Daily Papers

A faithful and interpretable explanation of an AI model's behavior and internal structure is a high-level explanation that is human-intelligible but also consistent with the known, but often opaque low-level causal details of the model. We argue that the theory of causal abstraction provides the mathematical foundations for the desired kinds of model explanations. In causal abstraction analysis, we use interventions on model-internal states to rigorously assess whether an interpretable high-level causal model is a faithful description of an AI model. Our contributions in this area are: (1) We generalize causal abstraction to cyclic causal structures and typed high-level variables. (2) We show how multi-source interchange interventions can be used to conduct causal abstraction analyses. (3) We define a notion of approximate causal abstraction that allows us to assess the degree to which a high-level causal model is a causal abstraction of a lower-level one. (4) We prove constructive causal abstraction can be decomposed into three operations we refer to as marginalization, variable-merge, and value-merge. (5) We formalize the XAI methods of LIME, causal effect estimation, causal mediation analysis, iterated nullspace projection, and circuit-based explanations as special cases of causal abstraction analysis.

Causal abstraction is a promising theoretical framework for explainable artificial intelligence that defines when an interpretable high-level causal model is a faithful simplification of a low-level deep learning system. However, existing causal abstraction methods have two major limitations: they require a brute-force search over alignments between the high-level model and the low-level one, and they presuppose that variables in the high-level model will align with disjoint sets of neurons in the low-level one. In this paper, we present distributed alignment search (DAS), which overcomes these limitations. In DAS, we find the alignment between high-level and low-level models using gradient descent rather than conducting a brute-force search, and we allow individual neurons to play multiple distinct roles by analyzing representations in non-standard bases-distributed representations. Our experiments show that DAS can discover internal structure that prior approaches miss. Overall, DAS removes previous obstacles to conducting causal abstraction analyses and allows us to find conceptual structure in trained neural nets.

Causal reasoning and compositional reasoning are two core aspirations in generative AI. Measuring the extent of these behaviors requires principled evaluation methods. We explore a unified perspective that considers both behaviors simultaneously, termed compositional causal reasoning (CCR): the ability to infer how causal measures compose and, equivalently, how causal quantities propagate through graphs. We instantiate a framework for the systematic evaluation of CCR for the average treatment effect and the probability of necessity and sufficiency. As proof of concept, we demonstrate the design of CCR tasks for language models in the LLama, Phi, and GPT families. On a math word problem, our framework revealed a range of taxonomically distinct error patterns. Additionally, CCR errors increased with the complexity of causal paths for all models except o1.

For text-based AI systems to interact in the real world, causal reasoning is an essential skill. Since interventional data is costly to generate, we study to what extent an agent can learn causal reasoning from passive data. Specifically, we consider an axiomatic training setup where an agent learns from multiple demonstrations of a causal axiom (or rule), rather than incorporating the axiom as an inductive bias or inferring it from data values. A key question is whether the agent would learn to generalize from the axiom demonstrations to new scenarios. For example, if a transformer model is trained on demonstrations of the causal transitivity axiom over small graphs, would it generalize to applying the transitivity axiom over large graphs? Our results, based on a novel axiomatic training scheme, indicate that such generalization is possible. We consider the task of inferring whether a variable causes another variable, given a causal graph structure. We find that a 67 million parameter transformer model, when trained on linear causal chains (along with some noisy variations) can generalize well to new kinds of graphs, including longer causal chains, causal chains with reversed order, and graphs with branching; even when it is not explicitly trained for such settings. Our model performs at par (or even better) than many larger language models such as GPT-4, Gemini Pro, and Phi-3. Overall, our axiomatic training framework provides a new paradigm of learning causal reasoning from passive data that can be used to learn arbitrary axioms, as long as sufficient demonstrations can be generated.

Causal reasoning, the ability to identify cause-and-effect relationship, is crucial in human thinking. Although large language models (LLMs) succeed in many NLP tasks, it is still challenging for them to conduct complex causal reasoning like abductive reasoning and counterfactual reasoning. Given the fact that programming code may express causal relations more often and explicitly with conditional statements like ``if``, we want to explore whether Code-LLMs acquire better causal reasoning abilities. Our experiments show that compared to text-only LLMs, Code-LLMs with code prompts are significantly better in causal reasoning. We further intervene on the prompts from different aspects, and discover that the programming structure is crucial in code prompt design, while Code-LLMs are robust towards format perturbations.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.

Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.

Recent work on neural algorithmic reasoning has investigated the reasoning capabilities of neural networks, effectively demonstrating they can learn to execute classical algorithms on unseen data coming from the train distribution. However, the performance of existing neural reasoners significantly degrades on out-of-distribution (OOD) test data, where inputs have larger sizes. In this work, we make an important observation: there are many different inputs for which an algorithm will perform certain intermediate computations identically. This insight allows us to develop data augmentation procedures that, given an algorithm's intermediate trajectory, produce inputs for which the target algorithm would have exactly the same next trajectory step. Then, we employ a causal framework to design a corresponding self-supervised objective, and we prove that it improves the OOD generalisation capabilities of the reasoner. We evaluate our method on the CLRS algorithmic reasoning benchmark, where we show up to 3times improvements on the OOD test data.

Large Language Models (LLMs) have shown state-of-the-art performance in a variety of tasks, including arithmetic and reasoning; however, to gauge the intellectual capabilities of LLMs, causal reasoning has become a reliable proxy for validating a general understanding of the mechanics and intricacies of the world similar to humans. Previous works in natural language processing (NLP) have either focused on open-ended causal reasoning via causal commonsense reasoning (CCR) or framed a symbolic representation-based question answering for theoretically backed-up analysis via a causal inference engine. The former adds an advantage of real-world grounding but lacks theoretically backed-up analysis/validation, whereas the latter is far from real-world grounding. In this work, we bridge this gap by proposing the COLD (Causal reasOning in cLosed Daily activities) framework, which is built upon human understanding of daily real-world activities to reason about the causal nature of events. We show that the proposed framework facilitates the creation of enormous causal queries (~ 9 million) and comes close to the mini-turing test, simulating causal reasoning to evaluate the understanding of a daily real-world task. We evaluate multiple LLMs on the created causal queries and find that causal reasoning is challenging even for activities trivial to humans. We further explore (the causal reasoning abilities of LLMs) using the backdoor criterion to determine the causal strength between events.

While interpretability research has shed light on some internal algorithms utilized by transformer-based LLMs, reasoning in natural language, with its deep contextuality and ambiguity, defies easy categorization. As a result, formulating clear and motivating questions for circuit analysis that rely on well-defined in-domain and out-of-domain examples required for causal interventions is challenging. Although significant work has investigated circuits for specific tasks, such as indirect object identification (IOI), deciphering natural language reasoning through circuits remains difficult due to its inherent complexity. In this work, we take initial steps to characterize causal reasoning in LLMs by analyzing clear-cut cause-and-effect sentences like "I opened an umbrella because it started raining," where causal interventions may be possible through carefully crafted scenarios using GPT-2 small. Our findings indicate that causal syntax is localized within the first 2-3 layers, while certain heads in later layers exhibit heightened sensitivity to nonsensical variations of causal sentences. This suggests that models may infer reasoning by (1) detecting syntactic cues and (2) isolating distinct heads in the final layers that focus on semantic relationships.

Causal analysis plays a foundational role in scientific discovery and reliable decision-making, yet it remains largely inaccessible to domain experts due to its conceptual and algorithmic complexity. This disconnect between causal methodology and practical usability presents a dual challenge: domain experts are unable to leverage recent advances in causal learning, while causal researchers lack broad, real-world deployment to test and refine their methods. To address this, we introduce Causal-Copilot, an autonomous agent that operationalizes expert-level causal analysis within a large language model framework. Causal-Copilot automates the full pipeline of causal analysis for both tabular and time-series data -- including causal discovery, causal inference, algorithm selection, hyperparameter optimization, result interpretation, and generation of actionable insights. It supports interactive refinement through natural language, lowering the barrier for non-specialists while preserving methodological rigor. By integrating over 20 state-of-the-art causal analysis techniques, our system fosters a virtuous cycle -- expanding access to advanced causal methods for domain experts while generating rich, real-world applications that inform and advance causal theory. Empirical evaluations demonstrate that Causal-Copilot achieves superior performance compared to existing baselines, offering a reliable, scalable, and extensible solution that bridges the gap between theoretical sophistication and real-world applicability in causal analysis. A live interactive demo of Causal-Copilot is available at https://causalcopilot.com/.

