educational software engineers

Abstract: Reinforcement learning from verifiable rewards (RLVR) is limited by sparse outcome-level feedback on hard reasoning tasks: when all rollouts in a group fail, rewards provide no learning signal. Stronger teachers can provide additional guidance, but this raises a central question: how can such signals be incorporated into RLVR to support successful rollouts while remaining learnable for the student? We distinguish two complementary mechanisms: trajectory-level intervention, which improves access to reward-bearing trajectories, and token-level supervision, which provides dense targets to guide student learning. Our controlled experiments show that either mechanism alone can remain insufficient, motivating their combination. We therefore introduce PIVOT, which inserts teacher-generated corrections into student rollouts and applies token-level KL supervision to these segments alongside the RLVR objective. Beyond their combination, we systematically analyze where to intervene and how to supervise, yielding a recipe for effective guidance. Across hard logic games and mathematical reasoning benchmarks, PIVOT consistently outperforms existing methods, nearly doubling mean avg@8 on logic games from 19.5% for the best-performing baseline to 35.6%.

Abstract: Rubrics are widely used to evaluate open-ended question answering by breaking overall quality into explicit criteria. These explicit criteria make rubrics a rich source of learning guidance, yet their potential for guiding the training process has been largely overlooked. Existing methods use rubrics mainly as direct feedback signals, without explicitly modeling the capabilities behind their criteria. This leaves their capability structure largely unused in guiding the training process. We introduce Rubric-Structured Reinforcement Learning (RSRL), an RL framework that unlocks the full potential of rubrics by exploiting their structure throughout the training process, rather than treating them simply as direct reward signals. At its core, RSRL builds on three key designs: (1) Rubric-to-Capability Structuring first recovers the capability structure hidden in rubric criteria, (2) Self-Sufficient Capability Learning then uses this structure to bootstrap underdeveloped capabilities into effective learning, (3) Capability-Residual Credit Routing finally preserves capability-specific gains during optimization. Experiments show that RSRL consistently improves both overall performance and underdeveloped capabilities, boosting downstream scientific question-answering performance by up to 7.43 over the initial policy and 7.60 over non-rubric structured RL baselines, showing that reinforcement learning can substantially benefit from the capability structure encoded in rubrics.

Abstract: Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for improving the reasoning capabilities of LLMs. However, the role of supervised fine-tuning (SFT) data in enabling effective downstream RL remains underexplored. In this paper, we investigate a key hypothesis: the diversity of reasoning steps in chain-of-thought (CoT) during SFT is a critical enabler of RLVR performance. To test this hypothesis, we introduce EquivAug, a data augmentation framework that uses symbolic equivalence transformations to generate diverse yet provably correct reasoning paths. By converting CoT solutions into formal symbolic representations, applying equivalence transformations, and reconstructing natural-language explanations, EquivAug produces training data that differs in reasoning steps rather than surface-level lexical variation. Experiments on GSM8K and FOLIO across model scales demonstrate that EquivAug consistently achieves the highest reasoning path diversity after SFT and the strongest accuracy after GRPO. Our results establish that CoT diversity during SFT is positively correlated with downstream RLVR performance.

Abstract: It is assumed that a natural way to improve the pedagogical quality of large language model tutors is to define a metric of instructional performance and fine-tune the model against it. To test this strategy, we designed a metric of pedagogical adaptivity that scores each instructional decision in a learning sequence against the conditions of the learning situation, which is the standard used for automated pedagogical scoring. We audited a frontier tutor across 2,000 learner scenarios, corrected its weakest cases by fine-tuning an open-weights proxy, and asked 31 trained educators to rate the pedagogical alignment of the outputs blind, before and after correction. The metric increased from +0.05 to +0.42 for the corrected cases, while the expert ratings decreased from 4.46 to 3.03, with the unmodified controls remaining unchanged and a base-proxy control ruling out the change of model. The tutor performed worse because any metric that scores decisions independently and averages them is maximized by repeating the single best decision, and the fine-tuned model collapsed to that exact optimum in every case, in and out of sample. Educators identified the repetition, which such metrics cannot represent, and preserving the learner's trajectory in the score reduced, but did not reverse, the metric's verdict. Weight analysis traced the correction to the model's output projection, where it had memorized its training strings rather than learned to adapt. We conclude that measurement validity does not imply optimization validity, and we derive design principles for benchmarks that assess or train AI-tutor instruction.

Abstract: Corrective feedback is among the best-evidenced drivers of second-language acquisition, yet corrections delivered during lessons rarely accumulate into an actionable view of grammar mastery. Prompted frontier models can provide such a view from learner--tutor lesson transcripts, but they are costly at scale. We close this gap by fine-tuning Qwen3.5 small language models (SLMs) on filtered and rebalanced teacher-generated supervision, then deploying an efficient 0.8B model in an end-to-end grammar mastery tracker for all English learners on our platform. Internalizing the annotation contract into adapter weights enables pairing the 0.8B model with a compact matched prompt rather than verbose instructions. On two human-curated benchmarks, both the deployed 0.8B model and a 4B reference comparator outperform prompted GPT-5.4 and GPT-5.6 Sol in precision and recall under nested matching criteria of increasing strictness: concept, evidence span, and correctness. The deployed 0.8B SLM reduces serving cost by approximately 16$\times$. A feature-level online experiment shows significant gains in learner engagement ($+15.8\%$) and key business metrics, including scheduled hours ($+2.1\%$) and GMV from new lessons ($+13.2\%$).

