We limit the target languages for this augmentation process to Arabic, Finnish, Japanese, Korean, Russian, Spanish, Swedish, Hebrew, Thai,Danish,French,Italian,Dutch,Polish,andPortuguese. Interestingly,justaddingthislanguage code effectively changes the outputs as shown in Table 7. We further subsample 50% of the synthetically generated questions. During inference, we first retrieve top 15 passages using mDPR, and then feed the questions andconcatenated passages intothemGEN model, withlanguage tags. The gray dots concentrated in the lower right part in the first figure represent encoded Thai embeddings.

Yet, despite recent progress, CO problems still pose a significant challenge to neural networks. Successful models often rely on supervision, either in the form of labeled instances [45, 62, 35] or of expert demonstrations [27]. This success comes with drawbacks: obtaining labels for hard problem instances can be computationally infeasible [86],and direct supervision can lead topoor generalization[36].

In the digital world, visual media has proven to be a mixed blessing.

In theorem proving, the task of selecting useful premises from alarge library to unlock the proof of a given conjecture is crucially important. This presents a challenge foralltheorem provers,especially theonesbasedonlanguage models, due to their relative inability to reason over huge volumes of premises in text form.