Recent advances in model distillation show that data from advanced reasoning models can effectively train smaller student models. However, standard practices discard incorrect reasoning traces—valuable, yet underutilized data. This paper addresses the critical question: How can both positive and negative distilled reasoning traces be effectively leveraged to maximize LLM reasoning performance in an offline setting? We employ a two-stage training recipe: first, Supervised Fine-Tuning (SFT) on positive traces, followed by a refinement stage using both positive and negative traces. We find that a simple REINFORCE-style objective, which we term the Reinforcement Distillation (REDI) objective, outperforms established preference optimization methods like DPO and SimPO in this distillation context. Our empirical evaluations demonstrate the effectiveness of this approach. Notably, our Qwen-REDI-1.5B model, trained on just 131k traces from the open Open-R1 dataset, achieves an 83.1% score on MATH-500. Its performance matches that of DeepSeek-R1-Distill-Qwen-1.5B, a model trained on 800k proprietary data. This result showcases the remarkable data efficiency of utilizing previously discarded negative traces.

It has been demonstrated that the utilization of a monolingual corpus in neural Grammatical Error Correction (GEC) systems can significantly improve the system performance. The previous state-of-the-art neural GEC system is an ensemble of four Transformer models pretrained on a large amount of Wikipedia Edits. The Singsound GEC system follows a similar approach but is equipped with a sophisticated erroneous data generating component. Our system achieved an F0:5 of 66.61 in the BEA 2019 Shared Task: Grammatical Error Correction. With our novel erroneous data generating component, the Singsound neural GEC system yielded an M2 of 63.2 on the CoNLL-2014 benchmark (8.4% relative improvement over the previous state-of-the-art system).

Second Language Acquisition Modeling is the task to predict whether a second language learner would respond correctly in future exercises based on their learning history. In this paper, we propose a neural network based system to utilize rich contextual, linguistic and user information. Our neural model consists of a Context encoder, a Linguistic feature encoder, a User information encoder and a Format information encoder (CLUF). Furthermore, a decoder is introduced to combine such encoded features and make final predictions. Our system ranked in first place in the English track and second place in the Spanish and French track with an AUROC score of 0.861, 0.835 and 0.854 respectively.