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Table 10 
Analysis of symmetric re-weighting–based refinement applied to the same initial mappings of our adversarial autoencoder of Es, De, It, and Fi languages on the Conneau data set.
 En-EsEn-DeEn-ItEn-Fi
→←→←→←→←
Symmetric re-weighting 82.8 84.8 75.7 74.5 79.1 80.0 47.6 64.0 
OLS 76.2 81.3 72.4 72.3 76.9 76.6 42.9 60.1 
OLS + Orthogonality 82.7 84.6 75.9 74.7 79.5 79.9 47.7 63.8 
OLS with L1 regularizer (LASSO) 75.8 81.4 72.4 72.9 76.8 76.8 43.3 59.8 
LASSO + Orthogonality 82.3 84.6 75.6 74.7 79.2 79.8 47.4 62.9 
OLS with L2 regularizer (RIDGE) 75.7 81.1 72.2 72.7 77.3 77.6 42.9 60.2 
RIDGE + Orthogonality 82.5 84.5 76.2 74.3 79.3 80.1 47.4 63.3 
OLS with L1 & L2 regularizers (E-NET) 76.0 80.7 72.2 72.9 77.2 77.6 43.5 61.0 
E-NET + Orthogonality 82.7 84.9 75.7 74.7 79.2 80.1 47.3 63.6 
 En-EsEn-DeEn-ItEn-Fi
→←→←→←→←
Symmetric re-weighting 82.8 84.8 75.7 74.5 79.1 80.0 47.6 64.0 
OLS 76.2 81.3 72.4 72.3 76.9 76.6 42.9 60.1 
OLS + Orthogonality 82.7 84.6 75.9 74.7 79.5 79.9 47.7 63.8 
OLS with L1 regularizer (LASSO) 75.8 81.4 72.4 72.9 76.8 76.8 43.3 59.8 
LASSO + Orthogonality 82.3 84.6 75.6 74.7 79.2 79.8 47.4 62.9 
OLS with L2 regularizer (RIDGE) 75.7 81.1 72.2 72.7 77.3 77.6 42.9 60.2 
RIDGE + Orthogonality 82.5 84.5 76.2 74.3 79.3 80.1 47.4 63.3 
OLS with L1 & L2 regularizers (E-NET) 76.0 80.7 72.2 72.9 77.2 77.6 43.5 61.0 
E-NET + Orthogonality 82.7 84.9 75.7 74.7 79.2 80.1 47.3 63.6 
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