Dongkuan

Tahreem Yasir, Sutapa Dey Tithi, Benyamin Tabarsi et al.

Large language models (LLMs) are increasingly used for automated tutoring, but their reliability in structured symbolic domains remains unclear. We study step-level feedback for propositional logic proofs, which require precise symbolic reasoning aligned with a learner's current proof state. We introduce a knowledge-graph-grounded benchmark of 516 unique proof states with step-level annotations and difficulty metrics. Unlike prior tutoring evaluations that rely on model self-assessment or binary correctness, our framework enables fine-grained analysis of feedback quality against verified solution paths. We evaluate three role-specialized pipelines with varying solution access: Tutor (partial solution access), Teacher (full derivation access), and Judge (verification of Tutor feedback). Our results reveal a striking asymmetry: verification improves outcomes when upstream feedback is error-prone (<70% accuracy), but degrades performance by 4-6 percentage points through over-specification when feedback is already reliable (>85%). Critically, we identify a shared complexity ceiling; no model or pipeline reliably succeeds on proof states exceeding complexity 4-5. These findings challenge the assumption that adding verifiers or richer context universally improves tutoring, motivating adaptive, difficulty-aware architectures that route problems by estimated complexity and upstream reliability.

Aditya Basarkar, Benyamin Tabarsi, Tiffany Barnes et al.

Mathematical problem solving is a fundamental benchmark for assessing the reasoning capabilities of artificial intelligence and a gateway to applications in education, science, and engineering where reliable symbolic reasoning is essential. Although recent advances in multi-agent LLM-based systems have enhanced their mathematical reasoning capabilities, they still lack a reliably revisable representation of the reasoning process. Existing agents either operate in rigid sequential pipelines that cannot correct earlier steps or rely on heuristic self-evaluation that can fail to identify and fix errors. In addition, programmatic context can distract language models and degrade accuracy. To address these gaps, we introduce Iteratively Improved Program Construction (IIPC), a reasoning method that iteratively refines programmatic reasoning chains and combines execution feedback with the native Chain-of-thought abilities of the base LLM to maintain high-level contextual focus. IIPC surpasses competing approaches in the majority of reasoning benchmarks on multiple base LLMs. All code and implementations are released as open source.

Pengfei Gu, Huimin Li, Haoteng Tang et al.

Modern deep neural networks have shown remarkable performance in medical image classification. However, such networks either emphasize pixel-intensity features instead of fundamental anatomical structures (e.g., those encoded by topological invariants), or they capture only simple topological features via single-parameter persistence. In this paper, we propose a new topology-guided classification framework that extracts multi-scale and multi-filtration persistent topological features and integrates them into vision classification backbones. For an input image, we first compute cubical persistence diagrams (PDs) across multiple image resolutions/scales. We then develop a ``vineyard'' algorithm that consolidates these PDs into a single, stable diagram capturing signatures at varying granularities, from global anatomy to subtle local irregularities that may indicate early-stage disease. To further exploit richer topological representations produced by multiple filtrations, we design a cross-attention-based neural network that directly processes the consolidated final PDs. The resulting topological embeddings are fused with feature maps from CNNs or Transformers. By integrating multi-scale and multi-filtration topologies into an end-to-end architecture, our approach enhances the model's capacity to recognize complex anatomical structures. Evaluations on three public datasets show consistent, considerable improvements over strong baselines and state-of-the-art methods, demonstrating the value of our comprehensive topological perspective for robust and interpretable medical image classification.