Problem Solving Capability

Solving problems through repeated attempts is a sequential modeling task: at each step, the solver receives feedback and decides how to revise their solutions. Predicting whether performance improves, plateaus, or regresses across attempts is central to understanding any iterative problem-solving process in both human learners and autonomous agents. Beyond outcomes, modeling what errors persist and how strategies shift across attempts provides deeper insight into the mechanics of sequential learning. Studying these dynamics requires observing many solvers as they attempt, receive feedback, and revise. Programming courses with automated grading provide this setting, as students iteratively submit code to test suites and receive feedback on every attempt. We therefore curate CodeInsight, a large-scale dataset of over 3 million submissions from 3,286 undergraduates across 2 introductory C++ courses in 2 academic years, with test-case-level outcomes, timestamps, and source code. On this dataset, we build a benchmark that evaluates models spanning parametric, sequential, and generative traditions under a shared calibration-and-scoring protocol, including a Recurrent State Space Model (RSSM) adapted to track solver characteristics through discrete latent variables and an LLM-based predictor that generates explicit solutions. The adapted RSSM achieves the strongest predictive accuracy on three of the four courses. The LLM predictor is less accurate but produces full submissions at each attempt, enabling direct analysis of failure modes. We find that the model's coding proficiency is inversely related to predictive performance in this setting, with the LLM better understood as a generative solver conditioned on context rather than a faithful predictor of solver behavior. We publicly release our code and the dataset on request to facilitate future research.

Humans need to study only a handful of well-written textbooks to master a discipline and attempt its hardest problems. We argue that an ideal self-evolution method should share the same property, that is autonomously learning from raw training material for transferable problem-solving capability. However, we still lack a direct measurement for it. We introduce StudyBench, a controlled physics benchmark that directly measures how efficiently a self-evolution method converts training material into capability. We organise the test set into an Application Set, consisting of difficult textbook problems and evaluating absorption ability, and a Transfer Set, consisting of olympiad-level problems and evaluating transfer ability. Benchmarking representative self-evolution methods across three base models, we find that improvements on the Application Set rarely translate to the harder Transfer Set. A guidance ablation exposes a Guidance Gap: even the strongest method closes only a small fraction of what the same material unlocks when supplied as in-context guidance. Besides, every method hits a Compute Plateau, saturating well before exhausting its compute budget. The remaining gap is therefore a method problem rather than a data or compute problem. By offering a clean and controlled benchmark, StudyBench turns self-evolution progress from an open-ended pursuit into a measurable target for future research. Our code is released at https://github.com/thunlp/StudyBench.

On-policy self-distillation (OPSD) improves reasoning by using a privileged view of a model conditioned on reference solutions to supervise a student view that observes only the question. However, the teacher-provided token-level targets may depend on reference-specific information unavailable at inference time. We propose Problem-Space-Guided OPSD (PS-OPSD), which replaces the complete solution with trajectory-grounded guidance describing the initial state, goal conditions, constraints, and a selected state-transition path. The student rollout and OPSD objective remain unchanged. Across three mathematical reasoning benchmarks and model scales ranging from 1.7B to 8B, PS-OPSD achieves the highest aggregate question-only accuracy among the compared methods. Controlled experiments further indicate that guidance relevance and path coherence contribute to these gains, highlighting the representation of privileged information as an important design choice in OPSD.

Reasoning or inference-scaling models are the new generation of Large Language Models (LLMs) capable of complex problem solving. To investigate their problem-solving capability in physics, we evaluated model o4-mini by OpenAI on solving traditional, end-of-chapter problems from Halliday and Resnick's "Fundamentals of Physics," spanning core topics in the undergraduate physics curriculum. Performance was analyzed across modality and problem difficulty. The model solved the problems with overall accuracy of about 90%, but performance depended strongly on representation: accuracy was much higher on text-only problems (96%) than on problems requiring coordinated interpretation of text and images (79%). Accuracy also declined significantly as the problem difficulty increased from low to medium to high. These results show that state-of-the-art LLMs can solve much of the standard introductory physics problems, but that their performance remains uneven and constrained by problem modality and problem difficulty.

