Geometry problem solving (GPS) poses significant challenges for Multimodal Large Language Models (MLLMs) in diagram comprehension, knowledge application, long-step reasoning, and auxiliary line construction. However, current benchmarks lack fine-grained evaluation for long-step problems necessitating auxiliary construction. To address these limitations, we present GeoLaux, a fine-grained annotated dataset comprising 2186 calculation and proof problems. It features long-step reasoning (with an average solution length of 6.51 steps, maximum of 24 steps) and auxiliary line construction (required in 41.8% of problems). Building on the dataset, we conduct a comprehensive five-dimensional evaluation of 23 leading MLLMs. The evaluation yields three pivotal findings: First, models perform significantly worse on long-step problems compared to short-step ones, with 18 models exhibiting a performance drop of over 50%. Second, it is crucial to enhance models’ understanding, awareness, and proficiency in auxiliary line construction, which is vital for overall geometric reasoning. Third, limited answer hints effectively improve process correctness, whereas explicit answers lead models to neglect intermediate reasoning steps. These findings position GeoLaux both to benchmark MLLMs geometry reasoning abilities and to guide their improvement. Data and code are available at https://github.com/Candice-yu/GeoLaux

Large language models (LLMs) have achieved good performance in multiple reasoning tasks. However, they are limited to adapt the rapid knowledge updates in the real-world scenario without retraining the entire LLM or modifying the model weights. Excluding these consuming methods, knowledge graphs (KGs) are used as external memory under knowledge updating because of their structural knowledge and efficient updating ability, which is yet limited by the gap between structural KG and LLM, and the deficient entity-independent semantics. To this end, we propose an LLM reasoning framework with hierarchical relational retrieval for large-scale knowledge updating, named G-HiRel. To integrate the structural edited KG into continuous LLMs, G-HiRel generates hierarchical instructions based on natural language questions. In order to handle the knowledge inconsistency between the KG and LLM and obtain the entity independence, G-HiRel utilizes a designed hierarchical relational retrieval for relational path candidates, which are selected by a designed semantics-based strategy. Finally, top entity-independent relational paths are instantiated and integrated into LLMs to generate the answer, in order to verify the reasoning performance under knowledge edits. Extensive experiments of G-HiRel on three benchmarks show that G-HiRel achieves superiority in terms of accuracy and interpretability. The code of G-HiRel is available at the link: https://github.com/HJJ-designed/G-HiRel.

Despite the remarkable progress of Large Language Models (LLMs) in abstract reasoning tasks, they continue to struggle with physics problem solving due to difficulties in decoding implicit constraints and maintaining physical consistency. To address these challenges, Process Reward Models (PRMs) have emerged as a promising approach to verify intermediate reasoning steps. Existing PRMs attempt to mitigate reasoning errors but typically rely on scalar scoring, which lacks the explanatory power necessary to diagnose complex physical misconceptions. In this work, we introduce PhysPRM, a Generative PRM that treats evaluation as a generative task to produce fine-grained diagnoses comprising critiques, final judgments, and specific error types. To facilitate this, we develop an automated data synthesis pipeline to construct PhysPRM30K, a comprehensive training dataset, and PhysProcessBench, a rigorously human-verified benchmark. By employing a two-stage training paradigm that integrates Supervised Fine-Tuning with Group Relative Policy Optimization, PhysPRM significantly enhances the physics reasoning capabilities of various LLMs. Extensive experiments demonstrate that PhysPRM improves performance across seven benchmarks in both Best-of-N and critique refinement strategies.

Long-term conversational memory is a core capability for LLM-baseddialogue systems, yet existing benchmarks and evaluation protocolsprimarily focus on surface-level factual recall.In realistic interactions, appropriate responses often depend onimplicit constraints such as user state, goals, or values that are notexplicitly queried later.To evaluate this setting, we introduce LoCoMo-Plus, a benchmarkfor assessing cognitive memory under cue–trigger semantic disconnect,where models must retain and apply latent constraints across longconversational contexts.We further show that conventional string-matching metrics and explicittask-type prompting are misaligned with such scenarios, and propose aunified evaluation framework based on constraint consistency.Experiments across diverse backbone models, retrieval-based methods, andmemory systems demonstrate that cognitive memory remains challenging andreveals failures not captured by existing benchmarks.Our code and evaluation framework are publicly available at https://github.com/xjtuleeyf/Locomo-Plus.

