Computerized adaptive testing (CA T), as a tool that can efficiently measure student's ability, has been widely used in various standardized tests (e.g., GMA T and

Therefore, long-tailed classification is the key to deep learning at scale. However, existing methods are mainly based on reweighting/re-sampling heuristics that lack a fundamental theory. In this paper, weestablish acausal inference framework,which notonlyunravelsthewhysof previous methods, but also derives a new principled solution.

Next, we introduce two additional approximations we use to apply Eq. (S.9). An SCM matches a set of assignments to a causal graph. This implies that the error of the approximation Eq. (S.13) is mainly dominated by the gradients of g at hao, and the variance ofnao. Specifically, we use a positive differentiable measure of the statistical dependence, denoted by I. PIDA measures disentanglement of representations for models that are trained from unsupervised data. As a result, we have the following: Minimizing Eq. (S.21) leads topdo(a,o)(ˆφa0) approaching p(ˆφa0|a), which as we have just shown, leads top(ˆφa0|a) approaching pdo(a)(ˆφa0).

Unfortunately, learning systems struggle with compositional generalization because they often build on features that are correlated with class labels even if they are not "essential" for the class.

We thank the reviewers for their insightful and valuable feedback and for their unanimous support of the paper.1 Unfortunately, it is not clear that zero-shot can work well6 with strongly entangled pairs because every case could be special. Three insights worth mentioning: (1) Even the7 fully disentangled case is still very challenging. They reflect as-12 sumptions about the noise level in the data-generation process (Suppl L508-513), i.e. that the mapping from the13 core-features (φa and φo) to the image (x) is not too noisy and the latent vector can be recovered from the image.14 We deliberately proposed a model close to baselines (L186)21 to surgically demonstrate the strength of the proposed approach. Instead of learning explicit values for the means, we learn MLPs25 that output the means (using gradient updates L138,143,178).