While traditional evolutionary algorithms hard-code reproduction, self-replication can emerge spontaneously within digital ``primordial soups''. This paper investigates the coevolution of such emergent self-replication alongside problem-solving capabilities. We initialize a population of random 32-byte Z80 assembly programs, requiring self-replication to arise purely through random assembly-level mutations and pairwise program interactions. To couple computation with reproduction, we introduce a task-based validation step: correctly evaluating a polynomial raises a program's interaction probability above a baseline rate. Our experiments yield four primary findings. First, self-replication and mathematical problem-solving successfully coevolve from initial randomness. Second, the pressure to compute accelerates the emergence of compact, robust reproductive architectures that preserve memory for task execution. Third, applying metabolic constraints that penalize runtime promotes the emergence of sophisticated conditional execution patterns that reduce energy use. Finally, partitioning programs into interconnected task niches generates an emergent learning curriculum that utilizes simple solutions as stepping stones toward more complex tasks. Altogether, these results demonstrate an interactive feedback loop: environmental task demands actively shape the physical architecture of self-replication, while spontaneous replication alters the evolutionary trajectory of functional problem-solving.

Large Language Model (LLM)-based agents can solve complex procedural tasks by interacting with environments over multiple turns, but this ability typically depends on large models, long contexts, and repeated inference calls. This makes advanced memory-augmented agents difficult to deploy on resource-constrained devices. We introduce DuoMem, a dual-space distillation framework that transfers procedural problem-solving ability from a large teacher model to compact student models. DuoMem distils in two complementary spaces: (1)context-space distillation, which replaces student-generated memories with higher-quality teacher-generated procedural memories prepended to the student's input, and (2)parameter-space distillation, which fine-tunes lightweight LoRA adapters on successful teacher trajectories. Evaluated on ALFWorld, a challenging embodied decision-making benchmark, DuoMem boosts a 4B-parameter model from 4.3% to 77.9% task success rate, closing most of the gap to a 72B teacher model (87.1%), while adding fewer than 10M trainable parameters and only a few megabytes of pre-computed teacher memories. Moreover, the DuoMem-enhanced 4B model completes tasks over 3x faster than the 72B teacher in wall-clock time, making it viable for real-time edge deployment, which would be challenging for the teacher.Extensive ablations across eight models spanning 2B-72B parameters reveal that both distillation axes contribute complementary

Distilling reasoning capabilities from strong to weak language models typically involves imitating specific solution trajectories, effectively transferring what to answer rather than how to reason. This trajectory-level imitation encourages memorization of instance-specific steps rather than acquisition of transferable problem-solving skills, limiting generalization to novel problems. We propose Strategy-Guided Policy Optimization (SGPO), which replaces instance-level trajectory imitation with reusable strategy distillation. SGPO extracts structured strategy descriptions from strong-model responses and, for each problem, constructs both autonomous and strategy-guided trajectories to enable direct comparison of the model's behavior with and without strategic guidance. The framework then addresses two key questions. For how to distill, a token-level forward-KL objective selectively transfers the distributional shift induced by strategy conditioning into the unguided policy, with proximal constraints ensuring stability. For when to distill, adaptive instance-level weighting strengthens guidance when autonomous exploration falls short and reduces it as the model's own competence grows. Experiments on four mathematical benchmarks across two model families show that SGPO consistently outperforms SFT, on-policy RL, and hybrid-policy baselines, improving the average score by 2.2 points over the strongest baseline on Qwen2.5-7B-Instruct. Analysis reveals that the forward-KL objective provides an inherently selective distillation signal that outperforms direct trajectory imitation, and that strategy distillation exhibits complementary scaling with base model capability.

Generative AI tools provide novice programmers with instant, personalized support, but also raise concerns about whether AI use supports or bypasses students' regulation of problem-solving. Existing work has largely focused on correctness, usability, or overall usage frequency, with less attention to how student--AI help-seeking unfolds. This study addresses this gap by analyzing AI-assisted help-seeking trajectories in university-level programming. Using an SRL-informed analytical framework that links prompt-level help-seeking codes to conceptual, implementation, debugging, and reflective forms of support, we analyzed 1,290 task-specific student prompts linked to 17,190 code submissions from 71 students in introductory Python programming courses. Specifically, we examined how help-seeking interactions were structured across turns and attempts, and how trajectory patterns related to task scores and the number of code submissions. Results indicate that many students primarily used AI for reactive troubleshooting rather than for planned, self-regulated problem-solving. Although trajectory patterns were not associated with significant differences in task scores, they differed substantially in the number of code submissions required. These findings suggest that the educational significance of AI support lies not only in whether students use AI, but in how their help-seeking trajectories develop during programming problem-solving.

