On-the-fly reasoning often requires adaptation to novel problems under limited data and distribution shift. This work introduces CausalARC: an experimental testbed for AI reasoning in low-data and out-of-distribution regimes, modeled after the Abstraction and Reasoning Corpus (ARC). Each CausalARC reasoning task is sampled from a fully specified causal world model, formally expressed as a structural causal model. Principled data augmentations provide observational, interventional, and counterfactual feedback about the world model in the form of few-shot, in-context learning demonstrations. As a proof-of-concept, we illustrate the use of CausalARC for four language model evaluation settings: (1) abstract reasoning with test-time training, (2) counterfactual reasoning with in-context learning, (3) program synthesis, and (4) causal discovery with logical reasoning. Within- and between-model performance varied heavily across tasks, indicating room for significant improvement in language model reasoning.

While LLMs exhibit impressive fluency and factual recall, they struggle with robust causal reasoning, often relying on spurious correlations and brittle patterns. Similarly, traditional Reinforcement Learning agents also lack causal understanding, optimizing for rewards without modeling why actions lead to outcomes. We introduce Causal Reflection, a framework that explicitly models causality as a dynamic function over state, action, time, and perturbation, enabling agents to reason about delayed and nonlinear effects. Additionally, we define a formal Reflect mechanism that identifies mismatches between predicted and observed outcomes and generates causal hypotheses to revise the agent's internal model. In this architecture, LLMs serve not as black-box reasoners, but as structured inference engines translating formal causal outputs into natural language explanations and counterfactuals. Our framework lays the theoretical groundwork for Causal Reflective agents that can adapt, self-correct, and communicate causal understanding in evolving environments.

Identifying a causal model of an IT system is fundamental to many branches of systems engineering and operation. Such a model can be used to predict the effects of control actions, optimize operations, diagnose failures, detect intrusions, etc., which is central to achieving the longstanding goal of automating network and system management tasks. Traditionally, causal models have been designed and maintained by domain experts. This, however, proves increasingly challenging with the growing complexity and dynamism of modern IT systems. In this paper, we present the first principled method for online, data-driven identification of an IT system in the form of a causal model. The method, which we call active causal learning, estimates causal functions that capture the dependencies among system variables in an iterative fashion using Gaussian process regression based on system measurements, which are collected through a rollout-based intervention policy. We prove that this method is optimal in the Bayesian sense and that it produces effective interventions. Experimental validation on a testbed shows that our method enables accurate identification of a causal system model while inducing low interference with system operations.

This paper proposes methods of estimation and uniform inference for a general class of causal functions, such as the conditional average treatment effects and the continuous treatment effects, under multiway clustering. The causal function is identified as a conditional expectation of an adjusted (Neyman-orthogonal) signal that depends on high-dimensional nuisance parameters. We propose a two-step procedure where the first step uses machine learning to estimate the high-dimensional nuisance parameters. The second step projects the estimated Neyman-orthogonal signal onto a dictionary of basis functions whose dimension grows with the sample size. For this two-step procedure, we propose both the full-sample and the multiway cross-fitting estimation approaches. A functional limit theory is derived for these estimators. To construct the uniform confidence bands, we develop a novel resampling procedure, called the multiway cluster-robust sieve score bootstrap, that extends the sieve score bootstrap (Chen and Christensen, 2018) to the novel setting with multiway clustering. Extensive numerical simulations showcase that our methods achieve desirable finite-sample behaviors. We apply the proposed methods to analyze the causal relationship between mistrust levels in Africa and the historical slave trade. Our analysis rejects the null hypothesis of uniformly zero effects and reveals heterogeneous treatment effects, with significant impacts at higher levels of trade volumes.

Length generalization (LG) is a challenging problem in learning to reason. It refers to the phenomenon that when trained on reasoning problems of smaller lengths or sizes, the resulting model struggles with problems of larger sizes or lengths. Although LG has been studied by many researchers, the challenge remains. This paper proposes a theoretical study of LG for problems whose reasoning processes can be modeled as DAGs (directed acyclic graphs). The paper first identifies and proves the conditions under which LG can be achieved in learning to reason. It then designs problem representations based on the theory to learn to solve challenging reasoning problems like parity, addition, and multiplication, using a Transformer to achieve perfect LG.

