harryrobert/nav2tex-decoder-latex-pretrain huggingface dataset:
\mathrm { ~ p ~ e ~ r ~ t ~ u ~ r ~ b ~ a ~ t ~ i ~ o ~ n ~ } = 1 0 0 \times ( \mathrm { ~ g ~ i ~ v ~ e ~ n ~ m ~ o ~ d ~ e ~ l ~ } - \mathrm { ~ s ~ t ~ a ~ r ~ t ~ i ~ n ~ g ~ m ~ o ~ d ~ e ~ l ~ } ) / \mathrm { ~ s ~ t ~ a ~ r ~ t ~ i ~ n ~ g ~ m ~ o ~ d ~ e ~ l ~ }
\begin{array} { r } { r \otimes n \theta ( l \varphi _ { t i t } ( m \otimes m ^ { \prime } ) \otimes n ^ { \prime } ) = r \otimes \zeta ( n \otimes l \varphi _ { t i t } ( m \otimes m ^ { \prime } ) ) n ^ { \prime } } \\ { = r \otimes \zeta ( n \otimes l ) \varphi _ { t i t } ( m \otimes m ^ { \prime } ) n ^ { \prime } = r \otimes \varphi _ { t i t } ( \zeta ( n \otimes l ) m \otimes m ^ { \prime } ) n ^ { \prime } } \\ { = r \varphi _ { t i t } ( \zeta ( n \otimes l ) m \otimes m ^ { \prime } ) \otimes n ^ { \prime } = \varphi _ { t i t } ( r \zeta ( n \otimes l ) m \otimes m ^ { \prime } ) \otimes n ^ { \prime } } \\ { = \varphi _ { t i t } ( \lambda _ { M _ { t i } } ^ { R } ( \mu _ { R } ( r \otimes \zeta ( n \otimes l ) ) \otimes m ) \otimes m ^ { \prime } ) \otimes n ^ { \prime } . } \end{array}
\begin{array} { r l } { \chi ^ { \mathrm { ~ h ~ o ~ m ~ } } ( \mathbf { E } } & { { } : y ) = S ( A B ) - H \left( \nu ^ { \mathrm { ~ h ~ o ~ m ~ } } \right) , } \\ { \chi ^ { \mathrm { ~ h ~ e ~ t ~ } } ( \mathbf { E } } & { { } : y ) = S ( A B ) - H \left( \nu ^ { \mathrm { ~ h ~ e ~ t ~ } } \right) . } \end{array}
\begin{array} { r l } { T _ { n , 1 } ^ { 1 } ( \theta ) = T _ { n , - 1 } ^ { 1 } ( \theta ) } & { { } = - \mu _ { n } \pi _ { n } ( \theta ) , } \\ { T _ { n , 1 } ^ { 2 } ( \theta ) = - T _ { n , - 1 } ^ { 2 } ( \theta ) } & { { } = - \mu _ { n } n ( n + 1 ) \sin ( \theta ) \pi _ { n } ( \theta ) , } \\ { T _ { n , 1 } ^ { 3 } ( \theta ) = - T _ { n , - 1 } ^ { 3 } ( \theta ) } & { { } = - \mu _ { n } \tau _ { n } ( \theta ) , } \end{array}