Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions

Algebraic reasoning remains one of the most informative stress tests for large language models, yet current benchmarks provide no mechanism for attributing failure to a specific cause. When a model fails an algebraic problem, a single accuracy score cannot reveal whether the expression was too deeply nested, the operator too uncommon, the intermediate state count too high, or the dependency chain too long. Prior work has studied individual failure modes in isolation, but no framework has varied each complexity factor independently under strict experimental control. No prior system has offered automatic generation and verification of problems of increasing complexity to track model progress over time. We introduce a nine-dimension algebraic complexity framework in which each factor is varied independently while all others are held fixed, with problem generation and verification handled by a parametric pipeline requiring no human annotation. Each dimension is grounded in a documented LLM failure mode and captures a structurally distinct aspect of algebraic difficulty, including expression nesting depth, simultaneous intermediate result count, sub-expression complexity, operator hardness, and dependent reasoning chain length. We evaluated seven instruction-tuned models spanning 8B to 235B parameters across all nine dimensions and find that working memory is the dominant scale-invariant bottleneck. Every model collapses between 20 and 30 parallel branches regardless of parameter count, pointing to a hard architectural constraint rather than a solvable capacity limitation. Our analysis further identifies a minimal yet diagnostically sufficient subset of five dimensions that together span the full space of documented algebraic failure modes, providing a complete complexity profile of a model's algebraic reasoning capacity.

LUDOBENCH: Evaluating LLM Behavioural Decision-Making Through Spot-Based Board Game Scenarios in Ludo

We introduce LudoBench, a benchmark for evaluating LLM strategic reasoning in Ludo, a stochastic multi-agent board game whose dice mechanics, piece capture, safe-square navigation, and home-path progression introduce meaningful planning complexity. LudoBench comprises 480 handcrafted spot scenarios across 12 behaviorally distinct decision categories, each isolating a specific strategic choice. We additionally contribute a fully functional 4-player Ludo simulator supporting Random, Heuristic, Game-Theory, and LLM agents. The game-theory agent uses Expectiminimax search with depth-limited lookahead to provide a principled strategic ceiling beyond greedy heuristics. Evaluating six models spanning four model families, we find that all models agree with the game-theory baseline only 40-46% of the time. Models split into distinct behavioral archetypes: finishers that complete pieces but neglect development, and builders that develop but never finish. Each archetype captures only half of the game theory strategy. Models also display measurable behavioral shifts under history-conditioned grudge framing on identical board states, revealing prompt-sensitivity as a key vulnerability. LudoBench provides a lightweight and interpretable framework for benchmarking LLM strategic reasoning under uncertainty. All code, the spot dataset (480 entries) and model outputs are available at https://anonymous.4open.science/r/LudoBench-5CBF/

LLM-as-a-Judge for Time Series Explanations

Evaluating factual correctness of LLM generated natural language explanations grounded in time series data remains an open challenge. Although modern models generate textual interpretations of numerical signals, existing evaluation methods are limited: reference based similarity metrics and consistency checking models require ground truth explanations, while traditional time series methods operate purely on numerical values and cannot assess free form textual reasoning. Thus, no general purpose method exists to directly verify whether an explanation is faithful to underlying time series data without predefined references or task specific rules. We study large language models as both generators and evaluators of time series explanations in a reference free setting, where given a time series, question, and candidate explanation, the evaluator assigns a ternary correctness label based on pattern identification, numeric accuracy, and answer faithfulness, enabling principled scoring and comparison. To support this, we construct a synthetic benchmark of 350 time series cases across seven query types, each paired with correct, partially correct, and incorrect explanations. We evaluate models across four tasks: explanation generation, relative ranking, independent scoring, and multi anomaly detection. Results show a clear asymmetry: generation is highly pattern dependent and exhibits systematic failures on certain query types, with accuracies ranging from 0.00 to 0.12 for Seasonal Drop and Volatility Shift, to 0.94 to 0.96 for Structural Break, while evaluation is more stable, with models correctly ranking and scoring explanations even when their own outputs are incorrect. These findings demonstrate feasibility of data grounded LLM based evaluation for time series explanations and highlight their potential as reliable evaluators of data grounded reasoning in the time series domain.