While Large Language Models (LLMs) demonstrate remarkable reasoning, complex optimization tasks remain challenging, requiring domain knowledge and robust implementation. However, existing benchmarks focus narrowly on Mathematical Programming and Combinatorial Optimization, hindering comprehensive evaluation. To address this, we introduce OptiVerse, a comprehensive benchmark of 1,000 curated problems spanning neglected domains, including Stochastic Optimization, Dynamic Optimization, Game Optimization, and Optimal Control, across three difficulty levels: Easy, Medium, and Hard. The experiments with 22 LLMs of different sizes reveal sharp performance degradation on hard problems, where even advanced models like GPT-5.2 and Gemini-3 struggle to exceed 27% accuracy. Through error analysis, we identify that modeling logic errors remain the primary bottleneck. Consequently, we propose a Dual-View Auditor Agent that improves the accuracy of the LLM modeling process without introducing significant time overhead. OptiVerse will serve as a foundational platform for advancing LLMs in solving complex optimization challenges.

While Large Language Models (LLMs) have achieved remarkable capabilities, they unintentionally memorize sensitive data, posing critical privacy and security risks.Machine unlearning is pivotal for mitigating these risks, yet existing paradigms face a fundamental dilemma: aggressive unlearning often induces catastrophic forgetting that degrades model utility, whereas conservative strategies risk superficial forgetting, leaving models vulnerable to adversarial recovery. To address this trade-off, we propose AGTAO (Adversarial Gating Training with Adaptive Orthogonality), a unified framework designed to reconcile robust erasure with utility preservation. Specifically, our approach introduces Adaptive Orthogonality (AO) to dynamically mitigate geometric gradient conflicts between forgetting and retention objectives, thereby minimizing unintended knowledge degradation. Concurrently, Adversarial Gating Training (AGT) formulates unlearning as a latent-space min-max game, employing a curriculum-based gating mechanism to simulate and counter internal recovery attempts. Extensive experiments demonstrate that AGTAO achieves a superior trade-off between unlearning efficacy (KUR ≈ 0.01) and model utility (MMLU 58.30).[Code is available at <https://anonymous.4open.science/r/AGT-unlearning>.].

Large Language Model (LLM) Agents exhibit inherent reasoning abilities through the collaboration of multiple tools.However, during agent inference, existing methods often suffer from (i) locally myopic generation, due to the absence of lookahead, and (ii) trajectory instability, where minor early errors can escalate into divergent reasoning paths. These issues make it difficult to balance global effectiveness and computational efficiency. To address these two issues, we propose meta-adaptive exploration with LLM agents (MAXS)[<https://github.com/exoskeletonzj/MAXS>], a meta-adaptive reasoning framework based on LLM Agents that flexibly integrates tool execution and reasoning planning. MAXS employs a lookahead strategy to extend reasoning paths a few steps ahead, estimating the advantage value of tool usage, and combines step consistency variance and inter-step trend slopes to jointly select stable, consistent, and high-value reasoning steps. Additionally, we introduce a trajectory convergence mechanism that controls computational cost by halting further rollouts once path consistency is achieved, enabling a balance between resource efficiency and global effectiveness in multi-tool reasoning. We conduct extensive empirical studies across three base models (MiMo-VL-7B, Qwen2.5-VL-7B, Qwen2.5-VL-32B) and five datasets, demonstrating that MAXS consistently outperforms existing methods in both performance and inference efficiency. Further analysis confirms the effectiveness of our lookahead strategy and tool usage.

Large Language Models (LLMs) often struggle with structural ambiguity in optimization problems, where a single problem admits multiple related but conflicting modeling paradigms, hindering effective solution generation. To address this, we propose Dual-Cluster Memory Agent (DCM-Agent) to enhance performance by leveraging historical solutions in a training-free manner. Central to this is Dual-Cluster Memory Construction. This agent assigns historical solutions to modeling and coding clusters, then distills each cluster’s content into three structured types: Approach, Checklist, and Pitfall. This process derives generalizable guidance knowledge. Furthermore, this agent introduces Memory-augmented Inference to dynamically navigate solution paths, detect and repair errors, and adaptively switch reasoning paths with structured knowledge. The experiments across seven optimization benchmarks demonstrate that DCM-Agent achieves an average performance improvement of 11%- 21%. Notably, our analysis reveals a “knowledge inheritance” phenomenon: memory constructed by larger models can guide smaller models toward superior performance, highlighting the framework’s scalability and efficiency.