Effective machine learning depends not only on how we model data, but also on what data we choose to collect. While large sequence models have revolutionized data modeling, the problem of automated data selection, or "intrinsic curiosity", remains a significant challenge. Classic approaches incentivize exploration by rewarding an agent based on its "learning progress", which measures how much a newly acquired observation improves a world model's predictive ability. However, evaluating these rewards traditionally requires expensive inner loops of gradient descent updates within each trajectory, rendering them computationally impractical at scale. In this work, we investigate whether the emergent in-context learning (ICL) capabilities of sequence models can eliminate this bottleneck by serving as immediate, update-free world models. Specifically, we evaluate whether an exploration policy can be trained to maximize learning progress, using solely the prediction errors and counterfactual context manipulations of an in-context learner. We first prove that in general Markov decision processes, this is in fact impossible in an unbiased way: the resulting intrinsic rewards either suffer from nuisance terms that bias their estimation of true learning progress, or they cannot be implemented using an in-context learner's prediction errors. Conversely, we prove a positive result for a broad subclass of non-temporal settings, encompassing active learning and Bayesian Experimental Design: here, ICL-derived rewards successfully bound and asymptotically converge to the true learning progress. We corroborate our theory with controlled experiments across continuous and symbolic environments, demonstrating that our ICL-driven framework successfully trains curious data-collection policies that explore optimally.

AI agent performance is not just a modeling problem, it is fundamentally a systems problem. The advanced capabilities of models are realized through agent harnesses. Therefore, a gap between model assumptions and harness behavior can easily prevent the model's full capabilities from translating into agent performance. We formalize this as the intent-execution' gap: the mismatch between what the model intends and what the harness executes, and vice versa. We argue that minimizing this intent-execution gap is as important as other aspects of harness design such as tools and execution loops. To illustrate the impact of this harness-model alignment, we develop a simple and customizable harness called Simple Strands Agent' (SSA). SSA aims to find the bulk of common patterns which generalize across different model families (such as Claude, Gemini, GPT, Grok, Qwen), as well as a small number of model-specific preferences. We make two contributions: (i) we reproduce or improve on the pass@1 performance reported by diverse model-provider families on popular agentic benchmarks (SWE-Pro, SWE-Verified and Terminal-Bench-2), and (ii) building on an analysis of 138k trajectories generated by SSA, we look beyond the pass@1 numbers which tend to be relatively even across frontier models. By representing agent trajectories in code state-spaces, we observe model-level differences in problem-solving behavior. Finer-grained metrics such as edit frequency, testing activity, and phase-transitions reveal how individual models allocate effort across different stages of autonomous problem solving.

Large language models are increasingly proposed as educational tutors, yet stronger task-solving ability does not necessarily imply stronger learning support. Motivated by recent calls to measure the social impact of NLP systems in practice, we study whether public LLM tutoring benchmarks distinguish learning-supportive behavior from mere answer production. We propose a lightweight diagnostic based on the gap between solving-oriented and pedagogy-oriented benchmark performance. Using public MathTutorBench leaderboard results, we show that these dimensions are only partially aligned: across eight publicly reported models, the correlation between solving and pedagogy composites is 0.421, and several models shift meaningfully in rank when evaluation moves from solving to pedagogy. We then analyze the public TutorBench sample and show that agency-relevant behaviors are explicitly encoded in benchmark rubrics, especially in active-learning settings that reward guiding questions, calibrated hints, and non-disclosive scaffolding. Together, these findings suggest that educational-impact evaluation should not treat task success as a sufficient proxy for learning support. We argue that public tutoring benchmarks can better support positive-impact evaluation by reporting solving-oriented and pedagogy-oriented scores separately and by making disclosure-sensitive, student-agency-preserving criteria more explicit.

