Gumbel Machine: Counterfactual Student Writing Generation via Gumbel Noise Steering

An effective method of teaching across disciplines is to provide examples of high-quality work. However, an example may be significantly different from a student's current work, making it challenging for them to emulate. An ideal learning demonstration is a counterfactual version of the student work, an improved version that is still similar to their own. Existing automated approaches for counterfactual text generation using Large Language Models (LLMs) result in domain-specific systems that are difficult to translate into practical applications. We present the Gumbel Machine, a flexible, modular approach to generating counterfactuals that leverages LLM instruction-following capabilities while encouraging similarity to a reference factual text. Central to our approach is a novel, controlled decoding algorithm, $β$-Hindsight control, which uses latent randomness as a tunable similarity control mechanism during counterfactual generation. Experiments on datasets of student writing, scored on various criteria, demonstrate the effectiveness of our approach at generating counterfactuals both rubric-consistent and similar to a reference.