We consider the task of out-of-distribution (OOD) generalization, where the distribution shift is due to an unobserved confounder ($Z$) affecting both the covariates ($X$) and the labels ($Y$). This confounding introduces heterogeneity in the predictor, i.e., $P(Y \mid X) = E_{P(Z \mid X)}[P(Y \mid X,Z)]$, making traditional covariate and label shift assumptions unsuitable. OOD generalization differs from traditional domain adaptation in that it does not assume access to the covariate distribution ($X^\text{te}$) of the test samples during training. These conditions create a challenging scenario for OOD robustness: (a) $Z^\text{tr}$ is an unobserved confounder during training, (b) $P^\text{te}(Z) \neq P^\text{tr}(Z)$, (c) $X^\text{te}$ is unavailable during training, and (d) the predictive distribution depends on $P^\text{te}(Z)$. While prior work has developed complex predictors requiring multiple additional variables for identifiability of the latent distribution, we explore a set of identifiability assumptions that yield a surprisingly simple predictor using only a single additional variable. Our approach demonstrates superior empirical performance on several benchmark tasks.

Discovering causal structures with latent variables from observational data is a fundamental challenge in causal discovery. Existing methods often rely on constraint-based, iterative discrete searches, limiting their scalability for large numbers of variables. Moreover, these methods frequently assume linearity or invertibility, restricting their applicability to real-world scenarios. We present new theoretical results on the identifiability of non-linear latent hierarchical causal models, relaxing previous assumptions in the literature about the deterministic nature of latent variables and exogenous noise. Building on these insights, we develop a novel differentiable causal discovery algorithm that efficiently estimates the structure of such models. To the best of our knowledge, this is the first work to propose a differentiable causal discovery method for non-linear latent hierarchical models. Our approach outperforms existing methods in both accuracy and scalability. Furthermore, we demonstrate its practical utility by learning interpretable hierarchical latent structures from high-dimensional image data and demonstrate its effectiveness on downstream tasks such as transfer learning.

As language models scale, their performance improves dramatically across a wide range of tasks, but so does their tendency to memorize and regurgitate parts of their training data verbatim. This tradeoff poses serious legal, ethical, and safety concerns, especially in real-world deployments. Existing mitigation techniques, such as differential privacy or model unlearning, often require retraining or access to internal weights making them impractical for most users. In this work, we introduce TokenSwap, a lightweight, post-hoc defense designed for realistic settings where the user can only access token-level outputs. Our key insight is that while large models are necessary for high task performance, small models (e.g., DistilGPT-2) are often sufficient to assign fluent, grammatically plausible probabilities to common function words - and crucially, they memorize far less. By selectively swapping token probabilities between models, TokenSwap preserves the capabilities of large models while reducing their propensity for verbatim reproduction. Evaluations on Pythia-6.9B and Llama-3-8B show up to a 10$\times$ drop in exact memorization with negligible task degradation. Our method offers a practical, accessible solution for mitigating memorized generation in deployed LLMs. Code is available at https://github.com/parjanya20/verbatim-llm.