Causal disentanglement aims to uncover a representation of data using latent variables that are interrelated through a causal model. Such a representation is identifiable if the latent model that explains the data is unique. In this paper, we focus on the scenario where unpaired observational and interventional data are available, with each intervention changing the mechanism of a latent variable. When the causal variables are fully observed, statistically consistent algorithms have been developed to identify the causal model under faithfulness assumptions. We here show that identifiability can still be achieved with unobserved causal variables, given a generalized notion of faithfulness. Our results guarantee that we can recover the latent causal model up to an equivalence class and predict the effect of unseen combinations of interventions, in the limit of infinite data. We implement our causal disentanglement framework by developing an autoencoding variational Bayes algorithm and apply it to the problem of predicting combinatorial perturbation effects in genomics.

Learning high-level causal representations together with a causal model from unstructured low-level data such as pixels is impossible from observational data alone. We prove under mild assumptions that this representation is however identifiable in a weakly supervised setting. This involves a dataset with paired samples before and after random, unknown interventions, but no further labels. We then introduce implicit latent causal models, variational autoencoders that represent causal variables and causal structure without having to optimize an explicit discrete graph structure. On simple image data, including a novel dataset of simulated robotic manipulation, we demonstrate that such models can reliably identify the causal structure and disentangle causal variables.

Causal discovery aims to recover causal structures or models underlying the observed data. Despite its success in certain domains, most existing methods focus on causal relations between observed variables, while in many scenarios the observed ones may not be the underlying causal variables (e.g., image pixels), but are generated by latent causal variables or confounders that are causally related. To this end, in this paper, we consider Linear, Non-Gaussian Latent variable Models (LiNGLaMs), in which latent confounders are also causally related, and propose a Generalized Independent Noise (GIN) condition to estimate such latent variable graphs. Specifically, for two observed random vectors $\mathbf{Y}$ and $\mathbf{Z}$, GIN holds if and only if $\omega^{\intercal}\mathbf{Y}$ and $\mathbf{Z}$ are statistically independent, where $\omega$ is a parameter vector characterized from the cross-covariance between $\mathbf{Y}$ and $\mathbf{Z}$. From the graphical view, roughly speaking, GIN implies that causally earlier latent common causes of variables in $\mathbf{Y}$ d-separate $\mathbf{Y}$ from $\mathbf{Z}$. Interestingly, we find that the independent noise condition, i.e., if there is no confounder, causes are independent from the error of regressing the effect on the causes, can be seen as a special case of GIN. Moreover, we show that GIN helps locate latent variables and identify their causal structure, including causal directions. We further develop a recursive learning algorithm to achieve these goals. Experimental results on synthetic and real-world data demonstrate the effectiveness of our method.

The standard tools of causal inference have been developed to answer simple causal queries which can be easily formalized as a small number of statistical estimands in the context of a particular structural causal model (SCM); however, scientific theories often make diffuse predictions about a large number of causal variables. This article proposes a framework for parameterizing such complex causal queries as the maximum difference in causal effects associated with two sets of causal variables that have a researcher specified probability of occurring. We term this estimand the Maximum Causal Set Effect (MCSE) and develop an estimator for it that is asymptotically consistent and conservative in finite samples under assumptions that are standard in the causal inference literature. This estimator is also asymptotically normal and amenable to the non-parametric bootstrap, facilitating classical statistical inference about this novel estimand. We compare this estimator to more common latent variable approaches and find that it can uncover larger causal effects in both real world and simulated data.

Mechanistic interpretability (MI) seeks to uncover how language models (LMs) implement specific behaviors, yet measuring progress in MI remains challenging. The recently released Mechanistic Interpretability Benchmark (MIB; Mueller et al., 2025) provides a standardized framework for evaluating circuit and causal variable localization. Building on this foundation, the BlackboxNLP 2025 Shared Task extends MIB into a community-wide reproducible comparison of MI techniques. The shared task features two tracks: circuit localization, which assesses methods that identify causally influential components and interactions driving model behavior, and causal variable localization, which evaluates approaches that map activations into interpretable features. With three teams spanning eight different methods, participants achieved notable gains in circuit localization using ensemble and regularization strategies for circuit discovery. With one team spanning two methods, participants achieved significant gains in causal variable localization using low-dimensional and non-linear projections to featurize activation vectors. The MIB leaderboard remains open; we encourage continued work in this standard evaluation framework to measure progress in MI research going forward.

In label-noise learning, the noise transition matrix reveals how an instance transitions from its clean label to its noisy label. Accurately estimating an instance's noise transition matrix is crucial for estimating its clean label.

Causal reasoning and discovery, two fundamental tasks of causal analysis, often face challenges in applications due to the complexity, noisiness, and high-dimensionality of real-world data. Despite recent progress in identifying latent causal structures using causal representation learning (CRL), what makes learned representations useful for causal downstream tasks and how to evaluate them are still not well understood. In this paper, we reinterpret CRL using a measurement model framework, where the learned representations are viewed as proxy measurements of the latent causal variables. Our approach clarifies the conditions under which learned representations support downstream causal reasoning and provides a principled basis for quantitatively assessing the quality of representations using a new Test-based Measurement EXclusivity (T-MEX) score. We validate T-MEX across diverse causal inference scenarios, including numerical simulations and real-world ecological video analysis, demonstrating that the proposed framework and corresponding score effectively assess the identification of learned representations and their usefulness for causal downstream tasks.

In the following we provide additional results and details that did not fit into our main paper. In Appendix A we provide precise definitions and a complete proof of our identifiability theorem. We then discuss the assumptions underlying this result and their generalization in Appendix B. Appendix C covers implicit latent causal models (ILCMs) and their training, while Appendix D provides details for our experiments. We describe causal structure with SCMs. Qualcomm AI Research is an initiative of Qualcomm Technologies, Inc. a probability measure We will need to reason about vectors being "equal up to permutation and elementwise reparameteri-zations".

Learning high-level causal representations together with a causal model from unstructured low-level data such as pixels is impossible from observational data alone. We prove under mild assumptions that this representation is however identifiable in a weakly supervised setting.