Abstract:An LLM's factuality and refusal training can be compromised by simple changes to a prompt. Models often adopt user beliefs (sycophancy) or satisfy inappropriate requests which are wrapped within special text (jailbreaking). We explore \emph{consistency training}, a self-supervised paradigm that teaches a model to be invariant to certain irrelevant cues in the prompt. Instead of teaching the model what exact response to give on a particular prompt, we aim to teach the model to behave identically across prompt data augmentations (like adding leading questions or jailbreak text). We try enforcing this invariance in two ways: over the model's external outputs (\emph{Bias-augmented Consistency Training} (BCT) from Chua et al. [2025]) and over its internal activations (\emph{Activation Consistency Training} (ACT), a method we introduce). Both methods reduce Gemini 2.5 Flash's susceptibility to irrelevant cues. Because consistency training uses responses from the model itself as training data, it avoids issues that arise from stale training data, such as degrading model capabilities or enforcing outdated response guidelines. While BCT and ACT reduce sycophancy equally well, BCT does better at jailbreak reduction. We think that BCT can simplify training pipelines by removing reliance on static datasets. We argue that some alignment problems are better viewed not in terms of optimal responses, but rather as consistency issues.