Finally, we describe the training setup for our back-translation experiments. We continue to differentiate our method from other existing works. Our method does not train multiple peer models with EM training either. In each round, a forward (or backward) model takes turn to play the "back-translation" role to train The role is switched in the next round. In other words, source and target are identical.

Our method is applicable to all NMT models. It does not require extra monolingual data like back-translation, nor does it add more computations and parameters like ensembles ofmodels.

We study theregretincurred bytheagent, firstwhen sheknowsherrewardfunction but does not know the distribution of the task duration, and then when she does not knowher reward function, either.

Withtheseconditions,adirectconsequenceisthat the singular values inon-manifold directions will not depend onσ2. Hence, if we fix the latent distribution to be standard Gaussian, wehavethat theNFused tolearnqσ2 must be f forall(u,v),i.e. However, these eigenvalues are exactly in direction of large variability, i.e. in on-manifolddirection. Thiswastobeshown. Let us assume thatσ21 = = σ2d in the following. B.1 Lolipop In [11], a manifold consisting of regions of different ID was considered - a 1 dimensional line segment, and atwodimensional disk such that theoverall manfiold resembles alolipop.

Therefore, representation learning is a very active area of research [33] with a wide range of applications ranging from neuroscience [27], molecular biology [28], bioinformatics [12]or image analysis [21].

Our findings reveal that: I)LLMs with higher accuracy may exhibit lower certainty; II) Larger-scale LLMs may display greater uncertainty compared to their smaller counterparts; and III)Instruction-finetuning tends to increase the uncertainty of LLMs. These results underscore the significance of incorporating uncertainty into the evaluation of LLMs.

Figure 2 compares Figure 3(a) gir.