# A Green AI Methodology Based on Persistent Homology for Compressing BERT
## 4 Empirical Evaluation
### Results and Analysis on the BERT Large Model  
In contrast to BERT Base, there are far fewer experimental results reported in the state of the art for BERT Large. Once again, PBCE outperforms RPP [34] in all tasks except for MRPC and RTE, while improving upon the original model in MNLI (0.4/0.33), QNLI (0.45), and CoLA (1.28) (Table 5) again, with only 40 epochs in the fine-tuning process for each of the tasks. In this case, the reduction in the number of parameters is significant, resulting in a compressed model with only 43% of the parameters (from 340 M to 146.2 M). This can be explained by the fact that BERT Large is much larger than BERT Base, hence it exhibits greater redundancy.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Method** & **MNLI-(m/mm)** & **QQP** & **QNLI** & **SST-2** & **CoLA** & **STS-B** & **MRPC** & **RTE** & **RP (M)** \\ \hline Original [1] & 84.6/83.4 & 71.2 & 90.5 & 93.5 & 52.1 & 85.8 & 88.9 & 66.4 & - \\ \hline AUBER [23] & - & - & - & - & 60.59 \(\pm\) 0.73 & - & 85.62 \(\pm\) 0.51 & 65.31 \(\pm\) 1.30 & - \\ \hline AE-BERT [27] & - & - & 88.7 & - & - & 86.1 & 89.5 & 69.7 & - \\ \hline ETDLSL [36] & 82.9 & 90.7 & 88.2 & 89.3 & 52.6 & 84.6 & 88.3 & 63.9 & - \\ \hline LotteryTicketBert [33] & - & - & 88.9 & - & 53.8 & 88.2 & 84.9 & 66 & - \\ \hline [PERSON] et al. [25] & - & - & - & - & 58.86 \(\pm\) 0.64 & - & 84.22 \(\pm\) 0.33 & 63.9 & - \\ \hline [PERSON] et al. [26] & - & - & - & - & 55.34 \(\pm\) 0.81 & - & 83.92 \(\pm\) 0.71 & 64.12 \(\pm\) 1.65 & - \\ \hline QBERT [35] & 77.02/76.56 & - & - & 84.63 & - & - & - & - & - \\ \hline YOCO-BERT [32] & 82.6 & 90.5 & 87.2 & 91.6 & 59.8 & - & 89.3 & 72.9 & 67 \\ \hline SENSIMIX [37] & - & 89.6 & 86.5 & 90.3 & - & - & 87.2 & - & **13.75** \\ \hline LAD [31] & 81.01/81.47 & 87.56 & 89.24 & 91.74 & - & - & 88.71 & 67.15 & 52.5 \\ \hline DDK [29] & 83.6 & 88.2 & 91.6 & **92.7** & 61.9 & 89.1 & 90.7 & **73.7** & 67 \\ \hline UEM [30] & - & 86.2 & 86.4 & 87.5 & 46.8 & - & 86.7 & - & 66.8 \\ \hline MicroBERT [28] & 80.3 & 86.6 & - & 89.6 & - & - & 88.7 & 62.8 & 14.5 \\ \hline
**PBCE** & **83.781.6** & **91.23** & **91.73** & 91.87 & **62.96** & **89.52** & **91.09** & 71.98 & 52 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results of compressing BERT Base on GLUE Benchmark tasks. For each metric and task, the higher the value the better (Table 1). For the remaining parameters value (RP), expressed in millions of parameters, the smaller the value the better. Best results are highlighted in bold (excluding original BERT).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Method** & **MNLI-(m/mm)** & **QQP** & **QNLI** & **SST-2** & **CoLA** & **STS-B** & **MRPC** & **RTE** & **RP (M)** \\ \hline Original [1] & 86.7/85.9 & 72.1 & 92.7 & 94.9 & 60.5 & 86.5 & 89.3 & 70.1 & - \\ \hline RPP [34] & 86.1/85.7 & - & - & - & 61.3 & - & 88.1 & 70.1 & 201 \\ \hline
**PBCE** & **87.1/86.2** & **71.9** & **93.2** & **94.7** & **62.1** & **85.2** & **88.6** & **71.7** & **146.2** \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of compressing BERT Large on GLUE Benchmark tasks. For each metric and task, the higher the value, the better it is (Table 1). For the remaining parameters value (RP), expressed in millions of parameters, the smaller the value, the better it is. Best results are highlighted in bold (excluding original BERT).