SlowGuess/ACL_2020_OCR huggingface dataset:
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A.1 Fine-tuning details
We used bert-base-uncased for all experiments. As is standard, we fine-tuned this pretrained model on MNLI by training a linear classifier to predict the label from the CLS token's final layer embedding, while continuing to update BERT's parameters (Devlin et al., 2019). The order of training examples was reshuffled for each model. All models were trained for three epochs.
A.2 Generating augmentation examples
The following list describes the augmentation strategies we used. Table A.1 illustrates all of these strategies as applied to a particular source sentence. Note that inversion generally changes the meaning of the sentence (the detective followed the suspect refers to a different event from the suspect followed the detective), but passivization on its own does not (the detective followed the suspect refers to the same event as the suspect was followed by the detective).
- Inversion (original premise): For a source example  $(p, h, \rightarrow)$ , generate  $(p, \mathrm{INV}(h), \rightarrow)$  where INV returns the source sentence with the subject and object switched. Ignore source examples whose label is  $\rightarrow$ .
- Inversion (transformed hypothesis): For a source  $(p, h)$  (with any label), discard the premise  $p$  and generate  $(h, \operatorname{INV}(h), \rightarrow)$ .
- Passivization (original premise): For a source  $(p, h)$  (with any label), generate  $(p, \mathrm{PASS}(h))$ , with the same label, where PASS returns the passive version of the source sentence (without changing its meaning).
- Passivization (transformed hypothesis): For a source  $(p, h)$ , discard the premise  $p$ , and generate two examples, one with an entailment label— $(h, \mathrm{PASS}(h), \rightarrow)$ —and one with a nonentailment label— $(h, \mathrm{PASS}(\mathrm{INV}(h)), \nrightarrow)$ .
We identified transitive sentences in MNLI that could serve as source sentences using the constituency parses provided with MNLI, excluding the noisier TELEPHONE genre. We did so by searching for matrix S nodes with exactly one NP daughter of the VP, where the subject and the object were both full noun phrases (i.e., neither were a personal pronoun such as  $me$ ), and where the verb lemma
was not be or have. We kept the original tense of the verb, and modified its agreement features if necessary (e.g., the movie stars Matt Dillon and Gary Sinise was transformed into Matt Dillon and Gary Sinise star the movie).
The size of the largest augmentation set was 1215 for all strategies. This size was determined based on the largest augmentation dataset we could generate from MNLI for the inversion with original premise strategy using the procedure mentioned above. For fair comparison, we kept the same size even for strategies where we could have generated a larger dataset. We also created a Medium dataset by randomly sampling 405 of the cases identifying using the procedure above, as well as a small dataset with 101 examples. We performed this process only once for each strategy: as such, runs varied only in the classifier's weight initialization and the order of examples but not in the augmentation examples included in training.
To create the Combined augmentation dataset, we concatenated the inversion and passivization datasets, then randomly discarded half of the examples (to match the size of the combined dataset with the others). As with the other datasets, we only did this once: the Combined augmentation set was the same across runs. One consequence of this procedure is that the number of passivization and inversion examples was not exactly identical.
A.3 Detailed Results
The following tables provide the detailed results of our experiments. Table A.2 shows each strategy's mean accuracy on MNLI, as well on the HANS cases that diagnose each of the three heuristics (the Lexical Overlap Heuristic, the Subsequence Heuristic, and the Constituent Heuristic), for which the correct label is non-entailment  $(\rightarrow)$ . Table A.3 zooms in on the best-performing augmentation strategy—subject/object inversion with a transformed hypothesis—on BERT's accuracy on HANS, both when the correct label is entailment  $(\rightarrow)$  and when the label is non-entailment  $(\rightarrow)$ . Finally, the last three tables detail the effect of augmentation by inversion with a transformed hypothesis on each of the 30 HANS subcases, broken down by the heuristic that they were designed to diagnose: the Lexical Overlap Heuristic (Table A.5), the Subsequence Heuristic (Table A.6), and the Constituent Heuristic (Table A.7).
There are 16 El Grecos in this small collection.  $\longrightarrow$
Original premise:
There are 16 El Grecos in this small collection.  $\nrightarrow$
16 El Grecos contain this small collection.
Transformed hypothesis:
This small collection contains 16 El Grecos.  $\nrightarrow$
Passivization
16 El Grecos are contained by this small collection.
Transformed hypothesis (entailment label):
This small collection contains 16 El Grecos.  $\longrightarrow$
16 El Grecos are contained by the small collection.
Transformed hypothesis (non-entailment label):
This small collection is contained by 16 El Grecos.
Random shuffling (with random label)
are collection. small El this in 16 There Grecos  $\twoheadrightarrow / \rightarrow$
collection This Grecos El small 16 contains.