We address causal reasoning in multivariate time series data generated by stochastic processes. Existing approaches are largely restricted to static settings, ignoring the continuity and emission of variations across time. In contrast, we propose a learning paradigm that directly establishes causation between events in the course of time. We present two key lemmas to compute causal contributions and frame them as reinforcement learning problems. Our approach offers formal and computational tools for uncovering and quantifying causal relationships in diffusion processes, subsuming various important settings such as discrete-time Markov decision processes. Finally, in fairly intricate experiments and through sheer learning, our framework reveals and quantifies causal links, which otherwise seem inexplicable.

We develop a method for generating causal post-hoc explanations of black-box classifiers based on a learned low-dimensional representation of the data. The explanation is causal in the sense that changing learned latent factors produces a change in the classifier output statistics. To construct these explanations, we design a learning framework that leverages a generative model and information-theoretic measures of causal influence. Our objective function encourages both the generative model to faithfully represent the data distribution and the latent factors to have a large causal influence on the classifier output. Our method learns both global and local explanations, is compatible with any classifier that admits class probabilities and a gradient, and does not require labeled attributes or knowledge of causal structure. Using carefully controlled test cases, we provide intuition that illuminates the function of our objective. We then demonstrate the practical utility of our method on image recognition tasks.

We investigate causal computations taking sequences of inputs to sequences of outputs where the nth output depends on the first n inputs only. We model these in category theory via a construction taking a Cartesian category C to another category St(C) with a novel trace-like operation called "delayed trace", which misses yanking and dinaturality axioms of the usual trace. The delayed trace operation provides a feedback mechanism in St(C) with an implicit guardedness guarantee. When C is equipped with a Cartesian differential operator, we construct a differential operator for St(C) using an abstract version of backpropagation through time, a technique from machine learning based on unrolling of functions. This obtains a swath of properties for backpropagation through time, including a chain rule and Schwartz theorem. Our differential operator is also able to compute the derivative of a stateful network without requiring the network to be unrolled.

Actual causality (AC), a fundamental aspect of causal reasoning (CR), is responsible for attribution and responsibility assignment in real-world scenarios. However, existing LLM-based methods lack grounding in formal AC theory, resulting in limited interpretability. Therefore, we propose AC-Reason, a semi-formal reasoning framework that identifies causally relevant events within an AC scenario, infers the values of their formal causal factors (e.g., sufficiency, necessity, and normality), and answers AC queries via a theory-guided algorithm with explanations. While AC-Reason does not explicitly construct a causal graph, it operates over variables in the underlying causal structure to support principled reasoning. To enable comprehensive evaluation, we introduce AC-Bench, a new benchmark built upon and substantially extending Big-Bench Hard Causal Judgment (BBH-CJ). AC-Bench comprises ~1K carefully annotated samples, each with detailed reasoning steps and focuses solely on actual causation. The case study shows that synthesized samples in AC-Bench present greater challenges for LLMs. Extensive experiments on BBH-CJ and AC-Bench show that AC-Reason consistently improves LLM performance over baselines. On BBH-CJ, all tested LLMs surpass the average human rater accuracy of 69.60%, with GPT-4 + AC-Reason achieving 75.04%. On AC-Bench, GPT-4 + AC-Reason again achieves the highest accuracy of 71.82%. AC-Bench further enables fine-grained analysis of reasoning faithfulness, revealing that only Qwen-2.5-72B-Instruct, Claude-3.5-Sonnet, and GPT-4o exhibit faithful reasoning, whereas GPT-4 tends to exploit shortcuts. Finally, our ablation study proves that integrating AC theory into LLMs is highly effective, with the proposed algorithm contributing the most significant performance gains.

Extracting causal relationships from observed correlations is a growing area in probabilistic reasoning, originating with the seminal work of Pearl and others from the early 1990s. This paper develops a new, categorically oriented view based on a clear distinction between syntax (string diagrams) and semantics (stochastic matrices), connected via interpretations as structure-preserving functors. A key notion in the identification of causal effects is that of an intervention, whereby a variable is forcefully set to a particular value independent of any prior propensities. We represent the effect of such an intervention as an endofunctor which performs `string diagram surgery' within the syntactic category of string diagrams. This diagram surgery in turn yields a new, interventional distribution via the interpretation functor. While in general there is no way to compute interventional distributions purely from observed data, we show that this is possible in certain special cases using a calculational tool called comb disintegration. We demonstrate the use of this technique on a well-known toy example, where we predict the causal effect of smoking on cancer in the presence of a confounding common cause. After developing this specific example, we show this technique provides simple sufficient conditions for computing interventions which apply to a wide variety of situations considered in the causal inference literature.

Answering counterfactual queries has many important applications such as knowledge discovery and explainability, but is challenging when causal variables are unobserved and we only see a projection onto an observation space, for instance, image pixels. One approach is to recover the latent Structural Causal Model (SCM), but this typically needs unrealistic assumptions, such as linearity of the causal mechanisms. Another approach is to use na\"ive ML approximations, such as generative models, to generate counterfactual samples; however, these lack guarantees of accuracy. In this work, we strive to strike a balance between practicality and theoretical guarantees by focusing on a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain (or environment). Concretely, by only assuming invertibility, sparse domain interventions and access to observational data from different domains, we aim to improve domain counterfactual estimation both theoretically and practically with less restrictive assumptions. We define domain counterfactually equivalent models and prove necessary and sufficient properties for equivalent models that provide a tight characterization of the domain counterfactual equivalence classes. Building upon this result, we prove that every equivalence class contains a model where all intervened variables are at the end when topologically sorted by the causal DAG. This surprising result suggests that a model design that only allows intervention in the last k latent variables may improve model estimation for counterfactuals. We then test this model design on extensive simulated and image-based experiments which show the sparse canonical model indeed improves counterfactual estimation over baseline non-sparse models.

Explainability methods for NLP systems encounter a version of the fundamental problem of causal inference: for a given ground-truth input text, we never truly observe the counterfactual texts necessary for isolating the causal effects of model representations on outputs. In response, many explainability methods make no use of counterfactual texts, assuming they will be unavailable. In this paper, we show that robust causal explainability methods can be created using approximate counterfactuals, which can be written by humans to approximate a specific counterfactual or simply sampled using metadata-guided heuristics. The core of our proposal is the Causal Proxy Model (CPM). A CPM explains a black-box model N because it is trained to have the same actual input/output behavior as N while creating neural representations that can be intervened upon to simulate the counterfactual input/output behavior of N. Furthermore, we show that the best CPM for N performs comparably to N in making factual predictions, which means that the CPM can simply replace N, leading to more explainable deployed models. Our code is available at https://github.com/frankaging/Causal-Proxy-Model.

Large Language Models (LLMs) have recently shown great promise in planning and reasoning applications. These tasks demand robust systems, which arguably require a causal understanding of the environment. While LLMs can acquire and reflect common sense causal knowledge from their pretraining data, this information is often incomplete, incorrect, or inapplicable to a specific environment. In contrast, causal representation learning (CRL) focuses on identifying the underlying causal structure within a given environment. We propose a framework that integrates CRLs with LLMs to enable causally-aware reasoning and planning. This framework learns a causal world model, with causal variables linked to natural language expressions. This mapping provides LLMs with a flexible interface to process and generate descriptions of actions and states in text form. Effectively, the causal world model acts as a simulator that the LLM can query and interact with. We evaluate the framework on causal inference and planning tasks across temporal scales and environmental complexities. Our experiments demonstrate the effectiveness of the approach, with the causally-aware method outperforming LLM-based reasoners, especially for longer planning horizons.

We propose a novel framework that leverages LLMs for full causal graph discovery. While previous LLM-based methods have used a pairwise query approach, this requires a quadratic number of queries which quickly becomes impractical for larger causal graphs. In contrast, the proposed framework uses a breadth-first search (BFS) approach which allows it to use only a linear number of queries. We also show that the proposed method can easily incorporate observational data when available, to improve performance. In addition to being more time and data-efficient, the proposed framework achieves state-of-the-art results on real-world causal graphs of varying sizes. The results demonstrate the effectiveness and efficiency of the proposed method in discovering causal relationships, showcasing its potential for broad applicability in causal graph discovery tasks across different domains.

We present a general causal generative modelling framework for accurate estimation of high fidelity image counterfactuals with deep structural causal models. Estimation of interventional and counterfactual queries for high-dimensional structured variables, such as images, remains a challenging task. We leverage ideas from causal mediation analysis and advances in generative modelling to design new deep causal mechanisms for structured variables in causal models. Our experiments demonstrate that our proposed mechanisms are capable of accurate abduction and estimation of direct, indirect and total effects as measured by axiomatic soundness of counterfactuals.

