SlowGuess/ACL_2020_OCR huggingface dataset:
Loss	BERT	InferSent
MNLI	Hard	Δ	MNLI	Hard	Δ
Development set results
CE	84.41	76.56	69.97	57.03
RUBi	84.48	77.13	+0.6	70.51	57.97	+0.9
DFL	83.72	77.37	+0.8	60.78	57.88	+0.9
PoE	84.58	78.02	+1.5	66.02	59.37	+2.3
Test set results
None	84.11	75.88	—	—	—
PoE	84.11	76.81	+0.9	—	—	—
C Syntactic Bias in NLI
Base model: We finetune all models for 3 epochs.
Bias-only model: We use a nonlinear classifier with 6 and 6 hidden units with Tanh nonlinearity.
Results: Table 8 shows the performance for each label (entailment and non_entailment) on individual heuristics of the HANS dataset.
Table 7: Results on the MNLI matched benchmark and MNLI matched hard set.  $\Delta$  are absolute differences with CE loss.
Loss	HANS
Constituent	Lexical	Subsequence
gold label: Entailment
CE	98.98±0.6	96.41±0.8	99.72±0.1
RUBi	99.22±0.3	95.59±0.8	99.50±0.3
DFL	90.90±4.3	84.78±5.0	94.33±4.9
PoE	97.24±1.9	92.16±0.9	98.58±0.5
gold label: Non-entailment
CE	20.12±5.8	48.86±5.7	7.18±0.7
RUBi	21.89±7.0	46.82±12.5	7.58±2.3
DFL	50.20±9.2	71.06±3.1	24.28±4.4
PoE	36.08±5.1	59.18±8.0	14.63±3.0
Table 8: Accuracy for each label (entailment or non-entailment) on individual heuristics of HANS.
D Transfer Performance
Mapping: We train all models on SNLI and evaluate their performance on other target datasets. SNLI contains three labels, contradiction, neutral, and entailment. Some of the datasets we consider contain only two labels. In the case of labels entailed and not-entailed, as in DPR, we map contradiction and neutral to the not-entailed class. In the case of labels entailment and neutral, as in SciTail, we map contradiction to neutral.
Comparison with Belinkov et al. (2019a): We modified the implementations of Belinkov et al. (2019a) and corrected some implementation issues in the InferSent baseline (Conneau et al., 2017). Compared to the original InferSent implementation, the main differences in our implementation include: (a) We incorporated the fixes suggested for the bugs in the implementation of mean/max-pooling over BiLSTM in the InferSent baseline $^{5}$  (b). We additionally observed that the aggregation of losses over each batch was computed with the average instead of the intended summation and we corrected it. $^{6}$  (c) We followed the implementation of InferSent and we removed out-of-vocabulary (OOV) words from the sentence representation, while Belinkov et al. keep
$^{5}$ https://github.com/facebookresearch/ InferSent/issues/51
The same observation is reported in https://github.com/facebookresearch/InferSent/pull/107.
Data	CE	DFL	Δ%	PoE	Δ%	M1	Δ%	M2	Δ%
SICK	54.09	55.00	1.68	55.79	3.14	49.77	-7.99	49.77	-7.99
ADD1	75.19	78.29	4.12	77.00	2.41	67.44	-10.31	67.44	-10.31
DPR	49.95	50.59	1.28	49.95	0.00	50.87	1.84	50.87	1.84
SPR	41.31	47.95	16.07	50.50	22.25	51.51	24.69	51.51	24.69
FN+	48.65	49.58	1.91	49.35	1.44	53.23	9.41	53.23	9.41
JOCI	46.47	46.48	0.02	47.53	2.28	44.83	-3.53	44.83	-3.53
MPE	60.60	60.70	0.17	61.80	1.98	56.40	-6.93	56.40	-6.93
SCITAIL	64.25	65.19	1.46	63.17	-1.68	56.40	-12.22	56.40	-12.22
GLUE	48.73	46.83	-3.90	49.09	0.74	43.93	-9.85	43.93	-9.85
QQP	61.80	66.24	7.18	66.36	7.38	62.46	1.07	62.46	1.07
MNLI	56.99	56.70	-0.51	56.59	-0.70	51.72	-9.25	51.72	-9.25
MNLI-M	57.01	57.75	1.30	57.84	1.46	53.99	-5.30	53.99	-5.30
Average	—	—	2.57	—	3.39	—	-2.36	—	-2.36
Table 9: Accuracy results of models with InferSent transferring to new target datasets. All models are trained on SNLI and tested on the target datasets. M1 and M2 are our re-implementation of Belinkov et al. (2019a).  $\Delta$  are relative differences in percentage with respect to CE loss.
them by introducing an OOV token. We additionally observed during the pre-processing of some of the target datasets in the implementation of Belinkov et al., some of the samples are not considered due to the preprocessing issues. We fix the pre-processing issues and evaluate our models and our reimplementations of Belinkov et al. (2019a) on the same corpora. We set the BiLSTM dimension to 512 across all models. Note that Belinkov et al. use BiLSTM dimension of 2048, and due to the mentioned differences in implementations and datasets, the results reported in Belinkov et al. (2019a) are not comparable. However, we still on average surpass their reported results substantially. Our reimplementations and scripts to reproduce the results are publicly available in https://github.com/rabeehk/robust-nli-fixed.
As used in prior work to adjust the learning-rate of the bias-only and baseline models (Belinkov et al., 2019a), we introduce a hyperparameter  $\beta$  for the bias-only model to modulate the loss of the bias-only model in ensembling. We sweep hyper-parameters  $\gamma, \alpha$  over  $\{0.02, 0.05, 0.1, 0.6, 2.0, 4.0, 5.0\}$  and  $\beta$  over  $\{0.05, 0.2, 0.4, 0.8, 1.0\}$ . Table 9 shows the results of our debiasing models (DFL, PoE), our re-implementations of proposed methods in Belinkov et al. (2019a) (M1, M2), and the baseline with InferSent (CE). The DFL model outperforms the baseline in 10 out of 12 datasets, while the PoE model outperforms the baseline in 9 datasets and does equally well on the DPR dataset. As shown in prior work (Belinkov et al., 2019a), the MNLI dataset has very sim
ilar biases to SNLI, which the models are trained on, so we do not expect any improvement in the relative performance of our models and the baseline for MNLI dataset. Interestingly, our methods obtain improvement on MNLI-M, in which the test data differs from training distribution. Our proposed debiasing methods, PoE and DFL, are highly effective, boosting the relative generalization performance of the baseline by  $3.39\%$  and  $2.57\%$  respectively, significantly surpassing the prior work of Belinkov et al. (2019a). Compared to M1 and M2, our methods outperform them on 9 datasets, while they do better on two datasets of SPR and  $\mathrm{FN + }$ , and slightly better on the DPR dataset. However, note that DPR is a very small dataset and all models perform close to random-chance on this dataset.
E Analysis of Debiased Focal Loss
Figure 4 shows the impact of  $\gamma$  on BERT trained with DFL.
Figure 4: Accuracy of the BERT model trained with DFL, on SNLI and SNLI hard sets for different  $\gamma$ .