Infinite Problem Generator: Verifiably Scaling Physics Reasoning Data with Agentic Workflows

Training large language models for complex reasoning is bottlenecked by the scarcity of verifiable, high-quality data. In domains like physics, standard text augmentation often introduces hallucinations, while static benchmarks lack the reasoning traces required for fine-tuning. We introduce the Infinite Problem Generator (IPG), an agentic framework that synthesizes physics problems with guaranteed solvability through a Formula-as-Code paradigm. Unlike probabilistic text generation, IPG constructs solutions as executable Python programs, enforcing strict mathematical consistency. As a proof-of-concept, we release ClassicalMechanicsV1, a high-fidelity corpus of 1,335 classical mechanics problems expanded from 165 expert seeds. The corpus demonstrates high structural diversity, spanning 102 unique physical formulas with an average complexity of 3.05 formulas per problem. Furthermore, we identify a Complexity Blueprint, demonstrating a strong linear correlation ($R^2 \approx 0.95$) between formula count and verification code length. This relationship establishes code complexity as a precise, proxy-free metric for problem difficulty, enabling controllable curriculum generation. We release the full IPG pipeline, the ClassicalMechanicsV1 dataset, and our evaluation report to support reproducible research in reasoning-intensive domains.

Trust Regions Sell, But Who's Buying? Overlap Geometry as an Alternative Trust Region for Policy Optimization

Standard trust-region methods constrain policy updates via Kullback-Leibler (KL) divergence. However, KL controls only an average divergence and does not directly prevent rare, large likelihood-ratio excursions that destabilize training--precisely the failure mode that motivates heuristics such as PPO's clipping. We propose overlap geometry as an alternative trust region, constraining distributional overlap via the Bhattacharyya coefficient (closely related to the Hellinger/Renyi-1/2 geometry). This objective penalizes separation in the ratio tails, yielding tighter control over likelihood-ratio excursions without relying on total variation bounds that can be loose in tail regimes. We derive Bhattacharyya-TRPO (BTRPO) and Bhattacharyya-PPO (BPPO), enforcing overlap constraints via square-root ratio updates: BPPO clips the square-root ratio q = sqrt(r), and BTRPO applies a quadratic Hellinger/Bhattacharyya penalty. Empirically, overlap-based updates improve robustness and aggregate performance as measured by RLiable under matched training budgets, suggesting overlap constraints as a practical, principled alternative to KL for stable policy optimization.

The Compliance Paradox: Semantic-Instruction Decoupling in Automated Academic Code Evaluation

The rapid integration of Large Language Models (LLMs) into educational assessment rests on the unverified assumption that instruction following capability translates directly to objective adjudication. We demonstrate that this assumption is fundamentally flawed. Instead of evaluating code quality, models frequently decouple from the submission's logic to satisfy hidden directives, a systemic vulnerability we term the Compliance Paradox, where models fine-tuned for extreme helpfulness are vulnerable to adversarial manipulation. To expose this, we introduce the Semantic-Preserving Adversarial Code Injection (SPACI) Framework and the Abstract Syntax Tree-Aware Semantic Injection Protocol (AST-ASIP). These methods exploit the Syntax-Semantics Gap by embedding adversarial directives into syntactically inert regions (trivia nodes) of the Abstract Syntax Tree. Through a large-scale evaluation of 9 SOTA models across 25,000 submissions in Python, C, C++, and Java, we reveal catastrophic failure rates (>95%) in high-capacity open-weights models like DeepSeek-V3, which systematically prioritize hidden formatting constraints over code correctness. We quantify this failure using our novel tripartite framework measuring Decoupling Probability, Score Divergence, and Pedagogical Severity to demonstrate the widespread "False Certification" of functionally broken code. Our findings suggest that current alignment paradigms create a "Trojan" vulnerability in automated grading, necessitating a shift from standard RLHF toward domain-specific Adjudicative Robustness, where models are conditioned to prioritize evidence over instruction compliance. We release our complete dataset and injection framework to facilitate further research on the topic.