Learning causal structure from observational data often assumes that we observe independent and identically distributed (i.\,i.\,d) data. The traditional approach aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that under i.\,i.\,d assumption, even with infinite data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation, recent work has explored using data originating from different, related environments to learn richer causal structure. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables identification of richer causal structures from grouped data. Here we present new causal de Finetti theorems which offer a first statistical formalization of ICM principle and show how causal structure identification is possible from exchangeable data. Our work provides theoretical justification for a broad range of techniques leveraging multi-environment data to learn causal structure.

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

The ability to perform causal reasoning is widely considered a core feature of intelligence. In this work, we investigate whether large language models (LLMs) can coherently reason about causality. Much of the existing work in natural language processing (NLP) focuses on evaluating commonsense causal reasoning in LLMs, thus failing to assess whether a model can perform causal inference in accordance with a set of well-defined formal rules. To address this, we propose a new NLP task, causal inference in natural language, inspired by the "causal inference engine" postulated by Judea Pearl et al. We compose a large dataset, CLadder, with 10K samples: based on a collection of causal graphs and queries (associational, interventional, and counterfactual), we obtain symbolic questions and ground-truth answers, through an oracle causal inference engine. These are then translated into natural language. We evaluate multiple LLMs on our dataset, and we introduce and evaluate a bespoke chain-of-thought prompting strategy, CausalCoT. We show that our task is highly challenging for LLMs, and we conduct an in-depth analysis to gain deeper insights into the causal reasoning abilities of LLMs. Our data is open-sourced at https://huggingface.co/datasets/causalNLP/cladder, and our code can be found at https://github.com/causalNLP/cladder.

We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both temporal and contemporaneous causal relations. One may ask if temporal and contemporaneous relations should be treated differently. The presented algorithm gradually refines a causal graph by learning long-term temporal relations before short-term ones, where contemporaneous relations are learned last. This ordering of causal relations to be learnt leads to a reduction in the required number of statistical tests. We validate this reduction empirically and demonstrate that it leads to higher accuracy for synthetic data and more plausible causal graphs for real-world data compared to state-of-the-art algorithms.

We introduce the concept of Automated Causal Discovery (AutoCD), defined as any system that aims to fully automate the application of causal discovery and causal reasoning methods. AutoCD's goal is to deliver all causal information that an expert human analyst would and answer a user's causal queries. We describe the architecture of such a platform, and illustrate its performance on synthetic data sets. As a case study, we apply it on temporal telecommunication data. The system is general and can be applied to a plethora of causal discovery problems.

The causal capabilities of large language models (LLMs) are a matter of significant debate, with critical implications for the use of LLMs in societally impactful domains such as medicine, science, law, and policy. We conduct a "behavorial" study of LLMs to benchmark their capability in generating causal arguments. Across a wide range of tasks, we find that LLMs can generate text corresponding to correct causal arguments with high probability, surpassing the best-performing existing methods. Algorithms based on GPT-3.5 and 4 outperform existing algorithms on a pairwise causal discovery task (97%, 13 points gain), counterfactual reasoning task (92%, 20 points gain) and event causality (86% accuracy in determining necessary and sufficient causes in vignettes). We perform robustness checks across tasks and show that the capabilities cannot be explained by dataset memorization alone, especially since LLMs generalize to novel datasets that were created after the training cutoff date. That said, LLMs exhibit unpredictable failure modes, and we discuss the kinds of errors that may be improved and what are the fundamental limits of LLM-based answers. Overall, by operating on the text metadata, LLMs bring capabilities so far understood to be restricted to humans, such as using collected knowledge to generate causal graphs or identifying background causal context from natural language. As a result, LLMs may be used by human domain experts to save effort in setting up a causal analysis, one of the biggest impediments to the widespread adoption of causal methods. Given that LLMs ignore the actual data, our results also point to a fruitful research direction of developing algorithms that combine LLMs with existing causal techniques. Code and datasets are available at https://github.com/py-why/pywhy-llm.

Causal discovery, i.e., inferring underlying cause-effect relationships from observations of a scene or system, is an inherent mechanism in human cognition, but has been shown to be highly challenging to automate. The majority of approaches in the literature aiming for this task consider constrained scenarios with fully observed variables or data from stationary time-series. In this work we aim for causal discovery in a more general class of scenarios, scenes with non-stationary behavior over time. For our purposes we here regard a scene as a composition objects interacting with each other over time. Non-stationarity is modeled as stationarity conditioned on an underlying variable, a state, which can be of varying dimension, more or less hidden given observations of the scene, and also depend more or less directly on these observations. We propose a probabilistic deep learning approach called State-Dependent Causal Inference (SDCI) for causal discovery in such conditionally stationary time-series data. Results in two different synthetic scenarios show that this method is able to recover the underlying causal dependencies with high accuracy even in cases with hidden states.

We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph. Under the faithfulness assumption, this natural family contains all exact structure-learning algorithms. We also provide a set of assumptions, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph. These assumptions can be thought of as a relaxation of faithfulness, and most of them can be directly tested from (the underlying distribution) of the data, particularly when one focuses on structural causal models. We specialize the definitions and results for structural causal models.

Understanding narratives requires reasoning about the cause-and-effect relationships between events mentioned in the text. While existing foundation models yield impressive results in many NLP tasks requiring reasoning, it is unclear whether they understand the complexity of the underlying network of causal relationships of events in narratives. In this work, we present CRAB, a new Causal Reasoning Assessment Benchmark designed to evaluate causal understanding of events in real-world narratives. CRAB contains fine-grained, contextual causality annotations for ~2.7K pairs of real-world events that describe various newsworthy event timelines (e.g., the acquisition of Twitter by Elon Musk). Using CRAB, we measure the performance of several large language models, demonstrating that most systems achieve poor performance on the task. Motivated by classical causal principles, we also analyze the causal structures of groups of events in CRAB, and find that models perform worse on causal reasoning when events are derived from complex causal structures compared to simple linear causal chains. We make our dataset and code available to the research community.

Scientists often infer abstract procedures from specific instances of problems and use the abstractions to generate new, related instances. For example, programs encoding the formal rules and properties of a system have been useful in fields ranging from RL (procedural environments) to physics (simulation engines). These programs can be seen as functions which execute to different outputs based on their parameterizations (e.g., gridworld configuration or initial physical conditions). We introduce the term EFA (Executable Functional Abstraction) to denote such programs for math problems. EFA-like constructs have been shown to be useful for math reasoning as problem generators for stress-testing models. However, prior work has been limited to abstractions for grade-school math (whose simple rules are easy to encode in programs), while generating EFAs for advanced math has thus far required human engineering. We explore the automatic construction of EFAs for advanced math problems. We operationalize the task of automatically constructing EFAs as a program synthesis task, and develop EFAGen, which conditions an LLM on a seed math problem and its step-by-step solution to generate candidate EFA programs that are faithful to the generalized problem and solution class underlying the seed problem. Furthermore, we formalize properties any valid EFA must possess in terms of executable unit tests, and show how the tests can be used as verifiable rewards to train LLMs to become better writers of EFAs. We demonstrate that EFAs constructed by EFAGen behave rationally by remaining faithful to seed problems, produce learnable problem variations, and that EFAGen can infer EFAs across multiple diverse sources of competition-level math problems. Finally, we show downstream uses of model-written EFAs e.g. finding problem variations that are harder or easier for a learner to solve, as well as data generation.

We present a conditional text generation framework that posits sentential expressions of possible causes and effects. This framework depends on two novel resources we develop in the course of this work: a very large-scale collection of English sentences expressing causal patterns CausalBank; and a refinement over previous work on constructing large lexical causal knowledge graphs Cause Effect Graph. Further, we extend prior work in lexically-constrained decoding to support disjunctive positive constraints. Human assessment confirms that our approach gives high-quality and diverse outputs. Finally, we use CausalBank to perform continued training of an encoder supporting a recent state-of-the-art model for causal reasoning, leading to a 3-point improvement on the COPA challenge set, with no change in model architecture.