A growing failure mode in agent evaluation and training is that models can achieve high evaluation scores by exploiting shortcuts instead of solving the intended task, producing deceptive performance. This makes evaluation scores unreliable as measures of true task-solving ability. We propose CapCode, a framework for constructing coding datasets with randomized tests whose best achievable non-cheating performance is deliberately capped below one. This capped-performance design gives evaluation scores a clearer interpretation: scores substantially above the cap are implausible and therefore provide evidence of cheating. To prevent cheating, we propose CapReward, a reward design based on the CapCode principle to discourage optimization beyond the cap. Experiments across multiple datasets show that CapCode detects cheating while preserving performance ranking of models, and CapReward reduces cheating behavior, yielding models that better follow the intended task specification.

Reasoning Large Language Models can improve problem-solving performance through deliberative inference, but invoking slow reasoning for every input is computationally expensive and often unnecessary. We propose IDPR, a framework for response-conditioned inhibitory deliberation. IDPR first generates a concise intuitive answer and then uses an inhibition controller to decide whether that specific response should be released or suppressed in favor of slow reasoning. Unlike input-only routers, the inhibition controller conditions on the fast answer and fast-side evidence, including confidence, logit margin, parseability, and generation cost. We train the controller from paired fast-slow outcomes and select the inhibition threshold on a held-out validation set under an accuracy-first slow-call budget. On a held-out 5,000-example mathematical reasoning test set, IDPR invokes slow reasoning on only 8.20% of examples and improves accuracy from 47.90% to 48.92%. Under the same slow-call budget, random routing decreases accuracy to 46.76%, while the strongest confidence-based baseline reaches 48.22%. IDPR also achieves the highest corrective precision, showing that response-conditioned inhibition better identifies fast answers that benefit from slow reasoning.

Agents are widely deployed as assistants over documents, tools, and code. However, they typically act only on explicit user requests, which surface only the problems the user has noticed, while many other important problems coexist, hidden in plain sight, within the broader user context, with their total number unknown in advance. We frame this as the task of discovering multiple hidden problems from context, in which coexisting problems should be uncovered, grounded in supporting evidence, and paired with concrete actions. To this end, we introduce TIDE, a template-guided iterative framework with two complementary mechanisms. Specifically, motivated by the observation that single-pass prediction anchors on the most salient cases and yields generic claims, we propose iterative discovery, which surfaces a small batch of candidates per round while conditioning on what has already been found, so subsequent rounds extend coverage; and thought templates, reusable schemas distilled from previously solved cases that specify what contextual signals to attend to and how to connect them, anchoring each prediction in a recognizable problem class. We validate TIDE on two realistic settings, personal workspaces and software repositories, across four model backbones, showing substantial gains over single-shot and parallel multi-agent baselines on task coverage, identification, and resolution.

This work presents a logic-driven framework to evaluate the performance of reinforcement learning (RL) algorithms in their ability to generalize to unseen tasks. Our framework defines a family of inductive reach-avoid tasks, characterized by structural similarities in task dynamics, enabling evaluation of generalization capabilities. We introduce a neural certificate function that validates trajectories generated by RL algorithms by enforcing key conditions, thereby serving as a litmus test for RL generalization. We empirically demonstrate our method's capability in certifying generalization for several state-of-the-art generalizable RL algorithms on challenging continuous environments. Our results show that a lower percentage of certificate function violations correlates with a higher number of test tasks successfully solved, highlighting the effectiveness of our framework in evaluating and distinguishing generalization capabilities of RL algorithms. This work provides a principled approach for benchmarking RL generalization.

Can a single LLM-based optimization system match specialized tools across fundamentally different domains? We show that when optimization problems are formulated as improving a text artifact evaluated by a scoring function, a single AI-based optimization system-supporting single-task search, multi-task search with cross-problem transfer, and generalization to unseen inputs-achieves state-of-the-art results across six diverse tasks. Our system discovers agent architectures that nearly triple Gemini Flash's ARC-AGI accuracy (32.5% to 89.5%), finds scheduling algorithms that cut cloud costs by 40%, generates CUDA kernels where 87% match or beat PyTorch, and outperforms AlphaEvolve's reported circle packing solution (n=26). Ablations across three domains reveal that actionable side information yields faster convergence and substantially higher final scores than score-only feedback, and that multi-task search outperforms independent optimization given equivalent per-problem budget through cross-task transfer, with benefits scaling with the number of related tasks. Together, we show for the first time that text optimization with LLM-based search is a general-purpose problem-solving paradigm, unifying tasks traditionally requiring domain-specific algorithms under a single framework. We open-source optimize_anything with support for multiple backends as part of the GEPA project at https://github.com/gepa-ai/gepa .

