5-Chat achieve the strongest overall diagnostic performance, while Gemini-2.5-Flash offers the best efficiency-performance trade-off. Among open-weight architectures, MedGemma-1.5-4B demonstrates the most promising results, as under few-shot prompting, it approaches the zero-shot performance of several proprietary models, while maintaining perfect structured output. These findings provide practical insights into performance, reliability, and efficiency trade-offs, supporting standardized evaluation of multimodal LLMs in neuroimaging.

LLMORPH: Automated Metamorphic Testing of Large Language Models

Automated testing is essential for evaluating and improving the reliability of Large Language Models (LLMs), yet the lack of automated oracles for verifying output correctness remains a key challenge. We present LLMORPH, an automated testing tool specifically designed for LLMs performing NLP tasks, which leverages Metamorphic Testing (MT) to uncover faulty behaviors without relying on human-labeled data. MT uses Metamorphic Relations (MRs) to generate follow-up inputs from source test input, enabling detection of inconsistencies in model outputs without the need of expensive labelled data. LLMORPH is aimed at researchers and developers who want to evaluate the robustness of LLM-based NLP systems. In this paper, we detail the design, implementation, and practical usage of LLMORPH, demonstrating how it can be easily extended to any LLM, NLP task, and set of MRs. In our evaluation, we applied 36 MRs across four NLP benchmarks, testing three state-of-the-art LLMs: GPT-4, LLAMA3, and HERMES 2. This produced over 561,000 test executions. Results demonstrate LLMORPH's effectiveness in automatically exposing inconsistencies.

CAPITU: A Benchmark for Evaluating Instruction-Following in Brazilian Portuguese with Literary Context

We introduce CAPITU, a benchmark for evaluating instruction-following capabilities of Large Language Models (LLMs) in Brazilian Portuguese. Unlike existing benchmarks that focus on English or use generic prompts, CAPITU contextualizes all tasks within eight canonical works of Brazilian literature, combining verifiable instruction constraints with culturally-grounded content. The benchmark comprises 59 instruction types organized into seven categories, all designed to be automatically verifiable without requiring LLM judges or human evaluation. Instruction types include Portuguese-specific linguistic constraints (word termination patterns like -ando/-endo/-indo, -inho/-inha, -mente) and structural requirements. We evaluate 18 state-of-the-art models across single-turn and multi-turn settings. Our results show that frontier reasoning models achieve strong performance (GPT-5.2 with reasoning: 98.5% strict accuracy), while Portuguese-specialized models offer competitive cost-efficiency (Sabiazinho-4: 87.0% at \$0.13 vs Claude-Haiku-4.5: 73.5% at \$1.12). Multi-turn evaluation reveals significant variation in constraint persistence, with conversation-level accuracy ranging from 60% to 96% across models. We identify specific challenges in morphological constraints, exact counting, and constraint persistence degradation across turns. We release the complete benchmark, evaluation code, and baseline results to facilitate research on instruction-following in Portuguese.

CayleyPy-4: AI-Holography. Towards analogs of holographic string dualities for AI tasks

This is the fourth paper in the CayleyPy project, which applies AI methods to the exploration of large graphs. In this work, we suggest the existence of a new discrete version of holographic string dualities for this setup, and discuss their relevance to AI systems and mathematics. Many modern AI tasks -- such as those addressed by GPT-style language models or RL systems -- can be viewed as direct analogues of predicting particle trajectories on graphs. We investigate this problem for a large family of Cayley graphs, for which we show that surprisingly it admits a dual description in terms of discrete strings. We hypothesize that such dualities may extend to a range of AI systems where they can lead to more efficient computational approaches. In particular, string holographic images of states are proposed as natural candidates for data embeddings, motivated by the "complexity = volume" principle in AdS/CFT. For Cayley graphs of the symmetric group S_n, our results indicate that the corresponding dual objects are flat, planar polygons. The diameter of the graph is equal to the number of integer points inside the polygon scaled by n. Vertices of the graph can be mapped holographically to paths inside the polygon, and the usual graph distances correspond to the area under the paths, thus directly realising the "complexity = volume" paradigm. We also find evidence for continuous CFTs and dual strings in the large n limit. We confirm this picture and other aspects of the duality in a large initial set of examples. We also present new datasets (obtained by a combination of ML and conventional tools) which should be instrumental in establishing the duality for more general cases.

Errors in AI-Assisted Retrieval of Medical Literature: A Comparative Study

Large language models (LLMs) assisted literature retrieval may lead to erroneous references, but these errors have not been rigorously quantified. Therefore, we quantitatively assess errors in reference retrieval of widely used free-version LLM platforms and identify the factors associated with retrieval errors. We evaluated 2,000 references retrieved by 5 LLMs (Grok-2, ChatGPT GPT-4.1, Google Gemini Flash 2.5, Perplexity AI, and DeepSeek GPT-4) for 40 randomly-selected original articles (10 per journal) published Jan. 2024 to July 2025 from British Medical Journal (BMJ), Journal of the American Medical Association, and The New England Journal of Medicine (NEJM). Primary outcomes were a multimetric score ratio combining validity of digital object identifier, PubMed ID, Google-Scholar link, and relevance; and complete miss rate (proportion of references failing all applicable metrics). Multivariable regression was used to examine independent associations. LLM platforms completely failed to retrieve correct reference data 47.8% of the time. The average score ratio of the 5 LLM platforms was 0.29 (standard deviation, 0.35; range, 0-1.25), with a higher score ratio indicating a higher accuracy in retrieving relevant references and correct bibliographic data. The highest and lowest accuracies were achieved by Grok (0.57) and Genimi (0.11), respectively. Compared with BMJ, NEJM articles had lower score ratios and higher complete miss rates. Multivariable analysis shows LLM platforms and journals were independently associated with score ratios and complete miss rate, respectively. We show modest overall performance of LLMs and significant variability in retrieval accuracy across platforms and journals. LLM platforms and journals are associated with LLM's performance in retrieving medical literature. Bibliographic data should be carefully reviewed when using LLM-assisted literature retrieval.

