Abstract: We explore loss functions for fact verification in the FEVER shared task. While the cross-entropy loss is a standard objective for training verdict predictors, it fails to capture the heterogeneity among the FEVER verdict classes. In this paper, we develop two task-specific objectives tailored to FEVER. Experimental results confirm that the proposed objective functions outperform the standard cross-entropy. Performance is further improved when these objectives are combined with simple class weighting, which effectively overcomes the imbalance in the training data. The source code is available (https://github.com/yuta-mukobara/RLF-KGAT).