Visual Question Generation (VQG) research focuses predominantly on natural images while neglecting the diagram, which is a critical component in educational materials. To meet the needs of pedagogical assessment, we propose the Diagram-Driven Course Questions Generation (DDCQG) task and construct DiagramQG, a comprehensive dataset with 15,720 diagrams and 25,798 questions across 37 subjects and 371 courses. Our approach employs course and input text constraints to generate course-relevant questions about specific diagram elements. We reveal three challenges of DDCQG: domain-specific knowledge requirements across courses, long-tail distribution in course coverage, and high information density in diagrams. To address these, we propose the Hierarchical Knowledge Integration framework (HKI-DDCQG), which utilizes trainable CLIP for identifying relevant diagram patches, leverages frozen vision-language models for knowledge extraction, and generates questions with trainable T5. Experiments demonstrate that HKI-DDCQG outperforms existing models on DiagramQG while maintaining strong generalizability across natural image datasets, establishing a strong baseline for DDCQG.

Large language models demonstrate remarkable capabilities across various domains, especially mathematics and logic reasoning. However, current evaluations overlook physics-based reasoning - a complex task requiring physics theorems and constraints. We present PhysReason, a 1,200-problem benchmark comprising knowledge-based (25%) and reasoning-based (75%) problems, where the latter are divided into three difficulty levels (easy, medium, hard). Notably, problems require an average of 8.1 solution steps, with hard requiring 15.6, reflecting the complexity of physics-based reasoning. We propose the Physics Solution Auto Scoring Framework, incorporating efficient answer-level and comprehensive step-level evaluations. Top-performing models like Deepseek-R1, Gemini-2.0-Flash-Thinking, and o3-mini-high achieve less than 60% on answer-level evaluation, with performance dropping from knowledge questions (75.11%) to hard problems (31.95%). Through step-level evaluation, we identified four key bottlenecks: Physics Theorem Application, Physics Process Understanding, Calculation, and Physics Condition Analysis. These findings position PhysReason as a novel and comprehensive benchmark for evaluating physics-based reasoning capabilities in large language models.

Current clustering-based open relation extraction (OpenRE) methods usually apply clustering algorithms on top of pre-trained language models. However, this practice has three drawbacks. First, embeddings from language models are high-dimensional and anisotropic, so using simple metrics to calculate distances between these embeddings may not accurately reflect the relational similarity. Second, there exists a gap between the pre-trained language models and downstream clustering for their different objective forms. Third, clustering with embeddings deviates from the primary aim of relation extraction, as it does not directly obtain relations. In this work, we propose a new idea for OpenRE in the era of LLMs, that is, extracting relational phrases and directly exploiting the knowledge in LLMs to assess the semantic similarity between phrases without relying on any additional metrics. Based on this idea, we developed a framework, oreLLM, that makes two LLMs work collaboratively to achieve clustering and address the above issues. Experimental results on different datasets show that oreLLM outperforms current baselines by 1.4%∼ 3.13% in terms of clustering accuracy.

Relation prediction in knowledge graphs (KGs) aims at predicting missing relations in incomplete triples, whereas the dominant embedding paradigm has a restriction on handling unseen entities during testing. In the real-world scenario, the inductive setting is more common because entities in the training process are finite. Previous methods capture an inductive ability by implicit logic in KGs. However, it would be challenging to preciously acquire entity-independent relational semantics of compositional logic rules and to deal with the deficient supervision of logic caused by the scarcity of relational semantics. To this end, we propose a novel graph convolutional network (GCN)-based model LogCo with logical reasoning by contrastive representations. LogCo firstly extracts enclosing subgraphs and relational paths between two entities to supply the entity-independence. Then a contrastive strategy for relational path instances and the subgraph is proposed for the issue of deficient supervision. The contrastive representations are learned for a joint training regime. Finally, prediction results and logic rules for reasoning are attained. Comprehensive experiments on twelve inductive datasets show that LogCo achieves outstanding performance comparing with state-of-the-art inductive relation prediction baselines.

Relation clustering is a general approach for open relation extraction (OpenRE). Current methods have two major problems. One is that their good performance relies on large amounts of labeled and pre-defined relational instances for pre-training, which are costly to acquire in reality. The other is that they only focus on learning a high-dimensional metric space to measure the similarity of novel relations and ignore the specific relational representations of clusters. In this work, we propose a new prompt-based framework named MatchPrompt, which can realize OpenRE with efficient knowledge transfer from only a few pre-defined relational instances as well as mine the specific meanings for cluster interpretability. To our best knowledge, we are the first to introduce a prompt-based framework for unlabeled clustering. Experimental results on different datasets show that MatchPrompt achieves the new SOTA results for OpenRE.