Procedural planning aims to implement complex high-level goals by decomposition into sequential simpler low-level steps. Although procedural planning is a basic skill set for humans in daily life, it remains a challenge for large language models (LLMs) that lack a deep understanding of the cause-effect relations in procedures. Previous methods require manual exemplars to acquire procedural planning knowledge from LLMs in the zero-shot setting. However, such elicited pre-trained knowledge in LLMs induces spurious correlations between goals and steps, which impair the model generalization to unseen tasks. In contrast, this paper proposes a neuro-symbolic procedural PLANner (PLAN) that elicits procedural planning knowledge from the LLMs with commonsense-infused prompting. To mitigate spurious goal-step correlations, we use symbolic program executors on the latent procedural representations to formalize prompts from commonsense knowledge bases as a causal intervention toward the Structural Causal Model. Both automatic and human evaluations on WikiHow and RobotHow show the superiority of PLAN on procedural planning without further training or manual exemplars.

Understanding and manipulating the causal generation mechanisms in language models is essential for controlling their behavior. Previous work has primarily relied on techniques such as representation surgery -- e.g., model ablations or manipulation of linear subspaces tied to specific concepts -- to intervene on these models. To understand the impact of interventions precisely, it is useful to examine counterfactuals -- e.g., how a given sentence would have appeared had it been generated by the model following a specific intervention. We highlight that counterfactual reasoning is conceptually distinct from interventions, as articulated in Pearl's causal hierarchy. Based on this observation, we propose a framework for generating true string counterfactuals by reformulating language models as Generalized Structural-equation. Models using the Gumbel-max trick. This allows us to model the joint distribution over original strings and their counterfactuals resulting from the same instantiation of the sampling noise. We develop an algorithm based on hindsight Gumbel sampling that allows us to infer the latent noise variables and generate counterfactuals of observed strings. Our experiments demonstrate that the approach produces meaningful counterfactuals while at the same time showing that commonly used intervention techniques have considerable undesired side effects.

With the rise of Large Language Models(LLMs), it has become crucial to understand their capabilities and limitations in deciphering and explaining the complex web of causal relationships that language entails. Current methods use either explicit or implicit causal reasoning, yet there is a strong need for a unified approach combining both to tackle a wide array of causal relationships more effectively. This research proposes a novel architecture called Context Aware Reasoning Enhancement with Counterfactual Analysis(CARE CA) framework to enhance causal reasoning and explainability. The proposed framework incorporates an explicit causal detection module with ConceptNet and counterfactual statements, as well as implicit causal detection through LLMs. Our framework goes one step further with a layer of counterfactual explanations to accentuate LLMs understanding of causality. The knowledge from ConceptNet enhances the performance of multiple causal reasoning tasks such as causal discovery, causal identification and counterfactual reasoning. The counterfactual sentences add explicit knowledge of the not caused by scenarios. By combining these powerful modules, our model aims to provide a deeper understanding of causal relationships, enabling enhanced interpretability. Evaluation of benchmark datasets shows improved performance across all metrics, such as accuracy, precision, recall, and F1 scores. We also introduce CausalNet, a new dataset accompanied by our code, to facilitate further research in this domain.

In this paper, we propose REASON, a novel framework that enables the automatic discovery of both intra-level (i.e., within-network) and inter-level (i.e., across-network) causal relationships for root cause localization. REASON consists of Topological Causal Discovery and Individual Causal Discovery. The Topological Causal Discovery component aims to model the fault propagation in order to trace back to the root causes. To achieve this, we propose novel hierarchical graph neural networks to construct interdependent causal networks by modeling both intra-level and inter-level non-linear causal relations. Based on the learned interdependent causal networks, we then leverage random walks with restarts to model the network propagation of a system fault. The Individual Causal Discovery component focuses on capturing abrupt change patterns of a single system entity. This component examines the temporal patterns of each entity's metric data (i.e., time series), and estimates its likelihood of being a root cause based on the Extreme Value theory. Combining the topological and individual causal scores, the top K system entities are identified as root causes. Extensive experiments on three real-world datasets with case studies demonstrate the effectiveness and superiority of the proposed framework.

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to directly predict the causal structure from observational or interventional data. This allows our inference model to acquire domain-specific inductive biases for causal discovery solely from data generated by a simulator, bypassing both the hand-engineering of suitable score functions and the search over graphs. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training. On synthetic data and semisynthetic gene expression data, our models exhibit robust generalization capabilities when subject to substantial distribution shifts and significantly outperform existing algorithms, especially in the challenging genomics domain. Our code and models are publicly available at: https://github.com/larslorch/avici.

Model-based methods have recently shown promising for offline reinforcement learning (RL), aiming to learn good policies from historical data without interacting with the environment. Previous model-based offline RL methods learn fully connected nets as world-models that map the states and actions to the next-step states. However, it is sensible that a world-model should adhere to the underlying causal effect such that it will support learning an effective policy generalizing well in unseen states. In this paper, We first provide theoretical results that causal world-models can outperform plain world-models for offline RL by incorporating the causal structure into the generalization error bound. We then propose a practical algorithm, oFfline mOdel-based reinforcement learning with CaUsal Structure (FOCUS), to illustrate the feasibility of learning and leveraging causal structure in offline RL. Experimental results on two benchmarks show that FOCUS reconstructs the underlying causal structure accurately and robustly. Consequently, it performs better than the plain model-based offline RL algorithms and other causal model-based RL algorithms.

We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) G^* while minimizing the number of interventions made. In our setting, we are additionally given side information about G^* as advice, e.g. a DAG G purported to be G^*. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on algorithms with predictions. When the advice is a DAG G, we design an adaptive search algorithm to recover G^* whose intervention cost is at most O(max{1, log psi}) times the cost for verifying G^*; here, psi is a distance measure between G and G^* that is upper bounded by the number of variables n, and is exactly 0 when G=G^*. Our approximation factor matches the state-of-the-art for the advice-less setting.

Conventional causal discovery methods rely on centralized data, which is inconsistent with the decentralized nature of data in many real-world situations. This discrepancy has motivated the development of federated causal discovery (FCD) approaches. However, existing FCD methods may be limited by their potentially restrictive assumptions of identifiable functional causal models or homogeneous data distributions, narrowing their applicability in diverse scenarios. In this paper, we propose a novel FCD method attempting to accommodate arbitrary causal models and heterogeneous data. We first utilize a surrogate variable corresponding to the client index to account for the data heterogeneity across different clients. We then develop a federated conditional independence test (FCIT) for causal skeleton discovery and establish a federated independent change principle (FICP) to determine causal directions. These approaches involve constructing summary statistics as a proxy of the raw data to protect data privacy. Owing to the nonparametric properties, FCIT and FICP make no assumption about particular functional forms, thereby facilitating the handling of arbitrary causal models. We conduct extensive experiments on synthetic and real datasets to show the efficacy of our method. The code is available at https://github.com/lokali/FedCDH.git.

Retrieval-Augmented Generation (RAG) has significantly enhanced large language models (LLMs) in knowledge-intensive tasks by incorporating external knowledge retrieval. However, existing RAG frameworks primarily rely on semantic similarity and correlation-driven retrieval, limiting their ability to distinguish true causal relationships from spurious associations. This results in responses that may be factually grounded but fail to establish cause-and-effect mechanisms, leading to incomplete or misleading insights. To address this issue, we introduce Causal Dynamic Feedback for Adaptive Retrieval-Augmented Generation (CDF-RAG), a framework designed to improve causal consistency, factual accuracy, and explainability in generative reasoning. CDF-RAG iteratively refines queries, retrieves structured causal graphs, and enables multi-hop causal reasoning across interconnected knowledge sources. Additionally, it validates responses against causal pathways, ensuring logically coherent and factually grounded outputs. We evaluate CDF-RAG on four diverse datasets, demonstrating its ability to improve response accuracy and causal correctness over existing RAG-based methods. Our code is publicly available at https://github.com/ elakhatibi/CDF-RAG.

Counterfactual reasoning is widely recognized as one of the most challenging and intricate aspects of causality in artificial intelligence. In this paper, we evaluate the performance of large language models (LLMs) in counterfactual reasoning. In contrast to previous studies that primarily focus on commonsense causal reasoning, where LLMs often rely on prior knowledge for inference, we specifically assess their ability to perform counterfactual inference using a set of formal rules. To support this evaluation, we introduce a new benchmark dataset, CounterBench, comprising 1K counterfactual reasoning questions. The dataset is designed with varying levels of difficulty, diverse causal graph structures, distinct types of counterfactual questions, and multiple nonsensical name variants. Our experiments demonstrate that counterfactual reasoning poses a significant challenge for LLMs, with most models performing at levels comparable to random guessing. To enhance LLM's counterfactual reasoning ability, we propose a novel reasoning paradigm, CoIn, which guides LLMs through iterative reasoning and backtracking to systematically explore counterfactual solutions. Experimental results show that our method significantly improves LLM performance on counterfactual reasoning tasks and consistently enhances performance across different LLMs.Our dataset is available at https://huggingface.co/datasets/CounterBench/CounterBench.