A Hybrid Supervised-LLM Pipeline for Actionable Suggestion Mining in Unstructured Customer Reviews

Extracting actionable suggestions from customer reviews is essential for operational decision-making, yet these directives are often embedded within mixed-intent, unstructured text. Existing approaches either classify suggestion-bearing sentences or generate high-level summaries, but rarely isolate the precise improvement instructions businesses need. We evaluate a hybrid pipeline combining a high-recall RoBERTa classifier trained with a precision-recall surrogate to reduce unrecoverable false negatives with a controlled, instruction-tuned LLM for suggestion extraction, categorization, clustering, and summarization. Across real-world hospitality and food datasets, the hybrid system outperforms prompt-only, rule-based, and classifier-only baselines in extraction accuracy and cluster coherence. Human evaluations further confirm that the resulting suggestions and summaries are clear, faithful, and interpretable. Overall, our results show that hybrid reasoning architectures achieve meaningful improvements fine-grained actionable suggestion mining while highlighting challenges in domain adaptation and efficient local deployment.

PhysicsSolutionAgent: Towards Multimodal Explanations for Numerical Physics Problem Solving

Explaining numerical physics problems often requires more than text-based solutions; clear visual reasoning can substantially improve conceptual understanding. While large language models (LLMs) demonstrate strong performance on many physics questions in textual form, their ability to generate long, high-quality visual explanations remains insufficiently explored. In this work, we introduce PhysicsSolutionAgent (PSA), an autonomous agent that generates physics-problem explanation videos of up to six minutes using Manim animations. To evaluate the generated videos, we design an assessment pipeline that performs automated checks across 15 quantitative parameters and incorporates feedback from a vision-language model (VLM) to iteratively improve video quality. We evaluate PSA on 32 videos spanning numerical and theoretical physics problems. Our results reveal systematic differences in video quality depending on problem difficulty and whether the task is numerical or theoretical. Using GPT-5-mini, PSA achieves a 100% video-completion rate with an average automated score of 3.8/5. However, qualitative analysis and human inspection uncover both minor and major issues, including visual layout inconsistencies and errors in how visual content is interpreted during feedback. These findings expose key limitations in reliable Manim code generation and highlight broader challenges in multimodal reasoning and evaluation for visual explanations of numerical physics problems. Our work underscores the need for improved visual understanding, verification, and evaluation frameworks in future multimodal educational systems

Actionable Advice from Reviews via Mixture of LoRA Experts: A Two-LLM Pipeline for Issue Extraction and Business Recommendations

Customer reviews contain detailed, domain specific signals about service failures and user expectations, but converting this unstructured feedback into actionable business decisions remains difficult. We study review-to-action generation: producing concrete, implementable recommendations grounded in review text. We propose a modular two-LLM framework in which an Issue model extracts salient issues and assigns coarse themes, and an Advice model generates targeted operational fixes conditioned on the extracted issue representation. To enable specialization without expensive full fine-tuning, we adapt the Advice model using a mixture of LoRA experts strategy: multiple low-rank adapters are trained and a lightweight gating mechanism performs token-level expert mixing at inference, combining complementary expertise across issue types. We construct synthetic review-issue-advice triples from Yelp reviews (airlines and restaurants) to supervise training, and evaluate recommendations using an eight dimension operational rubric spanning actionability, specificity, feasibility, expected impact, novelty, non-redundancy, bias, and clarity. Across both domains, our approach consistently outperforms prompting-only and single-adapter baselines, yielding higher actionability and specificity while retaining favorable efficiency-quality trade-offs.

A Multi-Agent System for Generating Actionable Business Advice

Customer reviews contain rich signals about product weaknesses and unmet user needs, yet existing analytic methods rarely move beyond descriptive tasks such as sentiment analysis or aspect extraction. While large language models (LLMs) can generate free-form suggestions, their outputs often lack accuracy and depth of reasoning. In this paper, we present a multi-agent, LLM-based framework for prescriptive decision support, which transforms large scale review corpora into actionable business advice. The framework integrates four components: clustering to select representative reviews, generation of advices, iterative evaluation, and feasibility based ranking. This design couples corpus distillation with feedback driven advice refinement to produce outputs that are specific, actionable, and practical. Experiments across three service domains and multiple model families show that our framework consistently outperform single model baselines on actionability, specificity, and non-redundancy, with medium sized models approaching the performance of large model frameworks.