Abstract: In this work, we explore joint energy-based model (EBM) training during the finetuning of pretrained text encoders (e.g., Roberta) for natural language understanding (NLU) tasks. Our experiments show that EBM training can help the model reach a better calibration that is competitive to strong baselines, with little or no loss in accuracy. We discuss three variants of energy functions (namely scalar, hidden, and sharp-hidden) that can be defined on top of a text encoder, and compare them in experiments. Due to the discreteness of text data, we adopt noise contrastive estimation (NCE) to train the energy-based model. To make NCE training more effective, we train an auto-regressive noise model with the masked language model (MLM) objective.