Table A.1: Syntactic augmentation strategies (full table).
MNLI	Overlap	Subsequence	Constituent
S	M	L	S	M	L	S	M	L	S	M	L
Original premise
Inversion	.84	.84	.84	.07	.40	.44	.01	.06	.12	.06	.09	.12
Passivization	.84	.84	.84	.23	.35	.54	.04	.05	.09	.13	.11	.15
Combined	.84	.84	.84	.42	.25	.36	.07	.05	.04	.14	.15	.12
Transformed hypothesis
Inversion	.84	.84	.84	.46	.71	.73	.09	.25	.23	.17	.23	.18
Passivization	.84	.84	.84	.41	.43	.31	.06	.06	.07	.13	.15	.17
Combined	.84	.84	.84	.32	.64	.71	.06	.13	.28	.15	.26	.22
Pass. (only pos)	.84	.84	.84	.30	.20	.29	.04	.04	.05	.10	.13	.11
Pass. (only neg)	.84	.84	.85	.36	.45	.39	.06	.06	.06	.15	.13	.13
Random shuffling	.84	.84	.84	.26	.19	.35	.05	.05	.06	.15	.14	.14
Unaugmented	.84	.28	.05	.13
Table A.2: Accuracy of models trained using each augmentation strategy when evaluated on HANS examples diagnostic of each of the three heuristics—lexical overlap, subsequence and constituent—for which the correct label is non-entailment  $(\rightarrow)$ . Augmentation set sizes are  $S$  (101 examples),  $M$  (405) and  $L$  (1215). Chance performance is 0.5.
Subset of HANS	Label	Unaugmented	Small	Medium	Large
MNLI	All	0.84	0.84	0.84	0.84
Subject/object swap	→	0.19	0.53	1.00	1.00
All other	→	0.96	0.93	0.77	0.77
lexical overlap	→	0.30	0.44	0.64	0.66
Subsequence	→	0.99	0.99	0.84	0.85
→	0.05	0.09	0.25	0.23
Constituent	→	0.99	0.98	0.97	0.97
→	0.13	0.17	0.23	0.18
Table A.3: Effect on HANS accuracy of augmentation using subject/object inversion with a transformed hypothesis. Results are shown for BERT fined-tuned on the MNLI training set augmented with the three size of augmentation sets (101, 405 and 1215 examples), as well as for BERT fine-tuned on the unaugmented MNLI training set.
Architecture or training method	Overall	Entailment	Non-entailment
L	S	C	L	S	C
Baseline (McCoy et al., 2019a)	0.57	0.96	0.99	0.99	0.28	0.05	0.13
Learned-Mixin + H (Clark et al., 2019)	0.69	0.68	0.84	0.81	0.77	0.45	0.60
DRiFt-HAND (He et al., 2019)	0.66	0.77	0.71	0.76	0.71	0.41	0.61
Product of experts (Mahabadi and Henderson, 2019)	0.67	0.94	0.96	0.98	0.62	0.19	0.30
HUBERT + (Moradshahi et al., 2019)	0.63	0.96	1.00	0.99	0.70	0.04	0.11
MT-DNN + LF (Pang et al., 2019)	0.61	0.99	0.99	0.94	0.07	0.07	0.13
BiLSTM forgettables (Yaghoobzadeh et al., 2019)	0.74	0.77	0.91	0.93	0.82	0.41	0.61
Ours:
Inversion (transformed hypothesis), small	0.60	0.93	0.99	0.98	0.46	0.09	0.17
Inversion (transformed hypothesis), medium	0.63	0.77	0.84	0.97	0.71	0.25	0.23
Inversion (transformed hypothesis), large	0.62	0.77	0.85	0.97	0.73	0.23	0.18
Combined (transformed hypothesis), medium	0.65	0.92	0.96	0.98	0.64	0.13	0.26
Table A.4: HANS accuracy from various architectures and training methods, broken down by the heuristic that the example is diagnostic of and by its gold label, as well as overall accuracy on HANS. All but MT-DNN + LF use BERT as base model.  $L$ ,  $S$ , and  $C$  stand for lexical overlap, subsequence, and constituent heuristics, respectively. Augmentation set sizes are  $n = 101$  for small,  $n = 405$  for medium, and  $n = 1215$  for large.
Subcase	Unaugmented	Small	Medium	Large
Subject-object swap	0.19	0.53	1.00	1.00
The senators mentioned the artist. → The artist mentioned the senators.
Sentences with PPs	0.41	0.61	0.81	0.89
The judge behind the manager saw the doctors. → The doctors saw the manager.