A Subgoal-driven Framework for Improving Long-Horizon LLM Agents

Large language model (LLM)-based agents have emerged as powerful autonomous controllers for digital environments, including mobile interfaces, operating systems, and web browsers. Web navigation, for example, requires handling dynamic content and long sequences of actions, making it particularly challenging. Existing LLM-based agents struggle with long-horizon planning in two main ways. During online execution, they often lose track as new information arrives, lacking a clear and adaptive path toward the final goal. This issue is further exacerbated during reinforcement learning (RL) fine-tuning, where sparse and delayed rewards make it difficult for agents to identify which actions lead to success, preventing them from maintaining coherent reasoning over extended tasks. To address these challenges, we propose two contributions. First, we introduce an agent framework that leverages proprietary models for online planning through subgoal decomposition. Second, we present MiRA (Milestoning your Reinforcement Learning Enhanced Agent), an RL training framework that uses dense, milestone-based reward signals. The real-time planning mechanism improves proprietary models such as Gemini by approximately a 10% absolute increase in success rate (SR) on the WebArena-Lite benchmark. Meanwhile, applying MiRA to the open Gemma3-12B model increases its success rate from 6.4% to 43.0%. This performance surpasses proprietary systems such as GPT-4-Turbo (17.6%) and GPT-4o (13.9%), as well as the previous open-model state of the art, WebRL (38.4%). Overall, our findings demonstrate that combining explicit inference-time planning with milestone-based rewards significantly improves an agent's long-horizon capabilities, paving the way for more robust and general-purpose autonomous systems.

RPMS: Enhancing LLM-Based Embodied Planning through Rule-Augmented Memory Synergy

LLM agents often fail in closed-world embodied environments because actions must satisfy strict preconditions -- such as location, inventory, and container states -- and failure feedback is sparse. We identify two structurally coupled failure modes: (P1) invalid action generation and (P2) state drift, each amplifying the other in a degenerative cycle. We present RPMS, a conflict-managed architecture that enforces action feasibility via structured rule retrieval, gates memory applicability via a lightweight belief state, and resolves conflicts between the two sources via rules-first arbitration. On ALFWorld (134 unseen tasks), RPMS achieves 59.7% single-trial success with Llama 3.1 8B (+23.9 pp over baseline) and 98.5% with Claude Sonnet 4.5 (+11.9 pp); of the 8B gain, rule retrieval alone contributes +14.9 pp (statistically significant), making it the dominant factor. A key finding is that episodic memory is conditionally useful: it harms performance on some task types when used without grounding, but becomes a stable net positive once filtered by current state and constrained by explicit action rules. Adapting RPMS to ScienceWorld with GPT-4 yields consistent gains across all ablation conditions (avg. score 54.0 vs. 44.9 for the ReAct baseline), providing transfer evidence that the core mechanisms hold across structurally distinct environments.

Draft-and-Prune: Improving the Reliability of Auto-formalization for Logical Reasoning

Auto-formalization (AF) translates natural-language reasoning problems into solver-executable programs, enabling symbolic solvers to perform sound logical deduction. In practice, however, AF pipelines are currently brittle: programs may fail to execute, or execute but encode incorrect semantics. While prior work largely mitigates syntactic failures via repairs based on solver feedback, reducing semantics failures remains a major bottleneck. We propose Draft-and-Prune (D&P), an inference-time framework that improves AF-based logical reasoning via diversity and verification. D&P first drafts multiple natural-language plans and conditions program generation on them. It further prunes executable but contradictory or ambiguous formalizations, and aggregates predictions from surviving paths via majority voting. Across four representative benchmarks (AR-LSAT, ProofWriter, PrOntoQA, LogicalDeduction), D&P substantially strengthens AF-based reasoning without extra supervision. On AR-LSAT, in the AF-only setting, D&P achieves 78.43% accuracy with GPT-4 and 78.00% accuracy with GPT-4o, significantly outperforming the strongest AF baselines MAD-LOGIC and CLOVER. D&P then attains near-ceiling performance on the other benchmarks, including 100% on PrOntoQA and LogicalDeduction.

Security Assessment and Mitigation Strategies for Large Language Models: A Comprehensive Defensive Framework

Large Language Models increasingly power critical infrastructure from healthcare to finance, yet their vulnerability to adversarial manipulation threatens system integrity and user safety. Despite growing deployment, no comprehensive comparative security assessment exists across major LLM architectures, leaving organizations unable to quantify risk or select appropriately secure LLMs for sensitive applications. This research addresses this gap by establishing a standardized vulnerability assessment framework and developing a multi-layered defensive system to protect against identified threats. We systematically evaluate five widely-deployed LLM families GPT-4, GPT-3.5 Turbo, Claude-3 Haiku, LLaMA-2-70B, and Gemini-2.5-pro against 10,000 adversarial prompts spanning six attack categories. Our assessment reveals critical security disparities, with vulnerability rates ranging from 11.9\% to 29.8\%, demonstrating that LLM capability does not correlate with security robustness. To mitigate these risks, we develop a production-ready defensive framework achieving 83\% average detection accuracy with only 5\% false positives. These results demonstrate that systematic security assessment combined with external defensive measures provides a viable path toward safer LLM deployment in production environments.