The need for interpretability in deep learning has driven interest in counterfactual explanations, which identify minimal changes to an instance that change a model's prediction. Current counterfactual (CF) generation methods require task-specific fine-tuning and produce low-quality text. Large Language Models (LLMs), though effective for high-quality text generation, struggle with label-flipping counterfactuals (i.e., counterfactuals that change the prediction) without fine-tuning. We introduce two simple classifier-guided approaches to support counterfactual generation by LLMs, eliminating the need for fine-tuning while preserving the strengths of LLMs. Despite their simplicity, our methods outperform state-of-the-art counterfactual generation methods and are effective across different LLMs, highlighting the benefits of guiding counterfactual generation by LLMs with classifier information. We further show that data augmentation by our generated CFs can improve a classifier's robustness. Our analysis reveals a critical issue in counterfactual generation by LLMs: LLMs rely on parametric knowledge rather than faithfully following the classifier.

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