We have recently witnessed a number of impressive results on hard mathematical reasoning problems with language models. At the same time, the robustness of these models has also been called into question; recent works have shown that models can rely on shallow patterns in the problem description when generating a solution. Building on the idea of behavioral testing, we propose a novel framework, which pins down the causal effect of various factors in the input, e.g., the surface form of the problem text, the operands, and math operators on the output solution. By grounding the behavioral analysis in a causal graph describing an intuitive reasoning process, we study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. We apply our framework on a test bed of math word problems. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.

Large language models (LLMs) have achieved significant success across various domains. However, the inherent complexity of causal problems and causal theory poses challenges in accurately describing them in natural language, making it difficult for LLMs to comprehend and use them effectively. Causal methods are not easily conveyed through natural language, which hinders LLMs' ability to apply them accurately. Additionally, causal datasets are typically tabular, while LLMs excel in handling natural language data, creating a structural mismatch that impedes effective reasoning with tabular data. This lack of causal reasoning capability limits the development of LLMs. To address these challenges, we have equipped the LLM with causal tools within an agent framework, named the Causal Agent, enabling it to tackle causal problems. The causal agent comprises tools, memory, and reasoning modules. In the tools module, the causal agent applies causal methods to align tabular data with natural language. In the reasoning module, the causal agent employs the ReAct framework to perform reasoning through multiple iterations with the tools. In the memory module, the causal agent maintains a dictionary instance where the keys are unique names and the values are causal graphs. To verify the causal ability of the causal agent, we established a benchmark consisting of four levels of causal problems: variable level, edge level, causal graph level, and causal effect level. We generated a test dataset of 1.3K using ChatGPT-3.5 for these four levels of issues and tested the causal agent on the datasets. Our methodology demonstrates remarkable efficacy on the four-level causal problems, with accuracy rates all above 80%. For further insights and implementation details, our code is accessible via the GitHub repository https://github.com/Kairong-Han/Causal_Agent.

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear representation" actually mean? And, how do we make sense of geometric notions (e.g., cosine similarity or projection) in the representation space? To answer these, we use the language of counterfactuals to give two formalizations of "linear representation", one in the output (word) representation space, and one in the input (sentence) space. We then prove these connect to linear probing and model steering, respectively. To make sense of geometric notions, we use the formalization to identify a particular (non-Euclidean) inner product that respects language structure in a sense we make precise. Using this causal inner product, we show how to unify all notions of linear representation. In particular, this allows the construction of probes and steering vectors using counterfactual pairs. Experiments with LLaMA-2 demonstrate the existence of linear representations of concepts, the connection to interpretation and control, and the fundamental role of the choice of inner product.

One well motivated explanation method for classifiers leverages counterfactuals which are hypothetical events identical to real observations in all aspects except for one categorical feature. Constructing such counterfactual poses specific challenges for texts, however, as some attribute values may not necessarily align with plausible real-world events. In this paper we propose a simple method for generating counterfactuals by intervening in the space of text representations which bypasses this limitation. We argue that our interventions are minimally disruptive and that they are theoretically sound as they align with counterfactuals as defined in Pearl's causal inference framework. To validate our method, we first conduct experiments on a synthetic dataset of counterfactuals, allowing for a direct comparison between classifier predictions based on ground truth counterfactuals (obtained through explicit text interventions) and our counterfactuals, derived through interventions in the representation space. Second, we study a real world scenario where our counterfactuals can be leveraged both for explaining a classifier and for bias mitigation.

It has long been hypothesised that causal reasoning plays a fundamental role in robust and general intelligence. However, it is not known if agents must learn causal models in order to generalise to new domains, or if other inductive biases are sufficient. We answer this question, showing that any agent capable of satisfying a regret bound under a large set of distributional shifts must have learned an approximate causal model of the data generating process, which converges to the true causal model for optimal agents. We discuss the implications of this result for several research areas including transfer learning and causal inference.

Recent work has shown promising results in causal discovery by leveraging interventional data with gradient-based methods, even when the intervened variables are unknown. However, previous work assumes that the correspondence between samples and interventions is known, which is often unrealistic. We envision a scenario with an extensive dataset sampled from multiple intervention distributions and one observation distribution, but where we do not know which distribution originated each sample and how the intervention affected the system, i.e., interventions are entirely latent. We propose a method based on neural networks and variational inference that addresses this scenario by framing it as learning a shared causal graph among an infinite mixture (under a Dirichlet process prior) of intervention structural causal models. Experiments with synthetic and real data show that our approach and its semi-supervised variant are able to discover causal relations in this challenging scenario.

Commonsense causality reasoning (CCR) aims at identifying plausible causes and effects in natural language descriptions that are deemed reasonable by an average person. Although being of great academic and practical interest, this problem is still shadowed by the lack of a well-posed theoretical framework; existing work usually relies on deep language models wholeheartedly, and is potentially susceptible to confounding co-occurrences. Motivated by classical causal principles, we articulate the central question of CCR and draw parallels between human subjects in observational studies and natural languages to adopt CCR to the potential-outcomes framework, which is the first such attempt for commonsense tasks. We propose a novel framework, ROCK, to Reason O(A)bout Commonsense K(C)ausality, which utilizes temporal signals as incidental supervision, and balances confounding effects using temporal propensities that are analogous to propensity scores. The ROCK implementation is modular and zero-shot, and demonstrates good CCR capabilities.

Understanding causality has vital importance for various Natural Language Processing (NLP) applications. Beyond the labeled instances, conceptual explanations of the causality can provide deep understanding of the causal facts to facilitate the causal reasoning process. However, such explanation information still remains absent in existing causal reasoning resources. In this paper, we fill this gap by presenting a human-annotated explainable CAusal REasoning dataset (e-CARE), which contains over 21K causal reasoning questions, together with natural language formed explanations of the causal questions. Experimental results show that generating valid explanations for causal facts still remains especially challenging for the state-of-the-art models, and the explanation information can be helpful for promoting the accuracy and stability of causal reasoning models.

Entities and events are crucial to natural language reasoning and common in procedural texts. Existing work has focused either exclusively on entity state tracking (e.g., whether a pan is hot) or on event reasoning (e.g., whether one would burn themselves by touching the pan), while these two tasks are often causally related. We propose CREPE, the first benchmark on causal reasoning of event plausibility and entity states. We show that most language models, including GPT-3, perform close to chance at .35 F1, lagging far behind human at .87 F1. We boost model performance to .59 F1 by creatively representing events as programming languages while prompting language models pretrained on code. By injecting the causal relations between entities and events as intermediate reasoning steps in our representation, we further boost the performance to .67 F1. Our findings indicate not only the challenge that CREPE brings for language models, but also the efficacy of code-like prompting combined with chain-of-thought prompting for multihop event reasoning.

We provide an optimization-based framework to perform counterfactual analysis in a dynamic model with hidden states. Our framework is grounded in the ``abduction, action, and prediction'' approach to answer counterfactual queries and handles two key challenges where (1) the states are hidden and (2) the model is dynamic. Recognizing the lack of knowledge on the underlying causal mechanism and the possibility of infinitely many such mechanisms, we optimize over this space and compute upper and lower bounds on the counterfactual quantity of interest. Our work brings together ideas from causality, state-space models, simulation, and optimization, and we apply it on a breast cancer case study. To the best of our knowledge, we are the first to compute lower and upper bounds on a counterfactual query in a dynamic latent-state model.

Interventions on model-internal states are fundamental operations in many areas of AI, including model editing, steering, robustness, and interpretability. To facilitate such research, we introduce pyvene, an open-source Python library that supports customizable interventions on a range of different PyTorch modules. pyvene supports complex intervention schemes with an intuitive configuration format, and its interventions can be static or include trainable parameters. We show how pyvene provides a unified and extensible framework for performing interventions on neural models and sharing the intervened upon models with others. We illustrate the power of the library via interpretability analyses using causal abstraction and knowledge localization. We publish our library through Python Package Index (PyPI) and provide code, documentation, and tutorials at https://github.com/stanfordnlp/pyvene.

