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A Best Learning Rate for RoBERTa-prompt
Here, we provide best learning rates (LR, searched from  $1e^{-5}, 5e^{-6}, 1e^{-6}$  as discussed in main paper) for  $\mathcal{L}_{\mathrm{halluc}}$  of EmbedHalluc for each task used in RoBERTa-large prompt-based fine-tuning.
Task	LR
SST-2	1e-6
Subj	1e-5
SST-5	1e-6
CoLA	1e-5
TREC	1e-6
MNLI	1e-5
MNLI-mm	1e-5
SNLI	1e-6
QNLI	5e-6
QQP	1e-6
RTE	1e-6
MRPC	1e-6
MR	5e-6
MPQA	5e-6
CR	5e-6
B EmbedHalluc with BERT
In addition to the experiments using RoBERTa shown in the main paper, here we show the results of BERT-large-cased with conventional fine-tuning as a further check on robustness of our method with respect to the choice of model. Table B.1 shows the results of the experiments. EmbedHalluc outperforms the baseline across 14 of the 15 tasks with an average improvement of 2.43 over the baseline.
Table A.1: Best learning rate for  $\mathcal{L}_{\mathrm{halluc}}$  found for RoBERTa-large prompt-based fine-tuning.
Task	fine-tuning	EmbedHalluc
SST-2 (acc)	73.9 (5.4)	76.6 (3.8)
Subj (acc)	85.2 (3.4)	89.0 (0.9)
SST-5 (acc)	37.6 (4.5)	38.9 (4.2)
CoLA (Matt.)	21.9 (10.0)	28.7 (7.2)
TREC (acc)	77.6 (6.3)	81.8 (3.1)
MNLI (acc)	35.5 (0.9)	36.1 (0.8)
MNLI-mm (acc)	36.0 (0.9)	36.7 (1.5)
SNLI (acc)	39.7 (3.6)	41.0 (3.2)
QNLI (acc)	53.9 (2.5)	55.1 (3.0)
QQP (acc)	56.7 (4.3)	59.5 (2.9)
RTE (acc)	50.9 (3.5)	54.2 (2.5)
MRPC (F1)	72.3 (6.5)	76.7 (2.8)
MR (acc)	73.2 (6.3)	66.4 (8.9)
MPQA (acc)	64.6 (5.6)	65.3 (4.0)
CR (acc)	67.9 (9.0)	77.5 (12.6)
C Regularization Methods with BERT
Besides the experiments with RoBERTa-large shown in the main paper, we present Re-Init and Mixout using BERT-large-cased in this section. The results are shown in Table C.1.
Qualitatively similar to what we observe with experiments using RoBERTa-large in the main paper, Re-Init and Mixout fail to outperform EmbedHsucc in most tasks, with the exceptions of SNLI and QNLI.
Table B.1: Comparison of conventional fine-tuning and our EmbedHalluc, using BERT-large-cased.
Task	fine-tuning	EmbedHalluc	Re-init	Mixout
SST-2	73.9 (5.4)	76.6 (3.8)	73.6 (4.2)	71.9 (3.9)
Subj	85.2 (3.4)	89.0 (0.9)	87.0 (2.5)	85.6 (1.1)
SST-5	37.6 (4.5)	38.9 (4.2)	36.4 (2.5)	36.0 (3.1)
CoLA	21.9 (10.0)	28.7 (7.2)	23.8 (11.8)	13.0 (11.2)
TREC	77.6 (6.3)	81.8 (3.1)	79.7 (3.4)	78.8 (4.4)
MNLI	35.5 (0.9)	36.1 (0.8)	35.1 (1.6)	33.2 (0.6)
MNLI-mm	36.0 (0.9)	36.7 (1.5)	35.6 (2.2)	33.6 (1.0)
SNLI	39.7 (3.6)	41.0 (3.2)	45.3 (3.3)	42.5 (3.2)
QNLI	53.9 (2.5)	55.1 (3.0)	55.9 (2.0)	55.0 (2.7)
QQP	56.7 (4.3)	59.5 (2.9)	58.9 (2.9)	56.6 (6.1)
RTE	50.9 (3.5)	54.2 (2.5)	51.5 (3.8)	50.8 (1.8)
MRPC	72.3 (6.5)	76.7 (2.8)	63.4 (4.6)	74.1 (3.2)
MR	73.2 (6.3)	66.4 (8.9)	60.8 (4.4)	63.0 (4.5)
MPQA	64.6 (5.6)	65.3 (4.0)	64.8 (5.8)	60.9 (2.9)
CR	67.9 (9.0)	77.5 (12.6)	71.6 (8.3)	75.9 (6.1)
D Learning Rate for Baselines
The baseline has only one loss  $\mathcal{L}_{\mathrm{real}}$ , whereas we are learning with an additional loss  $\mathcal{L}_{\mathrm{halluc}}$ , making the total loss to be  $\mathcal{L}_{\mathrm{real}} + \mathcal{L}_{\mathrm{halluc}}$ . The learning rate for  $\mathcal{L}_{\mathrm{real}}$  in the baselines and ours are kept the same. Note that we do not search for this learning rate for our method. We choose  $1e^{-5}$ , which is the most common learning rate to finetune BERT/RoBERTa. As we show in Table D.1, this learning rate produces reasonably good results for the baselines, being the best for 13 tasks and only marginally under-performing in the other 2 tasks. The results in Table D.1 are generated by running the baselines with a batch size of 2 and different learning rates  $1e^{-5}, 2e^{-5}, 5e^{-5}$  suggested by Gao et al. (2021).
Table C.1: Comparisons of EmbedHalluc to Re-init and Mixout, using BERT-large as the base models and conventional fine-tuning as the base learning method.
prompt	1e-5	2e-5	5e-5
SST-2	92.7 (0.4)	91.0 (2.4)	83.6 (7.8)
subj	91.3 (3.3)	87.8 (3.3)	83.9 (3.0)
SST-5	48.8 (1.0)	48.1 (1.0)	43.6 (1.9)
CoLA	7.3 (5.8)	8.7 (5.7)	10.5 (7.2)
trec	83.8 (5.3)	79.3 (5.2)	78.0 (0.7)
MNLI	69.7 (2.0)	66.5 (3.2)	60.0 (5.2)
MNLI-mm	71.5 (1.9)	68.7 (3.2)	62.9 (5.3)
SNLI	78.0 (3.0)	76.2 (2.3))	54.7 (10.3)
QNLI	68.6 (2.8)	64.9 (3.1)	63.0 (7.2)
QQP	70.2 (4.3)	64.2 (5.0)	57.7 (4.9)
RTE	70.9 (3.3)	63.3 (4.8)	55.8 (8.4)
MRPC	74.9 (6.8)	73.9 (3.8)	72.8 (2.6)
MR	86.8 (0.9)	84.5 (1.8)	80.1 (3.9)
MPQA	85.4 (1.8)	85.6 (1.1)	80.1 (3.9)
CR	91.1 (1.0)	90.6 (0.9)	85.3 (2.6)
Table D.1: Results of baseline with Roberta-large prompt-based fine-tuning on different learning rate.  $1e^{-5}$  is what we used in main experiments.