We propose a scaling law that takes into account model size and training data while explicitly splitting the latter into training steps and batch size (called three-term law). Fitting the proposed law on a large set of training runs, we find that it correctly recovers the scaling of the optimal batch size. Moreover, because it makes use of training runs with suboptimal batch size, our proposed law can be robustly fit with a significantly smaller amount of training runs. We further show that the three-term law can be used to derive scaling laws for suboptimal batch sizes, and that it matches previous empirical findings related to the critical batch size.

Additionally, we show generalization performance of our proposed method across differentvisualdomains. Withthegiven problemcategory(task),asubsetforlearning can be sampled (via domain episode module in Figure 4 in main text). Here, by replacingclass with task, K-shot andN-task reasoning framework can be defined. Here, we show analogical learning with the existing meta learning framework for fast adaptation fromthesourcedomain tothetargetdomain.

For this reason, the ML community started focusing on non-monotone problems with extra structural properties.

This is quite similar to what VCT can learn on the synthesized dataset Objects-Room. As the real-world dataset is more diverse, we observe several failure cases shown in Figure 8. We suppose those failure cases are due to VCT, trained withreconstruction loss,isnotgoodatsynthesizing counterfactual samples which arefarfromthe data distribution.

The tasks is to determine if the sentence has positive or negativesentiment. The task is to determine whether a given sentence is linguistically acceptableornot. RTE: Recognizing Textual Entailment [2, 10, 21, 17] contains 2.5K train examples from textual entailment challenges. Thefine-tuning costsare the same with BERT plus relativepositiveencodings as the same Transformer model is used.

Themodel outputs the normal distribution for the observations, conditional on hidden stateh(t). Since only some features are observed at atime, we mask out the missing values when calculatingLpre. We denote our predicted distribution withppre,and predicted distribution after updating the state with ppost.

Inparticular,fromtheexpressionabove,theattackerneeds to pick out batches such that the difference between the batch gradient and the true gradient is in the opposite direction from the true gradient. In this section, we further investigate an attacker's ability to approximate out-of-distribution data usingnaturaldata. Clearly we can not get withinanyaccuracywith this reconstruction. One can now attain exact bounds usinge.g. Theory outlined here highlights thedifferences inattack performance observedforbatch reorder and reshuffle.