Causal reasoning is viewed as crucial for achieving human-level machine intelligence. Recent advances in language models have expanded the horizons of artificial intelligence across various domains, sparking inquiries into their potential for causal reasoning. In this work, we introduce Causal evaluation of Language Models (CaLM), which, to the best of our knowledge, is the first comprehensive benchmark for evaluating the causal reasoning capabilities of language models. First, we propose the CaLM framework, which establishes a foundational taxonomy consisting of four modules: causal target (i.e., what to evaluate), adaptation (i.e., how to obtain the results), metric (i.e., how to measure the results), and error (i.e., how to analyze the bad results). This taxonomy defines a broad evaluation design space while systematically selecting criteria and priorities. Second, we compose the CaLM dataset, comprising 126,334 data samples, to provide curated sets of causal targets, adaptations, metrics, and errors, offering extensive coverage for diverse research pursuits. Third, we conduct an extensive evaluation of 28 leading language models on a core set of 92 causal targets, 9 adaptations, 7 metrics, and 12 error types. Fourth, we perform detailed analyses of the evaluation results across various dimensions (e.g., adaptation, scale). Fifth, we present 50 high-level empirical findings across 9 dimensions (e.g., model), providing valuable guidance for future language model development. Finally, we develop a multifaceted platform, including a website, leaderboards, datasets, and toolkits, to support scalable and adaptable assessments. We envision CaLM as an ever-evolving benchmark for the community, systematically updated with new causal targets, adaptations, models, metrics, and error types to reflect ongoing research advancements. Project website is at https://opencausalab.github.io/CaLM.

Interpreting the inner function of neural networks is crucial for the trustworthy development and deployment of these black-box models. Prior interpretability methods focus on correlation-based measures to attribute model decisions to individual examples. However, these measures are susceptible to noise and spurious correlations encoded in the model during the training phase (e.g., biased inputs, model overfitting, or misspecification). Moreover, this process has proven to result in noisy and unstable attributions that prevent any transparent understanding of the model's behavior. In this paper, we develop a robust interventional-based method grounded by causal analysis to capture cause-effect mechanisms in pre-trained neural networks and their relation to the prediction. Our novel approach relies on path interventions to infer the causal mechanisms within hidden layers and isolate relevant and necessary information (to model prediction), avoiding noisy ones. The result is task-specific causal explanatory graphs that can audit model behavior and express the actual causes underlying its performance. We apply our method to vision models trained on classification tasks. On image classification tasks, we provide extensive quantitative experiments to show that our approach can capture more stable and faithful explanations than standard attribution-based methods. Furthermore, the underlying causal graphs reveal the neural interactions in the model, making it a valuable tool in other applications (e.g., model repair).

We study counterfactual identifiability in causal models with bijective generation mechanisms (BGM), a class that generalizes several widely-used causal models in the literature. We establish their counterfactual identifiability for three common causal structures with unobserved confounding, and propose a practical learning method that casts learning a BGM as structured generative modeling. Learned BGMs enable efficient counterfactual estimation and can be obtained using a variety of deep conditional generative models. We evaluate our techniques in a visual task and demonstrate its application in a real-world video streaming simulation task.

We explore algorithms to select actions in the causal bandit setting where the learner can choose to intervene on a set of random variables related by a causal graph, and the learner sequentially chooses interventions and observes a sample from the interventional distribution. The learner's goal is to quickly find the intervention, among all interventions on observable variables, that maximizes the expectation of an outcome variable. We depart from previous literature by assuming no knowledge of the causal graph except that latent confounders between the outcome and its ancestors are not present. We first show that the unknown graph problem can be exponentially hard in the parents of the outcome. To remedy this, we adopt an additional additive assumption on the outcome which allows us to solve the problem by casting it as an additive combinatorial linear bandit problem with full-bandit feedback. We propose a novel action-elimination algorithm for this setting, show how to apply this algorithm to the causal bandit problem, provide sample complexity bounds, and empirically validate our findings on a suite of randomly generated causal models, effectively showing that one does not need to explicitly learn the parents of the outcome to identify the best intervention.

We propose a novel machine learning approach for inferring causal variables of a target variable from observations. Our focus is on directly inferring a set of causal factors without requiring full causal graph reconstruction, which is computationally challenging in large-scale systems. The identified causal set consists of all potential regulators of the target variable under experimental settings, enabling efficient regulation when intervention costs and feasibility vary across variables. To achieve this, we train a neural network using supervised learning on simulated data to infer causality. By employing a local-inference strategy, our approach scales with linear complexity in the number of variables, efficiently scaling up to thousands of variables. Empirical results demonstrate superior performance in identifying causal relationships within large-scale gene regulatory networks, outperforming existing methods that emphasize full-graph discovery. We validate our model's generalization capability across out-of-distribution graph structures and generating mechanisms, including gene regulatory networks of E. coli and the human K562 cell line. Implementation codes are available at https://github.com/snu-mllab/Targeted-Cause-Discovery.

We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We see how the property of convergence of global optimisation is a straightforward consequence of searchability. The abstract setting allows us to generalise searchability and continuity to higher-order functions, so that we can formulate novel convergence criteria for regression, derived from the convergence of global optimisation. All the theory and the motivating examples are fully formalised in the proof assistant Agda.

The recent phenomenal success of language models has reinvigorated machine learning research, and large sequence models such as transformers are being applied to a variety of domains. One important problem class that has remained relatively elusive however is purposeful adaptive behavior. Currently there is a common perception that sequence models "lack the understanding of the cause and effect of their actions" leading them to draw incorrect inferences due to auto-suggestive delusions. In this report we explain where this mismatch originates, and show that it can be resolved by treating actions as causal interventions. Finally, we show that in supervised learning, one can teach a system to condition or intervene on data by training with factual and counterfactual error signals respectively.

Time-series causal discovery (TSCD) is a fundamental problem of machine learning. However, existing synthetic datasets cannot properly evaluate or predict the algorithms' performance on real data. This study introduces the CausalTime pipeline to generate time-series that highly resemble the real data and with ground truth causal graphs for quantitative performance evaluation. The pipeline starts from real observations in a specific scenario and produces a matching benchmark dataset. Firstly, we harness deep neural networks along with normalizing flow to accurately capture realistic dynamics. Secondly, we extract hypothesized causal graphs by performing importance analysis on the neural network or leveraging prior knowledge. Thirdly, we derive the ground truth causal graphs by splitting the causal model into causal term, residual term, and noise term. Lastly, using the fitted network and the derived causal graph, we generate corresponding versatile time-series proper for algorithm assessment. In the experiments, we validate the fidelity of the generated data through qualitative and quantitative experiments, followed by a benchmarking of existing TSCD algorithms using these generated datasets. CausalTime offers a feasible solution to evaluating TSCD algorithms in real applications and can be generalized to a wide range of fields. For easy use of the proposed approach, we also provide a user-friendly website, hosted on www.causaltime.cc.

The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that often demands high-level abstract reasoning about program properties, which is challenging for verification tools. We propose a general methodology to combine the power of LLMs and automated reasoners for automated program verification. We formally describe this methodology as a set of derivation rules and prove its soundness. We instantiate the calculus as a sound automated verification procedure, which led to practical improvements on a set of synthetic and competition benchmarks.

Fair machine learning seeks to identify and mitigate biases in predictions against unfavorable populations characterized by demographic attributes, such as race and gender. Recently, a few works have extended fairness to graph data, such as social networks, but most of them neglect the causal relationships among data instances. This paper addresses the prevalent challenge in fairness-aware ML algorithms, which typically assume Independent and Identically Distributed (IID) data. We tackle the overlooked domain of non-IID, graph-based settings where data instances are interconnected, influencing the outcomes of fairness interventions. We base our research on the Network Structural Causal Model (NSCM) framework and posit two main assumptions: Decomposability and Graph Independence, which enable the computation of interventional distributions in non-IID settings using the do-calculus. Based on that, we develop the Message Passing Variational Autoencoder for Causal Inference (MPVA) to compute interventional distributions and facilitate causally fair node classification through estimated interventional distributions. Empirical evaluations on semi-synthetic and real-world datasets demonstrate that MPVA outperforms conventional methods by effectively approximating interventional distributions and mitigating bias. The implications of our findings underscore the potential of causality-based fairness in complex ML applications, setting the stage for further research into relaxing the initial assumptions to enhance model fairness.

