SlowGuess/ACL_2020_OCR huggingface dataset:
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annotator rationales. In Proceedings of the Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 31-40.
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For each model below, we use BERT-base-uncased (for SST, AgNews), Roberta-base (for Multirc), and SciBERT (scivocab-uncased) (for Evidence Inference) embeddings (from huggingface library (Wolf et al., 2019) as they appear in AllenNLP library (Gardner et al., 2018)) as corresponding pretrained transformer model.
Tokenization was performed using tokenizer associated with each pretrained transformer models. Only the top two layers of each model were finetuned. For documents greater than 512 in length, we used staggered position embeddings (for example, if an example of length 1024, the position embeddings used are 1,1,2,2,3,3,...).
Lei et al. and Bastings et al. Models We use transformer model to generate token embeddings (max-pooling embeddings from wordpieces) in the generator, placing a dense classification layer on top to return a binary decision. The encoder model also uses the transformer to encode selected tokens and the start token embedding was used to perform final classification.
For the movies dataset we used a slightly different model to get around the  $O(n^{2})$  memory bottleneck. Specifically, we first encode 512 token subsequences with the transformer and then run these through a 128-d BiLSTM on top of transformer embeddings. Wordpiece embeddings are averaged to create token embeddings and these embeddings are then used to make token level decisions for generator model. In the encoder model, they are collapsed using additive attention module (Bahdanau et al., 2015) into a single vector prior to the final classification.
We used cross-entropy loss to train the encoder, and the optimization was performed using the Adam Optimizer with a learning rate of 2e-5. For regularization, we used 0.2 dropout after
transformer embedding layer and placed an 0.001  $\ell_{2}$  loss over all weights of our network and a grad norm of 5.0. Models were trained for 20 epochs and we kept the best parameters on the basis of macro-F1 score on dev sets.
Hyperparameter search for Lei et al. (2016) models was performed over  $\lambda_{1}$  and  $\lambda_{2}$  parameters, with  $\lambda_{1}$  uniformly selected over log scale in range [1e-2, 1e-0] and  $\lambda_{2}$  selected from [0.0, 0.5, 1.0, 2.0]. We performed the hyperparameter search 20 times and selected the best of these on the basis of F1 score on dev sets.
Bastings et al. (2019) do not require hyperparameter search since it uses a Lagrangian relaxation based optimisation for its regularizers. We use the same initial hyperparameter settings used by the authors in their codebase. We use the Hard Kumaraswamy distribution as provided by the authors here https://github.com/bastings/interpretablepredictions.
FRESH For all three components of the FRESH model, we used the same transformer-based models as mentioned previously to encode tokens. Classification was performed using start token embeddings. Optimisation was performed using Adam optimizer (Kingma and Ba, 2015) with a learning rate of 2e-5. We insert a dropout layer following the BERT embedding layer for regularisation, and impose an  $0.001\ell_{2}$  loss over all weights of our network. We also enforce a grad norm of 5.0. The model was trained for 20 epochs, and we again kept the best models with respect to macro F1 scores on the dev sets.
For the movies dataset, we use similar modifications as discussed above.
B Hyperparameter sensitivity analysis
In Figure 7, we report the model accuracy for various hyperparameter searches on three of our datasets. Note that in many cases, the search does not converge to the desired length (it either selects the entire document or completely degenerates, selecting no tokens). We also show in Figure 6 an analysis of model performance with respect to hyperparameter search using the procedure described in (Dodge et al., 2019).
C Amazon Mechanical Turk Layouts
See Figures 8 and 9 for screenshots of the interfaces shown to annotators.
Figure 6: Plot of training duration for a single model vs Expected validation macro F1 scores as defined by (Dodge et al., 2019)
Figure 7: Plot of average rationale length vs model performance in terms of F1 score for 20 hyperparameter searches for (Lei et al., 2016)
D Additional Dataset Details
See Table 5.
E Global Discretization Heuristics
We use following method to construct globally optimal rationales :
Global top- $k$ . A ratio of tokens to maintain  $p$  is determined beforehand, but instead of taking the top  $p \cdot |x_i|$  tokens from each instance, the training set (resp. dev, test) is created by only taking the top  $p \cdot \sum_{x_i \in \mathcal{D}_{\sqcup \nabla}} |x_i|$  tokens from the entire initial training set (resp. dev, test). To avoid the possible complete removal of certain instances, we add a further constraint where each instance first secures the top  $q < p$ -proportion tokens, before filling up the remainder globally.
Global Contig. To limit the rationales to a contiguous text span, we first find the maximum-mass segments for the appropriate range of lengths on each instance, then run a greedy algorithm to find per-instance lengths for overall maximal mass: starting with the minimally-long spans, of total length  $L_{m}$ , we perform  $\mathcal{B} - L_{m}$  iterations of finding the next single-token addition in the entire dataset which will lead to the maximum increase in overall weight (each time ranking the marginal gains for each instance  $x_{i}$  of replacing the current  $k(x_{i})$ -length span with the best  $k(x_{i}) + 1$ -length span in the instance).
In Table 6 we provide average differences between using global vs instance heuristics to extract rationales from our documents, given saliency scores. We also ran a  $t$ -test to determine if global heuristics provided results significantly different from instance-level methods, finding that they did not.
