SlowGuess/ACL_2020_OCR huggingface dataset:
Table 5: Breakdown of solvability annotation counts by perturbation. Ambig. indicates the count of examples labeled as Ambiguous, Non-Ambig. is the number of remaining examples. Correct indicates the number of those which is solved correctly.
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- "who we had discussed _"
- "who he had discussed _"
- "who she had discussed _"
- "who you had discussed _"
which we had seen
- "which he had seen _"
which she had seen
- "which you had seen _"
- "who we know from _"
- "who he knows from _"
- "who she knows from _"
- "who you know from _"
- "that is mentioned in _"
- "that is located at _"
- "that is close to _"
- "that is known for _"
- "which had been _",
- "who you met _"
- "that is -"
which was put there
Synonym/Name substitution (SYN/NA) No appropriate synonyms were found for tide and wind in examples 130 and 131.
Adverbial qualification (ADV) Two instances (95 and 96) in which the main verb was already modified were excluded.
F Referent preferences
Table 6 shows the percentage of examples in the switchable subset of the datasets where the second referent in the text was assigned a higher probability than the first, for both the original and reversed referent order.
G Effect of perturbations
Nucleus Sampling Table 7 shows the average number of vocabulary items kept after Nucleus sampling with  $p = 0.9$  is applied.
Pert.	Original	Reversed
ORG	66.90	70.42
TEN	62.38	65.14
NUM	60.16	56.10
GEN	72.17	75.65
VC	38.14	39.83
RC	63.57	68.57
ADV	68.08	70.92
SYN/NA	59.12	64.23
Table 6: Percentage of examples in switchable subset with probabilities assigned to the second referent in the text rather than the first, for both the original and reversed referent order.
Probability shift is defined as the difference in the probability of a candidate before and after a perturbation is applied. Figure 9 shows the difference in average probability shift between the correct candidates and the incorrect candidates for each of the models per perturbation type. This provides a view that is meaningfully different from accuracy, as the probability of a candidate can shift without exceeding the threshold required to change a model's prediction. We find that there is a general trend of the incorrect candidates becoming more likely relative to the correct ones. This can be seen as confirming that, on average, nearly all perturbations make the problems more difficult for all models.
Hidden state representation distance is used to provide a more holistic view of the correspondence between the representations derived for the different perturbations. The analysis is conducted on the 128 examples which are common between all datasets. A representation is derived for each example by taking the max-pool of hidden-state representations of a model's final layer. For each of the seven perturbations  $p$ , we compute pairwise correlation distance[16] between each pair of original and perturbed example representations yielding a vector  $\vec{D_p} \in \mathbb{R}^{128}$ . The mean of  $\vec{D_p}$  is then computed as an aggregate measure of the distance between the representations derived from a perturbation  $p$  and the original  $o$ . Figure 10 shows a plot of this for all perturbations for each of the models.
This is preferable to other distance measures as it normalizes both the mean and variance of activity patterns over experimental conditions.
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Perturbation	BERT	ROBERTA	XLNET	BERT+WW	ROBERTA+WG
ORG	19.81	203	1.26	1.07	1021.44
TEN	23.88	165.84	1.26	1.09	947.53
NUM	90.35	341.05	1.57	1.30	1087.78
GEN	18.11	128.37	1.44	1.19	1039.84
VC	41.88	154.21	1.28	1.09	961.04
RC	21.02	97.35	1.35	1.14	952.09
ADV	17.01	145.35	1.23	1.10	1004.14
SYN/NA	31.50	199.26	1.39	1.11	1055.71
VOCAB. SIZE	30522	50265	32000	30522	50265
Table 7: Average number of vocabulary items left after probability distribution truncation with  $p = {0.9}$  is applied.
Figure 9: The difference between average probability shift for the correct and the incorrect referents per perturbation. Y-axis values above zero mean the correct referent became more likely on average after a perturbation and vice versa.
Figure 10: The correlation of pronoun hidden state representation distance from the original for each perturbation.
H Candidate probability correlations
Figure 11 shows the average correlation between a candidate's probability when it is the correct refer- erent and when it is not.
Figure 11: Correlation (Spearman's  $\rho$ ) between the probability of a candidate when it is the correct candidate and when it is the incorrect one. Candidates A and B are the first and second candidates in a WSC instance.
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