While Graphical User Interface (GUI) agents have shown promising performance in automated device interaction, they primarily depend on static parametric knowledge from pre-training or instruction tuning. This reliance fundamentally limits their ability to handle long-tailed tasks that require explicit procedural knowledge absent from model parameters, often forcing agents to resort to inefficient and brittle trial-and-error exploration. To mitigate this limitation, we introduce \textbf{Proactive Document-Guided Action} for GUI agents in dynamic, open-web environments, a novel paradigm that mirrors human problem-solving by enabling agents to autonomously search for relevant documentation to resolve long-tailed tasks. To evaluate agents' capability in this paradigm, we propose \textbf{DocOS}, a benchmark designed to assess document-guided problem solving in fully interactive environments. DocOS requires agents to autonomously navigate a web browser, locate relevant online documentation, comprehend procedural instructions, and faithfully ground them into executable GUI actions. Extensive experiments reveal that progress is strictly constrained by dual bottlenecks: agents struggle to reliably locate relevant information during proactive search and frequently fail to faithfully ground retrieved instructions into precise actions, pointing toward document-guided interaction as a crucial pathway for enabling self-evolving GUI agents in dynamic environments.

Students learning algorithms often need support as they interpret traces, debug reasoning errors, and apply procedures across unfamiliar problem instances. In this paper, we present KITE (Knowledge-Informed Tutoring Engine), a Retrieval-Augmented Generation (RAG)-based intelligent tutoring system designed to serve as a classroom teaching assistant for algorithmic reasoning and problem-solving tasks. KITE uses an intent-aware Socratic response strategy to tailor support to different student needs, responding with targeted hints, guiding questions, and progressive scaffolding intended to strengthen students' algorithmic problem-solving ability. To keep responses aligned with course content, KITE uses a multimodal RAG pipeline that retrieves relevant information from course materials. We evaluate KITE using three forms of assessment: RAGAs-based metrics for response grounding and quality, expert evaluation of pedagogical quality, and a simulated student pipeline in which a weaker language model interacts with KITE across two-turn dialogues and produces revised answers after receiving feedback. Results indicate that KITE produces contextually grounded and pedagogically appropriate responses. Further, using simulated students, KITE's feedback helped the student models produce more accurate follow-up responses on procedural and tracing questions, suggesting that its scaffolding can support algorithmic problem-solving. This work contributes a tutoring architecture and an evaluation approach for assessing retrieval-grounded explanations and scaffolded problem-solving feedback.

Many problems seem to require a flash of insight to solve. What form do these sudden insights take, and what impact do they have on how people approach similar problems in the future? In this work, we prompted participants (N = 189) to think aloud as they attempted to solve a sequence of five "matchstick-arithmetic" problems. These problems either all relied on the same kind of non-obvious solution (Same group) or a different kind each time (Different group). Our first observation was that Same participants improved more rapidly than Different participants. We then leveraged techniques from natural language processing to analyze participants' speech, and found that this accelerated improvement for Same participants was accompanied by changes in both how much they spoke and what they said. In particular, they were more likely to spontaneously label the kind of problem they were working on. Taken together, these findings suggest that a hallmark of transferable insights is their accessibility for verbal report, even if the underlying precursors of insight remain difficult to articulate.

The effectiveness of Reinforcement Learning (RL) in Large Language Models (LLMs) depends on the nature and diversity of the data used before and during RL. In particular, reasoning problems can often be approached in multiple ways that rely on different forms of reasoning, and exposure to only a limited range of such approaches in the training data may limit the effectiveness of RL. Motivated by this, we investigate using diverse self-generated data during mid-training as an intermediate step before RL training. Specifically, we adopt a bootstrapped data-generation framework guided by George Polya's problem-solving approaches for generating multiple variants of correct answers for each question in the training data, and then perform fine-tuning. We first provide a theoretical perspective on how mid-training on such data improves RL and explain how policy-gradient updates can incentivize combining multiple approaches. We then empirically demonstrate that RL-trained models initialized with our mid-training data achieve consistent improvements across various mathematical reasoning benchmarks and other OOD tasks like code generation and narrative reasoning. Overall, our investigative study shows that a language model learning multiple problem-solving approaches, through self-generated data helps subsequent RL.

