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Table 11 
Analysis of symmetric re-weighting–based refinement applied to the same initial mappings of our adversarial autoencoder of Ar, Ms, and He languages on the Conneau data set.
 En-ArEn-MsEn-He
Symmetric re-weighting 36.1 54.0 54.6 55.0 45.8 57.1 
OLS 27.2 48.0 39.4 44.2 34.5 51.1 
OLS + Orthogonality 33.7 53.2 51.6 53.4 42.6 56.4 
OLS with L1 regularizer (LASSO) 26.5 47.9 37.3 43.1 32.4 51.1 
LASSO + Orthogonality 34.3 52.8 51.5 52.6 42.6 56.4 
OLS with L2 regularizer (RIDGE) 25.8 47.3 37.3 42.1 32.9 50.8 
RIDGE + Orthogonality 33.7 52.8 51.1 52.8 42.3 56.8 
OLS with L1 & L2 regularizers (E-NET) 27.3 47.5 39.5 41.6 32.5 51.4 
E-NET + Orthogonality 33.8 52.2 51.4 53.5 41.9 56.9 
 En-ArEn-MsEn-He
Symmetric re-weighting 36.1 54.0 54.6 55.0 45.8 57.1 
OLS 27.2 48.0 39.4 44.2 34.5 51.1 
OLS + Orthogonality 33.7 53.2 51.6 53.4 42.6 56.4 
OLS with L1 regularizer (LASSO) 26.5 47.9 37.3 43.1 32.4 51.1 
LASSO + Orthogonality 34.3 52.8 51.5 52.6 42.6 56.4 
OLS with L2 regularizer (RIDGE) 25.8 47.3 37.3 42.1 32.9 50.8 
RIDGE + Orthogonality 33.7 52.8 51.1 52.8 42.3 56.8 
OLS with L1 & L2 regularizers (E-NET) 27.3 47.5 39.5 41.6 32.5 51.4 
E-NET + Orthogonality 33.8 52.2 51.4 53.5 41.9 56.9 
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