Abstract: Reinforcement learning can substantially improve a reasoning teacher, but it is unclear which of those improvements survive when the teacher supervises a smaller on-policy student. We study this question in mathematical reasoning by comparing teacher lineages before and after GRPO, multiple student scales, direct GRPO, and several on-policy distillation objectives. The central finding is that transfer is structured rather than scalar: teacher strength alone does not make dense distillation competitive, while an RL-improved teacher creates useful but metric-dependent student gains. This motivates Transfer-Stratified On-Policy Distillation (TS-OPD), which screens training problems by the joint sampled success of the student and teacher, routes acquisition problems to gated forward KL, routes consolidation problems to gated reverse KL, and adds an entropy brake to protect sampled coverage. Across the main comparison, TS-OPD is the strongest student objective for macro average correctness with the GRPO-improved teacher, while pass@K remains more mixed. Ablations show that the gains come from routing and token gating rather than skipping problems. These results support a transfer-aware view of OPD: stronger teachers help when the supervision direction and token budget match the student's observed ability, not merely because the teacher endpoint is stronger.

Abstract: Fluent guidance is not the same as useful intervention. LLM tutors are typically trained to generate the next teacher utterance, implicitly assuming that every student turn warrants a response. However, our experiments indicate that this conflates tutoring capability (what to say) with intervention necessity (whether to say it). We introduce DICE, a framework that decouples intervention decisions from response generation by first selecting an explicit pedagogical action. To calibrate this action selection policy, we define Intervention Value (IV), a rollout-grounded counterfactual metric that compares each action against non-intervention. IV shows that many prescribed interventions provide little or no marginal benefit. We further introduce DICE-Bench, a multi-variant math tutoring benchmark with skill-preserving problem variants for session-level evaluation. Using IV-weighted and KL-regularized policy optimization, DICE learns to intervene selectively while preserving tutoring effectiveness. In simulated tutoring sessions, DICE reduces the over-intervention rate to near zero while guiding students to correct solutions in approximately 3-4 fewer turns on average than existing Socratic tutoring baselines.

Abstract: Large reasoning models can produce correct yet unnecessarily long reasoning traces. Existing methods improve reasoning efficiency with trajectory-level objectives or local token- and step-level signals, but rarely model inter-step semantic dependencies. This limits their ability to distinguish redundant steps from those that support later deductions, making it harder to shorten reasoning without sacrificing accuracy. We introduce RECAP (REdundancy-aware Credit Assignment via Propagation), which addresses this limitation by assigning credit where it is due based on both a step's downstream role in the reasoning structure and its contribution to solving the problem correctly. We define structural responsibility to capture the step's downstream role by measuring how strongly later reasoning depends on it, using credit propagated backward from the final-answer node through an outcome-independent, LLM-annotated semantic dependency graph. However, a step can have high structural responsibility yet steer the reasoning away from the correct solution. RECAP therefore introduces step efficacy to measure answer-directed progress through changes in gold-answer log-likelihood as each step is added. Together, these signals reshape rollout-level GRPO advantages into step-specific updates. RECAP requires neither a separately trained process reward model nor preconstructed concise trajectories. Across two 7B models and four mathematical reasoning benchmarks, RECAP improves the accuracy-efficiency trade-off. On Qwen2.5-Math-7B, it improves pass@1 by 2.0-3.7 percentage points while reducing reasoning tokens by 8%-31% relative to GRPO across all four benchmarks. Analysis suggests these savings reflect fewer reasoning operations and less dead-end reasoning, rather than more compact expression.

Abstract: Many learning problems combine a dominant regularity with systematic exceptions. Motivated by U-shaped learning in language acquisition, we study this interaction in controlled quasiregular regression problems where regular and exceptional solutions are explicitly known. Neural networks can partially acquire exceptions, subsequently regress toward the dominant regularity, and finally recover. This overregularization becomes substantially stronger when exceptions are rare, despite their early acquisition, but does not emerge equally across all regularities considered. Our results isolate a simple form of competition between regularities and exceptions during neural learning.

Abstract: Existing Parsons problem tools primarily focus on correctness, indicating whether a student solved a problem, but providing limited visibility into the underlying problem-solving process. We address this gap by introducing Pulla, a Parsons problem tool that instruments programming assignments to capture fine-grained interaction data. These behavioral traces allow the system to surface recurring difficulty patterns, giving instructors actionable insights to inform targeted intervention decisions. This paper describes our experience in developing and deploying Pulla. We deployed the tool in two university courses: an upper-division software design course at the University of Houston (United States) and an introductory programming course at Aalto University (Finland). By analyzing the data collected, we identified common difficulty patterns, including misidentifying exception types, confusing return with the throw/raise mechanism, and incorrect control-flow ordering.