Causal inference is one of the hallmarks of human intelligence. While the field of CausalNLP has attracted much interest in the recent years, existing causal inference datasets in NLP primarily rely on discovering causality from empirical knowledge (e.g., commonsense knowledge). In this work, we propose the first benchmark dataset to test the pure causal inference skills of large language models (LLMs). Specifically, we formulate a novel task Corr2Cause, which takes a set of correlational statements and determines the causal relationship between the variables. We curate a large-scale dataset of more than 400K samples, on which we evaluate seventeen existing LLMs. Through our experiments, we identify a key shortcoming of LLMs in terms of their causal inference skills, and show that these models achieve almost close to random performance on the task. This shortcoming is somewhat mitigated when we try to re-purpose LLMs for this skill via finetuning, but we find that these models still fail to generalize -- they can only perform causal inference in in-distribution settings when variable names and textual expressions used in the queries are similar to those in the training set, but fail in out-of-distribution settings generated by perturbing these queries. Corr2Cause is a challenging task for LLMs, and would be helpful in guiding future research on improving LLMs' pure reasoning skills and generalizability. Our data is at https://huggingface.co/datasets/causalnlp/corr2cause. Our code is at https://github.com/causalNLP/corr2cause.

Understanding causality should be a core requirement of any attempt to build real impact through AI. Due to the inherent unobservability of counterfactuals, large randomised trials (RCTs) are the standard for causal inference. But large experiments are generically expensive, and randomisation carries its own costs, e.g. when suboptimal decisions are trialed. Recent work has proposed more sample-efficient alternatives to RCTs, but these are not adaptable to the downstream application for which the causal effect is sought. In this work, we develop a task-specific approach to experimental design and derive sampling strategies customised to particular downstream applications. Across a range of important tasks, real-world datasets, and sample sizes, our method outperforms other benchmarks, e.g. requiring an order-of-magnitude less data to match RCT performance on targeted marketing tasks.

Large Language Models have demonstrated remarkable capabilities in code generation, yet they often struggle with complex programming tasks that require deep algorithmic reasoning. While process supervision through learned reward models shows promise in guiding reasoning steps, it requires expensive training data and suffers from unreliable evaluation. We propose Outcome-Refining Process Supervision, a novel paradigm that treats outcome refinement itself as the process to be supervised. Our framework leverages concrete execution signals to ground the supervision of reasoning steps, while using tree-structured exploration to maintain multiple solution trajectories simultaneously. Experiments demonstrate that our approach enables even smaller models to achieve high success accuracy and performance metrics on competitive programming tasks, creates more reliable verification than traditional reward models without requiring training PRMs. Our approach achieves significant improvements across 5 models and 3 datasets: an average of 26.9% increase in correctness and 42.2% in efficiency. The results suggest that providing structured reasoning space with concrete verification signals is crucial for solving complex programming tasks. We open-source all our code and data at: https://github.com/zhuohaoyu/ORPS

Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference queries become tractable, such as model counting and most probable configuration. Recent works have explored analyzing probabilistic and causal inference queries as compositions of basic operators to derive tractability conditions. In this paper, we take an algebraic perspective for compositional inference, and show that a large class of queries - including marginal MAP, probabilistic answer set programming inference, and causal backdoor adjustment - correspond to a combination of basic operators over semirings: aggregation, product, and elementwise mapping. Using this framework, we uncover simple and general sufficient conditions for tractable composition of these operators, in terms of circuit properties (e.g., marginal determinism, compatibility) and conditions on the elementwise mappings. Applying our analysis, we derive novel tractability conditions for many such compositional queries. Our results unify tractability conditions for existing problems on circuits, while providing a blueprint for analysing novel compositional inference queries.

Causality knowledge is vital to building robust AI systems. Deep learning models often perform poorly on tasks that require causal reasoning, which is often derived using some form of commonsense knowledge not immediately available in the input but implicitly inferred by humans. Prior work has unraveled spurious observational biases that models fall prey to in the absence of causality. While language representation models preserve contextual knowledge within learned embeddings, they do not factor in causal relationships during training. By blending causal relationships with the input features to an existing model that performs visual cognition tasks (such as scene understanding, video captioning, video question-answering, etc.), better performance can be achieved owing to the insight causal relationships bring about. Recently, several models have been proposed that have tackled the task of mining causal data from either the visual or textual modality. However, there does not exist widespread research that mines causal relationships by juxtaposing the visual and language modalities. While images offer a rich and easy-to-process resource for us to mine causality knowledge from, videos are denser and consist of naturally time-ordered events. Also, textual information offers details that could be implicit in videos. We propose iReason, a framework that infers visual-semantic commonsense knowledge using both videos and natural language captions. Furthermore, iReason's architecture integrates a causal rationalization module to aid the process of interpretability, error analysis and bias detection. We demonstrate the effectiveness of iReason using a two-pronged comparative analysis with language representation learning models (BERT, GPT-2) as well as current state-of-the-art multimodal causality models.

Urban causal research is essential for understanding the complex dynamics of cities and informing evidence-based policies. However, it is challenged by the inefficiency and bias of hypothesis generation, barriers to multimodal data complexity, and the methodological fragility of causal experimentation. Recent advances in large language models (LLMs) present an opportunity to rethink how urban causal analysis is conducted. This Perspective examines current urban causal research by analyzing taxonomies that categorize research topics, data sources, and methodological approaches to identify structural gaps. We then introduce an LLM-driven conceptual framework, AutoUrbanCI, composed of four distinct modular agents responsible for hypothesis generation, data engineering, experiment design and execution, and results interpretation with policy recommendations. We propose evaluation criteria for rigor and transparency and reflect on implications for human-AI collaboration, equity, and accountability. We call for a new research agenda that embraces AI-augmented workflows not as replacements for human expertise but as tools to broaden participation, improve reproducibility, and unlock more inclusive forms of urban causal reasoning.

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

A directed acyclic graph (DAG) provides valuable prior knowledge that is often discarded in regression tasks in machine learning. We show that the independences arising from the presence of collider structures in DAGs provide meaningful inductive biases, which constrain the regression hypothesis space and improve predictive performance. We introduce collider regression, a framework to incorporate probabilistic causal knowledge from a collider in a regression problem. When the hypothesis space is a reproducing kernel Hilbert space, we prove a strictly positive generalisation benefit under mild assumptions and provide closed-form estimators of the empirical risk minimiser. Experiments on synthetic and climate model data demonstrate performance gains of the proposed methodology.

In causal bandit problems, the action set consists of interventions on variables of a causal graph. Several researchers have recently studied such bandit problems and pointed out their practical applications. However, all existing works rely on a restrictive and impractical assumption that the learner is given full knowledge of the causal graph structure upfront. In this paper, we develop novel causal bandit algorithms without knowing the causal graph. Our algorithms work well for causal trees, causal forests and a general class of causal graphs. The regret guarantees of our algorithms greatly improve upon those of standard multi-armed bandit (MAB) algorithms under mild conditions. Lastly, we prove our mild conditions are necessary: without them one cannot do better than standard MAB algorithms.

Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely out of reach for open models. To address this gap, we examine the potential of Generative Flow Networks as a fine-tuning method for LLMs to unlock advanced reasoning capabilities. In this paper, we present a proof of concept in the domain of formal reasoning, specifically in the Neural Theorem Proving (NTP) setting, where proofs specified in a formal language such as Lean can be deterministically and objectively verified. Unlike classical reward-maximization reinforcement learning, which frequently over-exploits high-reward actions and fails to effectively explore the state space, GFlowNets have emerged as a promising approach for sampling compositional objects, improving generalization, and enabling models to maintain diverse hypotheses. Our early results demonstrate GFlowNet fine-tuning's potential for enhancing model performance in a search setting, which is especially relevant given the paradigm shift towards inference time compute scaling and "thinking slowly."

Understanding commonsense causality is a unique mark of intelligence for humans. It helps people understand the principles of the real world better and benefits the decision-making process related to causation. For instance, commonsense causality is crucial in judging whether a defendant's action causes the plaintiff's loss in determining legal liability. Despite its significance, a systematic exploration of this topic is notably lacking. Our comprehensive survey bridges this gap by focusing on taxonomies, benchmarks, acquisition methods, qualitative reasoning, and quantitative measurements in commonsense causality, synthesizing insights from over 200 representative articles. Our work aims to provide a systematic overview, update scholars on recent advancements, provide a pragmatic guide for beginners, and highlight promising future research directions in this vital field.

