SlowGuess/NAACL_2021_OCR huggingface dataset:
the mean UAS of dependency trees generated by CLE algorithm with sentence constraints show a different trend, which may due to the concentration of the discourse information on single head as the model trained for more steps, as it shows in Figure.7.
Model	Const	Eisner	CLE
No Cons.	Sent Cons.	No Cons.	Sent Cons.	No Cons.	Sent Cons.
RSTDT
CNNDM-2-1	61.16 / 59.67	76.23 / 74.63	23.65 / 4.80	28.24 / 18.23	21.56 / 1.45	29.29 / 19.56
CNNDM-2-8	62.65 / 59.75	76.42 / 74.28	22.09 / 8.40	26.23 / 21.29	20.31 / 6.13	26.57 / 22.67
CNNDM-6-8	60.33 / 60.79	75.44 / 75.04	7.89 / 20.48	13.83 / 27.78	7.28 / 17.30	16.10 / 28.50
NYT-2-1	60.27 / 60.23	75.57 / 75.29	9.76 / 14.84	23.18 / 20.61	6.18 / 12.68	21.06 / 21.73
NYT-2-8	63.20 / 59.65	76.63 / 75.23	7.35 / 9.74	16.04 / 21.27	6.44 / 7.09	16.72 / 22.90
NYT-6-8	62.42 / 62.17	76.65 / 75.58	15.74 / 12.51	24.30 / 18.90	13.71 / 10.59	25.04 / 21.14
Random	58.60 (0.1)	74.10 (0.1)	11.16 (0.2)	20.28 (0.2)	1.67 (0.08)	18.72 (0.11)
Instruction
CNNDM-2-1	61.06 / 59.84	71.39 / 70.29	31.07 / 4.39	29.33 / 13.45	28.06 / 2.08	37.38 / 18.12
CNNDM-2-8	61.44 / 60.55	71.13 / 71.09	26.98 / 8.89	24.72 / 14.75	24.56 / 5.23	28.70 / 20.58
CNNDM-6-8	60.32 / 61.22	71.24 / 70.88	8.53 / 19.51	9.93 / 21.96	6.92 / 15.85	14.93 / 25.78
NYT-2-1	60.31 / 61.30	71.40 / 71.43	10.67 / 21.15	18.99 / 21.19	7.82 / 17.59	21.30 / 24.54
NYT-2-8	61.27 / 60.51	70.80 / 70.90	6.26 / 12.59	13.64 / 19.34	5.25 / 7.96	13.39 / 21.92
NYT-6-8	61.32 / 61.27	71.30 / 70.03	16.22 / 12.14	22.79 / 16.37	14.81 / 9.81	25.44 / 21.10
Random	59.49 (0.3)	70.53 (0.1)	13.14 (0.33)	19.31 (0.44)	2.94 (0.24)	17.88 (0.42)
GUM
CNNDM-2-1	58.74 / 57.69	72.73 / 71.92	21.28 / 2.24	27.26 / 16.12	19.50 / 0.70	28.77 / 17.92
CNNDM-2-8	59.98 / 58.43	72.69 / 71.95	19.45 / 4.98	25.00 / 19.25	18.03 / 2.92	25.07 / 20.40
CNNDM-6-8	58.92 / 59.30	72.40 / 72.69	4.74 / 15.80	11.53 / 24.79	4.01 / 13.14	14.85 / 25.37
NYT-2-1	57.81 / 58.84	71.95 / 72.23	5.64 / 12.84	19.94 / 20.19	2.92 / 9.79	18.23 / 19.68
NYT-2-8	60.17 / 58.22	71.98 / 71.82	5.66 / 7.22	15.21 / 18.81	4.54 / 3.96	15.25 / 19.31
NYT-6-8	59.62 / 59.25	72.19 / 71.56	12.58 / 9.61	23.35 / 17.14	10.67 / 8.23	22.99 / 19.53
Random	57.47 (0.1)	71.50 (0.2)	10.37 (0.23)	19.15 (0.26)	0.92 (0.05)	17.01 (0.2)
Table 8: The RST Parseval Scores of generated constituency trees, Unlabeled Attachment Score of generated dependency trees by Eisner algorithm and CLE algorithm on the three datasets. The numbers in each cell are represented as the performance of (Layer 0 / Layer 1) the results of Random are obtained by applying the parser on random generated matrices for 10 times, and are represented as 'Average (Std)'.
Model	Const	Eisner	CLE
No Cons.	Sent Cons.	No Cons.	Sent Cons.	No Cons.	Sent Cons.
RSTDT
CNNDM-6-8	61.13 / 61.63(1.11) / (1.35)	75.81 / 75.41(0.26) / (0.34)	10.32 / 20.99(4.03) / (2.80)	16.42 / 27.08(3.62) / (1.37)	9.40 / 18.16(3.92) / (3.25)	18.89 / 28.33(4.19) / (1.59)
Random	58.6 (0.1)	74.10 (0.1)	11.16 (0.2)	20.28 (0.2)	1.67 (0.08)	18.72 (0.11)
Instruction
CNNDM-6-8	61.87 / 61.06(1.17) / (0.98)	70.84 / 70.94(0.51) / (0.34)	11.50 / 19.78(5.71) / (2.17)	12.91 / 22.45(4.39) / (1.48)	9.79 / 16.53(5.31) / (2.73)	17.81 / 26.30(4.70) / (1.64)
Random	59.49 (0.3)	70.53 (0.1)	13.14 (0.33)	19.31 (0.44)	2.94 (0.24)	17.88 (0.42)
GUM
CNNDM-6-8	58.19 / 58.71(0.82) / (0.97)	72.28 / 72.48(0.27) / (0.16)	7.62 / 15.69(3.97) / (2.87)	14.62 / 24.02(3.77) / (1.36)	6.77 / 13.23(3.96) / (3.29)	17.32 / 25.13(3.85) / (1.22)
Random	57.47 (0.1)	71.50 (0.2)	10.37 (0.23)	19.15 (0.26)	0.92 (0.05)	17.01 (0.2)
Table 9: The average RST Parseval Scores of generated constituency trees, the average Unlabeled Attachment Scores of generated dependency trees by the Eisner and CLE algorithms, on the three datasets with 5 random initialization, the numbers in parenthesis are the standard deviation across different run
Figure 5: The heatmap of average UAS across three discourse datasets for all attention heads in the models with different initialization by the CLE algorithm.
Figure 6: Max and Mean UAS of dependency trees generated by CLE algorithm on all attention heads (48) of the model 'cnndm-6-8', after training for  $(0,1,5,10,20,23)$  K steps on RST-DT(top), Instructional(middle) and GUM(bottom) datasets. The corresponding ROUGE scores are increasing.
Figure 7: The heatmaps of the average UAS across the three discourse datasets for all the heads during training the summarization model.