Post-Training Reshapes Truth–Sycophancy Geometry

Language models can favor agreement with users over truthful answers, a behavior known as sycophancy. We investigate how post-training changes the internal relationship between truth and sycophancy directions, and whether this relationship affects model responses. We introduce the Geometric Fragility Signature (GFS), which measures how the truth and sycophancy directions are related in activation space. Across 22 matched base and instruction-tuned model pairs from nine families, we find that post-training makes the truth and sycophancy directions more negatively related. We find a similar relationship across two different factual datasets. We then change the angle between the truth and sycophancy directions to test whether this relationship can influence model responses. Under an instruction to prioritize agreement even when it requires flexibility with facts, this changes how often models abandon previously correct answers in seven of eight models. However, other internal directions can sometimes produce similar changes. Finally, we use the same directions to try to keep models truthful under pressure to agree. This helps some models but not others, and can even make models abandon more correct answers. Overall, our results show that post-training reshapes the internal relationship between truth and sycophancy directions, while interventions on these directions can change model responses but do not consistently reduce sycophancy across models.