Existing LLM-based molecular optimization methods frame the task as molecule-to-molecule mapping, forcing models to implicitly learn structure-property relationships from paired SMILES alone. We argue this misses a key ingredient: task-level chemical knowledge that tells the model which structural motifs to prefer or avoid for a given property direction, before it ever looks at a specific molecule. We propose SkillMol, which constructs compact task skills – sets of recommended and discouraged structural motifs for each optimization objective – from domain knowledge, and pairs them with an atom-anchored action interface that decomposes editing into discrete, executable operations. Skills are used twice: as explicit training context so the model learns skill-conditioned edit actions, and as functional-group constraints during inference search. A deterministic RDKit executor applies the proposed graph edits. On the MoleculeSTM benchmark across 14 molecular editing tasks, SkillMol achieves 92.5% loose and 80.0% strict hit ratio on single-property tasks and 65.3% average across loose and strict multi-property columns, outperforming strong LLM baselines. Our code can be found at https://github.com/jiajunyu1999/SkillMol.

Reliable rubric grading requires more than accurate score prediction. Each judgement must be grounded in the mark scheme and evidence from the student answer. Existing credit-assignment and intervention methods, primarily designed for self-contained reasoning tasks such as mathematics reasoning, struggle in this setting because they do not identify where grading reasoning goes wrong or how the model’s belief about the final mark changes during reasoning. We propose Evidence-Diagnosed Intervention Training (EDIT), a two-phase framework for training more rubric-faithful LLM graders. First, EDIT-SFT locates problematic reasoning steps using internal model signals: posterior belief over the final mark and input-grounding scores. It then revises only these local steps with help from a rubric checklist. Second, EDIT-RL calibrates the grader with belief-guided reward shaping, penalising large harmful belief drifts while still allowing helpful exploration. Experiments on two real-world, multi-subject grading benchmarks demonstrate that EDIT consistently outperforms strong supervised fine-tuning and reinforcement learning baselines on both in-domain and out-of-domain splits, with ablation studies confirming that internal-state diagnostics drive these gains. Under deterministic rubric-edit interventions, EDIT-SFT is the most rule-responsive of all evaluated systems, and EDIT-RL largely retains this responsiveness while improving accuracy.

Good tutoring adapts to the individual: it tracks what a learner knows, notices why they go wrong, and asks the next question that will help most. Most deployed tutoring tools instead serve fixed item banks and treat a wrong answer as a single bit of signal. We present CoLearn, an interactive, agentic tutor that supports an iterative tutoring loop: the learner practises, and the system builds an evidence-grounded memory of the learner’s mastery and misconceptions. This memory is updated as evidence accumulates and is used to generate the next personalised question. CoLearn has three components: (i) a persistent learner-state memory that updates per-topic mastery with a soft-evidence variant of Bayesian Knowledge Tracing, where a large language model acts as a continuous ob- servation function; (ii) adaptive question generation that targets the learner’s weakest topic and recurring misconceptions; and (iii) an evi- dence view that makes personalisation visible and testable through live progress visualisation and blind A/B comparison. In blind A/B evaluation, questions conditioned on this memory are preferred over non-personalised ones 68–69% of the time, and in persona simulations with hidden ground-truth mastery the agent’s belief converges toward the learner’s true mastery.