Reasoning is a fundamental capability of AI agents. Recently, large language models (LLMs) have shown remarkable abilities to perform reasoning tasks. However, numerous evaluations of the reasoning capabilities of LLMs have also showed some limitations. An outstanding limitation is length generalization, meaning that when trained on reasoning problems of smaller lengths or sizes, the resulting models struggle with problems of larger sizes or lengths. This potentially indicates some theoretical limitations of generalization in learning reasoning skills. These evaluations and their observations motivated us to perform a theoretical study of the length generalization problem. This work focuses on reasoning tasks that can be formulated as Markov dynamic processes (MDPs) and/or directed acyclic graphs (DAGs). It identifies and proves conditions that decide whether the length generalization problem can be solved or not for a reasoning task in a particular representation. Experiments are also conducted to verify the theoretical results.

When estimating the causal function between a vector of covariates X and a response Y in the presence of unobserved confounding, standard regression procedures such as ordinary least squares (OLS) are even asymptotically biased. Instrumental variable approaches (Wright, 1928; Imbens and Angrist, 1994; Newey, 2013) exploit the existence of exogenous heterogeneity in the form of an instrumental variable (IV) Z and estimate, under suitable conditions, the causal function consistently. Importantly, the errors in Y and the hidden confounders U should be uncorrelated with the instruments Z. Usually, this has to be argued for with background knowledge. When the data generating process is modeled by a structural causal model (SCM) (Pearl, 2009; Bongers et al., 2021) (so that the distribution is Markov with respect to the induced graph), then the above condition is satisfied if Y and U are d-separated from Z in the graph obtained by removing the edge from X to Y. Furthermore, in this case the errors in Y and U are even independent from Z. Using that the errors and instruments are not only uncorrelated but also independent comes with several benefits. For example, even in settings, where the causal function can be identified by classical approaches based on uncorrelatedness, the independence can be exploited to construct estimators that achieve the semiparametric efficiency bound, at least when the error distribution comes from a known, parametric family (Hansen et al., 2010). Furthermore, the independence constraint is stronger than uncorrelatedness and therefore yields stronger identifiability results, which has been reported in the field of econometrics (e.g., Imbens and Newey, 2009; Chesher, 2003).

We present a novel task that measures how people generalize objects' causal powers based on observing a single (Experiment 1) or a few (Experiment 2) causal interactions between object pairs. We propose a computational modeling framework that can synthesize human-like generalization patterns in our task setting, and sheds light on how people may navigate the compositional space of possible causal functions and categories efficiently. Our modeling framework combines a causal function generator that makes use of agent and recipient objects' features and relations, and a Bayesian non-parametric inference process to govern the degree of similarity-based generalization. Our model has a natural "resource-rational" variant that outperforms a naive Bayesian account in describing participants, in particular reproducing a generalization-order effect and causal asymmetry observed in our behavioral experiments. We argue that this modeling framework provides a computationally plausible mechanism for real world causal generalization.

Knowing the causal structure of a system is of fundamental interest in many areas of science and can aid the design of prediction algorithms that work well under manipulations to the system. The causal structure becomes identifiable from the observational distribution under certain restrictions. To learn the structure from data, score-based methods evaluate different graphs according to the quality of their fits. However, for large nonlinear models, these rely on heuristic optimization approaches with no general guarantees of recovering the true causal structure. In this paper, we consider structure learning of directed trees. We propose a fast and scalable method based on Chu-Liu-Edmonds' algorithm we call causal additive trees (CAT). For the case of Gaussian errors, we prove consistency in an asymptotic regime with a vanishing identifiability gap. We also introduce a method for testing substructure hypotheses with asymptotic family-wise error rate control that is valid post-selection and in unidentified settings. Furthermore, we study the identifiability gap, which quantifies how much better the true causal model fits the observational distribution, and prove that it is lower bounded by local properties of the causal model. Simulation studies demonstrate the favorable performance of CAT compared to competing structure learning methods.