Grammar competency estimation is essential for assessing linguistic proficiency in both written and spoken language; however, the spoken modality presents additional challenges due to its spontaneous, unstructured, and disfluent nature. Developing accurate grammar scoring models further requires extensive expert annotation, making large-scale data creation impractical. To address these limitations, we propose a zero-shot grammar competency estimation framework that leverages unlabeled data and Large Language Models (LLMs) without relying on manual labels. During training, we employ LLM-generated predictions on unlabeled data by using grammar competency rubric-based prompts. These predictions, treated as pseudo labels, are utilized to train a transformer-based model through a novel training framework designed to handle label noise effectively. We show that the choice of LLM for pseudo-label generation critically affects model performance and that the ratio of clean-to-noisy samples during training strongly influences stability and accuracy. Finally, a qualitative analysis of error intensity and score prediction confirms the robustness and interpretability of our approach. Experimental results demonstrate the efficacy of our approach in estimating grammar competency scores with high accuracy, paving the way for scalable, low-resource grammar assessment systems.

Automated Essay Scoring (AES) systems are widely popular in the market as they constitute a cost-effective and time-effective option for grading systems. Nevertheless, many studies have demonstrated that the AES system fails to assign lower grades to irrelevant responses. Thus, detecting the off-topic response in automated essay scoring is crucial in practical tasks where candidates write unrelated text responses to the given task in the question. In this paper, we are proposing an unsupervised technique that jointly scores essays and detects off-topic essays. The proposed Automated Open Essay Scoring (AOES) model uses a novel topic regularization module (TRM), which can be attached on top of a transformer model, and is trained using a proposed hybrid loss function. After training, the AOES model is further used to calculate the Mahalanobis distance score for off-topic essay detection. Our proposed method outperforms the baseline we created and earlier conventional methods on two essay-scoring datasets in off-topic detection as well as on-topic scoring. Experimental evaluation results on different adversarial strategies also show how the suggested method is robust for detecting possible human-level perturbations.