Recent methods for improving LLM mathematical reasoning, whether through MCTS-based test-time search or causal graph-guided knowledge injection, cannot identify which concepts causally contribute to a correct answer, as the observed association may be spurious, driven by confounders such as problem difficulty. We propose CIKA (Causal Intervention for Knowledge Activation), a framework that uses the LLM itself as an interventional simulator: a prompt sets the concept state to ``mastered'' and the correctness change estimates the causal effect. We formalize this quantity as an Interventional Capability Probe (ICP), which diagnoses whether the LLM can use a given concept -- distinct from merely possessing knowledge. Because the intervention exogenously sets the concept state independently of problem difficulty, ICP separates confounding that observational methods cannot. On 67 screened problems, the ICP of the top-ranked concept (+0.219) is significantly larger than that of the negative control (+0.039; paired $t$-test, $p < 10^{-6}$, Cohen's $d = 0.86$), confirming that the probe discriminates causally relevant concepts from irrelevant ones. Analysis of 601 Omni-MATH problems further shows that solved problems have 6.1$\times$ higher ATE than unsolved ones (0.338 vs. 0.055), confirming that ICP is predictive of problem-solving success. With a 7B-parameter LLM whose weights are entirely frozen, CIKA achieves 69.7% on the contamination-free Omni-MATH-Rule benchmark and 64.0% overall, compared to 60.5% for o1-mini, and 97.2% on GSM8K, 46--50% on AIME 2024--2026, and 46.2% on MathArena. The Causal Knowledge Activation component contributes 33.8% of correct answers on problems where the base model alone fails, demonstrating that the LLM already possessed but had not activated the requisite knowledge.

Large language models (LLMs) are widely used for tutoring, feedback generation, and content creation, but their broad pretraining makes them hard to constrain and poor substitutes for controllable learners. Educational systems often require inspectable and editable knowledge states: educators want to know what a system assumes the learner knows, and learners benefit when the system can justify actions in terms of explicit skills, misconceptions, and strategies. Inspired by cognitive architectures, we propose Cognitive Agent Compilation (CAC), a framework that uses a strong teacher LLM to compile problem-solving knowledge into an explicit target agent. CAC separates (i) knowledge representation, (ii) problem-solving policy, and (iii) verification and update rules, with the goal of making bounded problem solving more inspectable and editable in educational settings. We present an early proof of concept implemented with Small Language Models that surfaces key design trade-offs, particularly between explicit control and scalable generalization, and positions CAC as an initial step toward bounded-knowledge AI for educational applications.

Large Language Models (LLMs) have rapidly influenced many aspects of society, particularly education, due to their demonstrated ability to complete assignments and examinations across a wide range of subjects. Although prior studies have examined the educational impact of LLMs, much of the existing work relies on public or open problem datasets and lacks topic-specific analysis. In engineering education, especially within mechanical engineering, systematic investigations of LLM performance on specific problem types remain limited. Instead of using traditional methods that directly ask textbook questions to an LLM tool, our study adopts a model distillation process to evaluate LLM capabilities in solving statics problems. By distilling ChatGPT, we extracted 25 text-only statics questions and further constructed two additional datasets by adding diagrams and modifying their numerical values. Experimental results show that while LLMs perform well on text-only statics problems, their accuracy decreases when diagrams are introduced and the problems require multi-step reasoning. Further analysis suggests that this performance drop is not primarily caused by limitations in image recognition, but rather by difficulties in multi-step reasoning and in consistently applying extracted visual information across successive solution stages.

This study applied the Apriori algorithm to analyze behavioral interaction patterns associated with learned helplessness (LH) in mathematics tutoring system logs. Interaction data were examined across three dimensions: LH level (low vs. high), system-based intervention (with vs. without), and problem-solving outcomes (solved vs. unsolved). The analysis of the complete dataset showed that skipping problems without using hints was the most frequent pattern linked to unsolved outcomes, while persistence behaviors such as not skipping were less dominant overall. Comparisons by LH level showed that low-LH students had stronger links between problem solving and not skipping, as well as positive associations between hint use and solved outcomes. High-LH students showed more avoidance patterns, with skipping strongly tied to unsolved outcomes. In the comparison of system-based intervention conditions, students without intervention had the highest lift for persistence-success links, while the with-intervention group had stronger patterns involving skipping behaviors leading to unsolved outcomes. Outcome-specific analysis showed that not skipping was consistently associated with solved problems across all groups, while skipping without hints predicted unsolved outcomes. Practical implications and recommendations are discussed.

