Compete Then Collaborate: Frontier AI Teachers Build a Verifiable Curriculum to Improve a Coding Student Beyond Imitation

This paper investigates knowledge distillation from a large reasoning model (DeepSeek-R1) to a compact student model (Qwen2.5-7B). Using historical problems from the John O'Bryan Mathematics Competition at Northern Kentucky University (2011-2025), we build a Chain-of-Thought (CoT) training corpus through a dual-agent framework. The dataset is used to fine-tune the student model with Low-Rank Adaptation (LoRA) on Apple Silicon hardware using the MLX framework. The base Qwen2.5-7B model achieves 64.67% accuracy on competition problems, while the DeepSeek-R1 teacher achieves 91.40%. An initial 1,000-iteration training run revealed severe overfitting, with validation loss reaching a minimum at iteration 200 before rising steadily. Based on this finding, we ran five independent training runs each limited to 200 iterations with varied random seeds to assess result stability. Across these five runs, the fine-tuned student model achieves a mean accuracy of 69.43% (std dev 0.17%) on the competition dataset, a 4.76 percentage-point improvement over the base model, and generalizes to 73.1% (std dev 0.18%) on the MATH-500 benchmark. We further study how response length affects answer quality across six reasoning levels (R1-R6): accuracy declines consistently from 69.43% at R1 (mean 220 words) to 41.9% at R6 (mean 31.2 words), with the two-person speed section most sensitive to token reduction. These results demonstrate that CoT distillation improves compact student models and that response length is a critical factor in mathematical reasoning quality.

The rapid integration of Large Language Models (LLMs) into K-12 and higher education has outpaced the development of reliable methods for evaluating their pedagogical quality. As the research community starts to explore the space of automating evaluation of AI tutors, we introduce FATE (FLC AI Tutor Evaluator), a specialized 8B-parameter language model designed to evaluate AI tutors. Aligned with the four core evaluation tracks from the BEA 2025 Shared Task, our model assesses pedagogical ability across Mistake Identification, Mistake Location, Guidance, and Actionability. Because pedagogical evaluation is a specialized task with limited labeled data, we leverage knowledge distillation from a frontier LLM to generate additional supervision, yielding absolute performance gains up to 22.63 percentage points. Finally, we demonstrate FATE's utility as an automated evaluator by benchmarking instructional responses generated by popular commercial models, including ChatGPT, Claude, Gemini, and DeepSeek. On average, we have found that Gemini 2.5 Flash perfomed best (82.88%), then ChatGPT 5.5 Instant (80.75%), followed by DeepSeek V4 Flash (80.13%) and Claude Sonnet 4.6 (74.00%).

Can post-trained large language models (LLMs) further improve themselves using only unlabeled prompts, without external teachers or feedback from tools? We study this setting starting only from unlabeled seed questions with no ground-truth solutions, across three reasoning domains: math, science, and coding. We propose Self-Verified Distillation, a simple post-training refinement algorithm in which the model generates candidate solutions to these seed questions, filters them using prompt-based self-verification, and trains on the resulting self-curated dataset. Inspired by the UQ benchmark's use of multiple validators to screen candidate answers to hard unsolved questions, we adapt this validation-based filtering idea to self-training: the model filters its own generated solutions through a three-stage cascade of cycle-consistency, factuality, and correctness checks, accepting a solution only if it passes all stages with unanimous judge votes. We find that sampling more candidate generations and using a larger verification budget during training data construction produces higher-quality self-curated data and, in turn, better reasoning models. We then train Qwen3 models at multiple scales with Self-Verified Distillation and obtain gains across all three domains. For Qwen3-4B, our method improves aggregate held-out pass@1 by +16.7 points in math (AIME26 and HMMT), +11.1 points in science (GPQA Diamond and HLE), and +8.3 points in coding (LCBv5 and LCBv6), with gains also extending to 0.6B and 8B models. Compared to our test-time-only baseline (UQ-TTC), which improves performance by spending extra compute at inference time, Self-Verified Distillation achieves better performance in most settings while requiring only a single inference call at test time.