Figure 8: Amazon Mechanical Turk layout for Movies tasks.
Select the sentiment that best describes the text and a score indicating how confident you are. Some of these will not make any sense. If you're unsure, select any label and assign a confidence score of 0.
i believe that robert duvall ( who is the producer , director , writer , and main star of the apostle ) deserves an oscar for his performance as sonny the religious a performance which is so complex and realistic it ranks as one of the finest acting performances on offers the audience a completely honest look at southern the apostle would rank as one of the best movies of this i emphatically recommend the apostle for connoisseurs of stage and fine acting on film find the apostle a thought - provoking experience the apostle is a four star
What sentiment does this text convey?
$\mathbb{O}$  Positive
How confident are you that your answer is correct?
0- I'm not confident. I guessed randomly.
1-I'm a little confident.
2- I'm pretty confident.
3- I'm very confident.
How easy is the text to read and understand?
$\mathbb{O}$  Very difficult.
O Difficult.
O Neutral.
O Easy.
$\bigcirc$  Very Easy.
Figure 9: Amazon Mechanical Turk layout for MultiRC tasks.
Based on the passage, do you believe the answer to the question is correct? Rate how confident you are. Also assign a score about how easy the passage is to read. If you've seen a similar passage previously, only use the information in the current (given) passage. Some of these will not make sense. If you're unsure, select Yes or No and assign a confidence score of 0.
What were the results for Finland establishing its own language?
Answer: It opened up opportunities for a larger population of the society and diluted ties with Sweden
Finally, the elevation of Finnish from a language of the common people to a national language equal to Swedish opened opportunities for a larger proportion of the society. Encouraging Finnish nationalism and language can also be seen as an attempt to dilute ties with Sweden.
Based on the passage above, is the provided answer correct?
O Yes
How confident are you?
How easy is the passage to read and understand?
O Very difficult.
$\mathbb{O}$  Very Easy.
N	Doc Length	Query Length	Rationale Length	Label Distribution
Evidence Inference
train	5,789	363 / 1010	14 / 66	0.10 / 0.54	0.39 / 0.33 / 0.28
dev	684	369 / 602	14 / 108	0.11 / 0.35	0.40 / 0.35 / 0.25
test	720	362 / 617	16 / 100	0.10 / 0.34	0.39 / 0.35 / 0.26
MultiRC
train	24,029	305 / 618	18 / 92	0.17 / 0.73	0.56 / 0.44
dev	3,214	305 / 562	18 / 83	0.19 / 0.76	0.55 / 0.45
test	4,848	290 / 490	18 / 80	0.18 / 0.56	0.57 / 0.43
Movies
train	1,600	773 / 2,809	7 / 7	0.09 / 0.5	0.5 / 0.5
dev	200	761 / 1,880	7 / 7	0.07 / 0.26	0.5 / 0.5
test	199	795 / 2,122	7 / 7	0.31 / 0.91	0.5 / 0.5
SST
Train	6,920	17 / 48	-	-	0.52 / 0.48
Dev	872	17 / 44	-	-	0.51 / 0.49
Test	1,821	17 / 52	-	-	0.50 / 0.50
AgNews
Train	102,000	31 / 173	-	-	0.25 / 0.25 / 0.25 / 0.25
Dev	18,000	31 / 168	-	-	0.25 / 0.25 / 0.25 / 0.25
Test	7,600	30 / 129	-	-	0.25 / 0.25 / 0.25 / 0.25
Table 5: Dataset statistics. For document, query, and rationale lengths we provide mean and maximum values (formulated as mean/max), where available. We do not have human rationale annotations for SST and AgNews, hence we do not report query and rationale lengths for these.
dataset	saliency	rationale	Δ	t-statistic	p-value
SST	Gradient	contiguous	-0.0097	-1.8483	0.1383
Non contiguous	0.0120	1.9411	0.1242
[CLS] Attention	contiguous	-0.0133	-3.1281	0.0352
Non contiguous	-0.0025	-0.5036	0.6410
AgNews	Gradient	contiguous	-0.0433	-26.8053	0.0000
Non contiguous	-0.0014	-0.7530	0.4934
[CLS] Attention	contiguous	-0.0257	-19.4711	0.0000
Non contiguous	-1.0000	-1.0000	-1.0000
Evidence Inference	Gradient	contiguous	-0.0126	-0.5457	0.6143
Non contiguous	-0.0139	-0.9352	0.4026
[CLS] Attention	contiguous	-0.0145	-1.4655	0.2166
Non contiguous	0.0053	0.3776	0.7249
Movies	Gradient	contiguous	-0.0221	-6.4826	0.0029
Non contiguous	-0.0020	-0.2684	0.8016
[CLS] Attention	contiguous	-0.0232	-3.1249	0.0354
Non contiguous	0.0040	1.6500	0.1743
MultiRC	Gradient	contiguous	-0.0041	-1.4573	0.2188
Non contiguous	0.0066	0.8969	0.4205
[CLS] Attention	contiguous	-0.0038	-1.1710	0.3066
Non contiguous	0.0012	0.2832	0.7910
Table 6: Comparison of global rationales vs instance level rationale for each dataset, saliency and rationale type combination. The statistical test used was Welch's  $t$ -test (2-sided).  $\Delta =$  (Average F1 score for global) - (average F1 score for instance level) heuristics.
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