Large Language Models (LLMs) can achieve strong performance on everyday coding tasks, but they can fail on complex tasks that require non-trivial reasoning about program semantics. Finding training examples to teach LLMs to solve these tasks can be challenging. In this work, we explore a method to synthetically generate code reasoning training data based on a semantic inequivalence game SInQ: a generator agent creates program variants that are semantically distinct, derived from a dataset of real-world programming tasks, while an evaluator agent has to identify input examples that cause the original programs and the generated variants to diverge in their behaviour, with the agents training each other semi-adversarially. We prove that this setup enables theoretically unlimited improvement through self-play in the limit of infinite computational resources. We evaluated our approach on multiple code generation and understanding benchmarks, including cross-language vulnerability detection (Lu et al., 2021), where our method improves vulnerability detection in C/C++ code despite being trained exclusively on Python code, and the challenging Python builtin identifier swap benchmark (Miceli-Barone et al., 2023), showing that whereas modern LLMs still struggle with this benchmark, our approach yields substantial improvements. We release the code needed to replicate the experiments, as well as the generated synthetic data, which can be used to fine-tune LLMs.

Reinforcement finetuning (RFT) has shown great potential for enhancing the mathematical reasoning capabilities of large language models (LLMs), but it is often sample- and compute-inefficient, requiring extensive training. In this work, we introduce AdaRFT (Adaptive Curriculum Reinforcement Finetuning), a method that significantly improves both the efficiency and final accuracy of RFT through adaptive curriculum learning. AdaRFT dynamically adjusts the difficulty of training problems based on the model's recent reward signals, ensuring that the model consistently trains on tasks that are challenging but solvable. This adaptive sampling strategy accelerates learning by maintaining an optimal difficulty range, avoiding wasted computation on problems that are too easy or too hard. AdaRFT requires only a lightweight extension to standard RFT algorithms like Proximal Policy Optimization (PPO), without modifying the reward function or model architecture. Experiments on competition-level math datasets-including AMC, AIME, and IMO-style problems-demonstrate that AdaRFT significantly improves both training efficiency and reasoning performance. We evaluate AdaRFT across multiple data distributions and model sizes, showing that it reduces training time by up to 2x and improves accuracy by a considerable margin, offering a more scalable and effective RFT framework.

This work proposes a novel method to generate C-Tests; a deviated form of cloze tests (a gap filling exercise) where only the last part of a word is turned into a gap. In contrast to previous works that only consider varying the gap size or gap placement to achieve locally optimal solutions, we propose a mixed-integer programming (MIP) approach. This allows us to consider gap size and placement simultaneously, achieving globally optimal solutions, and to directly integrate state-of-the-art models for gap difficulty prediction into the optimization problem. A user study with 40 participants across four C-Test generation strategies (including GPT-4) shows that our approach (MIP) significantly outperforms two of the baseline strategies (based on gap placement and GPT-4); and performs on-par with the third (based on gap size). Our analysis shows that GPT-4 still struggles to fulfill explicit constraints during generation and that MIP produces C-Tests that correlate best with the perceived difficulty. We publish our code, model, and collected data consisting of 32 English C-Tests with 20 gaps each (totaling 3,200 individual gap responses) under an open source license.

Intelligent and adaptive online education systems aim to make high-quality education available for a diverse range of students. However, existing systems usually depend on a pool of hand-made questions, limiting how fine-grained and open-ended they can be in adapting to individual students. We explore targeted question generation as a controllable sequence generation task. We first show how to fine-tune pre-trained language models for deep knowledge tracing (LM-KT). This model accurately predicts the probability of a student answering a question correctly, and generalizes to questions not seen in training. We then use LM-KT to specify the objective and data for training a model to generate questions conditioned on the student and target difficulty. Our results show we succeed at generating novel, well-calibrated language translation questions for second language learners from a real online education platform.