Sentences with relative clauses	0.33	0.53	0.77	0.83
The actors called the banker who the tourists saw. → The banker called the tourists.
Passives	0.01	0.04	0.29	0.13
The senators were helped by the managers. → The senators helped the managers.
Conjunctions	0.45	0.59	0.69	0.81
The doctors saw the presidents and the tourists. → The presidents saw the tourists.
Untangling relative clauses	0.98	0.94	0.74	0.76
The athlete who the judges saw called the manager. → The judges saw the athlete.
Sentences with PPs	1.00	0.98	0.85	0.86
The tourists by the actor called the authors. → The tourists called the authors.
Sentences with relative clauses	0.99	0.98	0.89	0.89
The actors that danced encouraged the author. → The actors encouraged the author.
Conjunctions	0.83	0.78	0.68	0.66
The secretaries saw the scientists and the actors. → The secretaries saw the actors.
Passives	1.00	0.99	0.67	0.67
The authors were supported by the tourists. → The tourists supported the authors.
Table A.5: Subject/object inversion with a transformed hypothesis: results for the HANS subcases that are diagnostic of the lexical overlap heuristic, for four training regimens—unaugmented (trained only on MNLI), and with small  $(n = 101)$ , medium  $(n = 405)$  and large  $(n = 1215)$  augmentation sets. Chance performance is 0.5. Top: cases in which the gold label is non-entailment. Bottom: cases in which the gold label is entailment.
Subcase	Unaugmented	Small	Medium	Large
NP/S	0.02	0.03	0.47	0.50
The managers heard the secretary resigned. → The managers heard the secretary.
PP on subject	0.12	0.21	0.21	0.23
The managers near the scientist shouted. → The scientist shouted.
Relative clause on subject	0.07	0.13	0.14	0.13
The secretary that admired the senator saw the actor. → The senator saw the actor.
MV/RR	0.00	0.01	0.05	0.02
The senators paid in the office danced. → The senators paid in the office.
NP/Z	0.06	0.09	0.41	0.25
Before the actors presented the doctors arrived. → The actors presented the doctors.
Conjunctions	0.98	0.96	0.87	0.86
The actor and the professor shouted. → The professor shouted.
Adjectives	1.00	1.00	0.92	0.91
Happy professors mentioned the lawyer. → Professors mentioned the lawyer.
Understood argument	1.00	0.99	0.97	0.97
The author read the book. → The author read.
Relative clause on object	0.99	0.98	0.70	0.71
The artists avoided the actors that performed. → The artists avoided the actors.
PP on object	1.00	1.00	0.75	0.79
The authors called the judges near the doctor. → The authors called the judges.
Table A.6: Subject/object inversion with a transformed hypothesis: results for the HANS subcases diagnostic of the subsequence heuristic, for four training regimens—unaugmented (trained only on MNLI), and with small  $(n = 101)$ , medium  $(n = 405)$  and large  $(n = 1215)$  augmentation sets. Top: cases in which the gold label is non-entailment. Bottom: cases in which the gold label is entailment.
Subcase	Unaugmented	Small	Medium	Large
Embedded under preposition	0.41	0.43	0.57	0.49
Unless the senators ran, the professors recommended the doctor. → The senators ran.
Outside embedded clause	0.00	0.01	0.02	0.01
Unless the authors saw the students, the doctors resigned. → The doctors resigned.
Embedded under verb	0.17	0.25	0.28	0.22
The tourists said that the lawyer saw the banker. → The lawyer saw the banker.
Disjunction	0.01	0.01	0.04	0.03
The judges resigned, or the athletes saw the author. → The athletes saw the author.
Adverbs	0.06	0.13	0.25	0.13
Probably the artists saw the authors. → The artists saw the authors.
Embedded under preposition	0.96	0.94	0.94	0.95
Because the banker ran, the doctors saw the professors. → The banker ran.
Outside embedded clause	1.00	1.00	0.99	0.99
Although the secretaries slept, the judges danced. → The judges danced.
Embedded under verb	0.99	0.99	0.98	0.97
The president remembered that the actors performed. → The actors performed.
Conjunction	1.00	1.00	0.98	0.99
The lawyer danced, and the judge supported the doctors. → The lawyer danced.
Adverbs	1.00	1.00	0.93	0.96
Certainly the lawyers advised the manager. → The lawyers advised the manager.
Table A.7: Subject/object inversion with a transformed hypothesis: results for the HANS subcases diagnostic of the constituent heuristic, for four training regimens—unaugmented (trained only on MNLI), and with small  $(n = 101)$ , medium  $(n = 405)$  and large  $(n = 1215)$  augmentation sets. Chance performance is 0.5. Top: cases in which the gold label is non-entailment. Bottom: cases in which the gold label is entailment.