As frontier language models attain near-ceiling performance on static mathematical benchmarks, existing evaluations are increasingly unable to differentiate model capabilities, largely because they cast models solely as solvers of fixed problem sets. We introduce MathDuels, a self-play benchmark in which models occupy dual roles: each authors math problems under adversarial prompting and solves problems authored by every other participant. Problems are produced through a three-stage generation pipeline (meta-prompting, problem generation, and difficulty amplification), and validated by an independent verifier that excludes ill-posed questions. A Rasch model (Rasch, 1993) jointly estimates solver abilities and problem difficulties; author quality is derived from the difficulties of each model's authored problems. Experiments across 19 frontier models reveal that authoring and solving capabilities are partially decoupled, and that dual-role evaluation reveals capability separations invisible in single-role benchmarks. As newer models enter the arena, they produce problems that defeat previously dominant solvers, so the benchmark's difficulty co-evolves with participant strength rather than saturating at a fixed ceiling. We host a public leaderboard that updates as new models are released.

Knowledge Tracing (KT) aims to model student's knowledge state and predict future performance to enable personalized learning in Intelligent Tutoring Systems. However, traditional KT methods face fundamental limitations in explainability, as they rely solely on the response correctness, neglecting the rich information embedded in students' problem-solving processes. To address this gap, we propose Knowledge Tracing Leveraging Problem-Solving Process (KT-PSP), which incorporates students' problem-solving processes to capture the multidimensional aspects of mathematical proficiency. We also introduce KT-PSP-25, a new dataset specifically designed for KT-PSP. Building on this, we present StatusKT, a KT framework that employs a teacher-student-teacher three-stage LLM pipeline to extract students' Mathematical Proficiency (MP) as intermediate representation. In this pipeline, the teacher LLM first extracts problem-specific proficiency indicators, then a student LLM generates responses based on the student's solution process, and a teacher LLM evaluates these responses to determine mastery of each indicator. The experimental results on KT-PSP-25 demonstrate that StatusKT improves the prediction performance of existing KT methods. Moreover, StatusKT provides interpretable explanations for its predictions by explicitly modeling students' mathematical proficiency. Code is available \href{https://github.com/jungyangpark/KT-PSP-25}{here}.

LLM-based agents are increasingly moving towards proactivity: rather than awaiting instruction, they exercise agency to anticipate user needs and solve them autonomously. However, evaluating proactivity is challenging; current benchmarks are constrained to localized context, limiting their ability to test reasoning across sources and longer time horizons. To address this gap, we present PROBE (Proactive Resolution Of BottlEnecks). PROBE decomposes proactivity as a pipeline of three core capabilities: (1) searching for unspecified issues, (2) identifying specific bottlenecks, and (3) executing appropriate resolutions. We apply PROBE to evaluate leading LLMs and popular agentic frameworks, showing that even state-of-the-art models struggle to solve this benchmark. Computing our consistent measurements across frontier LLMs and agents, we find that the best end-to-end performance of 40% is achieved by both GPT-5 and Claude Opus-4.1. Additionally, we demonstrate the relative capabilities of each model and analyze mutual failure modes. Our results highlight the current limitations of autonomous action in agentic systems, and expose promising future research directions.

Large Language Models (LLM) can solve any computational problem without an algorithm in a runtime independent of the computational complexity of that problem. Instead of specifying precisely how to solve problem instance using programming, we ask an LLM to solve the problem instance using prompting. Outputs are sampled from a distribution rather than generated procedurally. In this vision paper, we explore the challenges and opportunities of this new form of computation and observe that its capabilities and limits cannot be understood within the classic, rationalist framework of computation. Hence, we appeal to the software engineering (SE) community to develop the foundations and techniques required to analyze the properties of this "empirical computation" as it generates solutions to computational problems: How can we analyze and improve the correctness of LLMs solving a computational problem in the general, in the problem-specific, or in the instance-specific? What are the properties and fundamental limits of empirical computation? This paper aims to establish empirical computation as a field in SE that is timely and rich with interesting problems.