Grammar Control for Language Learning with Sequential Monte Carlo and Small Language Models

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 ($+13.2\%$).

Practitioners have access to an abundance of language models and prompting strategies for solving many language modeling tasks; yet prior work shows that modeling performance is highly sensitive to both choices. Classical machine learning ensembling techniques offer a principled approach: aggregate predictions from multiple sources to achieve better performance than any single one. However, applying ensembling to language models during decoding is challenging: naively aggregating next-token probabilities yields samples from a locally normalized, biased approximation of the generally intractable ensemble distribution over strings. In this work, we introduce a unified framework for composing $K$ language models into $f$-ensemble distributions for a wide range of functions $f\colon\mathbb{R}_{\geq 0}^{K}\to\mathbb{R}_{\geq 0}$. To sample from these distributions, we propose a byte-level sequential Monte Carlo (SMC) algorithm that operates in a shared character space, enabling ensembles of models with mismatching vocabularies and consistent sampling in the limit. We evaluate a family of $f$-ensembles across prompt and model combinations for various structured text generation tasks, highlighting the benefits of alternative aggregation strategies over traditional probability averaging, and showing that better posterior approximations can yield better ensemble performance.

Grammar-constrained generation guarantees syntactic validity, but can substantially degrade semantic quality when the model's preferred outputs are poorly aligned with the imposed grammar. This trade-off is particularly severe when the prompt is underspecified or the model has limited instruction-following ability. Beam search can partially mitigate these failures by exploring multiple valid sequences, but its computational cost grows with beam width, while sequence-level probability is only an imperfect proxy for semantic quality. We introduce GrammarRL, a label-free reinforcement learning method that adapts language models to grammar constraints without requiring annotated data. GrammarRL optimizes the model using two complementary self-supervised rewards derived from its own likelihoods: a direct reward, measuring how likely the constrained output is given the input, and a reverse reward, measuring how well the input can be reconstructed from the generated output. We optimize these rewards with a Reinforce Leave-One-Out (RLOO) objective over groups of grammar-constrained rollouts, augmented with the top-1 beam-search hypothesis and regularized towards a frozen base model. We evaluate GrammarRL on sign language gloss translation, hierarchical text classification, and named entity recognition using Llama models ranging from 1B to 8B parameters. GrammarRL consistently outperforms constrained greedy decoding, with an average improvement of 9.8 points and gains of up to 22.8 BLEU. It matches or outperforms beam search on two of the three tasks while preserving greedy-decoding inference cost. Ablations further show that the two rewards are complementary: either reward alone can underperform the untrained baseline, whereas their combination consistently improves upon it.