Prompt-based probing has been widely used in evaluating the abilities of pretrained language models (PLMs). Unfortunately, recent studies have discovered such an evaluation may be inaccurate, inconsistent and unreliable. Furthermore, the lack of understanding its inner workings, combined with its wide applicability, has the potential to lead to unforeseen risks for evaluating and applying PLMs in real-world applications. To discover, understand and quantify the risks, this paper investigates the prompt-based probing from a causal view, highlights three critical biases which could induce biased results and conclusions, and proposes to conduct debiasing via causal intervention. This paper provides valuable insights for the design of unbiased datasets, better probing frameworks and more reliable evaluations of pretrained language models. Furthermore, our conclusions also echo that we need to rethink the criteria for identifying better pretrained language models. We openly released the source code and data at https://github.com/c-box/causalEval.

We design a suite of minimal algorithmic tasks that are a loose abstraction of open-ended real-world tasks. This allows us to cleanly and controllably quantify the creative limits of the present-day language model. Much like real-world tasks that require a creative, far-sighted leap of thought, our tasks require an implicit, open-ended stochastic planning step that either (a) discovers new connections in an abstract knowledge graph (like in wordplay, drawing analogies, or research) or (b) constructs new patterns (like in designing math problems or new proteins). In these tasks, we empirically and conceptually argue how next-token learning is myopic and memorizes excessively; comparatively, multi-token approaches, namely teacherless training and diffusion models, excel in producing diverse and original output. Secondly, in our tasks, we find that to elicit randomness from the Transformer without hurting coherence, it is better to inject noise right at the input layer (via a method we dub hash-conditioning) rather than defer to temperature sampling from the output layer. Thus, our work offers a principled, minimal test-bed for analyzing open-ended creative skills, and offers new arguments for going beyond next-token learning and softmax-based sampling. We make part of the code available under https://github.com/chenwu98/algorithmic-creativity

In order to avoid well-know paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type_0 : Type_1 : cdots . Such type systems are called cumulative if for any type A we have that A : Type_{i} implies A : Type_{i+1}. The predicative calculus of inductive constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present and establish the soundness of the predicative calculus of cumulative inductive constructions (pCuIC) which extends the cumulativity relation to inductive types.

We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties like exchangeability of conditions. Conditioning on equality of continuous random variables is nontrivial, as the exact observation may have probability zero; this is Borel's paradox. Using categorical formulations of conditional probability, we show that the good properties of our language are not particular to Gaussians, but can be derived from universal properties, thus generalizing to wider settings. We define the Cond construction, which internalizes conditioning as a morphism, providing general compositional semantics for probabilistic programming with exact conditioning.

The emergence of ChatGPT has once again sparked research in generative artificial intelligence (GAI). While people have been amazed by the generated results, they have also noticed the reasoning potential reflected in the generated textual content. However, this current ability for causal reasoning is primarily limited to the domain of language generation, such as in models like GPT-3. In visual modality, there is currently no equivalent research. Considering causal reasoning in visual content generation is significant. This is because visual information contains infinite granularity. Particularly, images can provide more intuitive and specific demonstrations for certain reasoning tasks, especially when compared to coarse-grained text. Hence, we propose a new image generation task called visual question answering with image (VQAI) and establish a dataset of the same name based on the classic Tom and Jerry animated series. Additionally, we develop a new paradigm for image generation to tackle the challenges of this task. Finally, we perform extensive experiments and analyses, including visualizations of the generated content and discussions on the potentials and limitations. The code and data are publicly available under the license of CC BY-NC-SA 4.0 for academic and non-commercial usage. The code and dataset are publicly available at: https://github.com/IEIT-AGI/MIX-Shannon/blob/main/projects/VQAI/lgd_vqai.md.

We extend the simply-typed guarded lambda-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming and reasoning about infinite stochastic processes like Markov chains. We demonstrate the logic sound by interpreting its judgements in the topos of trees and by using probabilistic couplings for the semantics of relational assertions over distributions on discrete types. The program logic is designed to support syntax-directed proofs in the style of relational refinement types, but retains the expressiveness of higher-order logic extended with discrete distributions, and the ability to reason relationally about expressions that have different types or syntactic structure. In addition, our proof system leverages a well-known theorem from the coupling literature to justify better proof rules for relational reasoning about probabilistic expressions. We illustrate these benefits with a broad range of examples that were beyond the scope of previous systems, including shift couplings and lump couplings between random walks.

Despite recent advances in video understanding, the capabilities of Large Video Language Models (LVLMs) to perform video-based causal reasoning remains underexplored, largely due to the absence of relevant and dedicated benchmarks for evaluating causal reasoning in visually grounded and goal-driven settings. To fill this gap, we introduce a novel benchmark named Video-based long-form Causal Reasoning (VCRBench). We create VCRBench using procedural videos of simple everyday activities, where the steps are deliberately shuffled with each clip capturing a key causal event, to test whether LVLMs can identify, reason about, and correctly sequence the events needed to accomplish a specific goal. Moreover, the benchmark is carefully designed to prevent LVLMs from exploiting linguistic shortcuts, as seen in multiple-choice or binary QA formats, while also avoiding the challenges associated with evaluating open-ended QA. Our evaluation of state-of-the-art LVLMs on VCRBench suggests that these models struggle with video-based long-form causal reasoning, primarily due to their difficulty in modeling long-range causal dependencies directly from visual observations. As a simple step toward enabling such capabilities, we propose Recognition-Reasoning Decomposition (RRD), a modular approach that breaks video-based causal reasoning into two sub-tasks of video recognition and causal reasoning. Our experiments on VCRBench show that RRD significantly boosts accuracy on VCRBench, with gains of up to 25.2%. Finally, our thorough analysis reveals interesting insights, for instance, that LVLMs primarily rely on language knowledge for complex video-based long-form causal reasoning tasks.

Procedural planning, which entails decomposing a high-level goal into a sequence of temporally ordered steps, is an important yet intricate task for machines. It involves integrating common-sense knowledge to reason about complex contextualized situations that are often counterfactual, e.g. "scheduling a doctor's appointment without a phone". While current approaches show encouraging results using large language models (LLMs), they are hindered by drawbacks such as costly API calls and reproducibility issues. In this paper, we advocate planning using smaller language models. We present PlaSma, a novel two-pronged approach to endow small language models with procedural knowledge and (counterfactual) planning capabilities. More concretely, we develop symbolic procedural knowledge distillation to enhance the implicit knowledge in small language models and an inference-time algorithm to facilitate more structured and accurate reasoning. In addition, we introduce a novel task, Counterfactual Planning, that requires a revision of a plan to cope with a counterfactual situation. In both the original and counterfactual setting, we show that orders-of-magnitude smaller models (770M-11B parameters) can compete and often surpass their larger teacher models' capabilities.

Fairness for machine learning predictions is widely required in practice for legal, ethical, and societal reasons. Existing work typically focuses on settings without unobserved confounding, even though unobserved confounding can lead to severe violations of causal fairness and, thus, unfair predictions. In this work, we analyze the sensitivity of causal fairness to unobserved confounding. Our contributions are three-fold. First, we derive bounds for causal fairness metrics under different sources of unobserved confounding. This enables practitioners to examine the sensitivity of their machine learning models to unobserved confounding in fairness-critical applications. Second, we propose a novel neural framework for learning fair predictions, which allows us to offer worst-case guarantees of the extent to which causal fairness can be violated due to unobserved confounding. Third, we demonstrate the effectiveness of our framework in a series of experiments, including a real-world case study about predicting prison sentences. To the best of our knowledge, ours is the first work to study causal fairness under unobserved confounding. To this end, our work is of direct practical value as a refutation strategy to ensure the fairness of predictions in high-stakes applications.

We study experiment design for unique identification of the causal graph of a simple SCM, where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skeleton of causal graphs with cycles may not be possible from merely the observational distribution. Furthermore, intervening on a variable in such graphs does not necessarily lead to orienting all the edges incident to it. In this paper, we propose an experiment design approach that can learn both cyclic and acyclic graphs and hence, unifies the task of experiment design for both types of graphs. We provide a lower bound on the number of experiments required to guarantee the unique identification of the causal graph in the worst case, showing that the proposed approach is order-optimal in terms of the number of experiments up to an additive logarithmic term. Moreover, we extend our result to the setting where the size of each experiment is bounded by a constant. For this case, we show that our approach is optimal in terms of the size of the largest experiment required for uniquely identifying the causal graph in the worst case.

An agent trained within a closed system can master any desired capability, as long as the following three conditions hold: (a) it receives sufficiently informative and aligned feedback, (b) its coverage of experience/data is broad enough, and (c) it has sufficient capacity and resource. In this position paper, we justify these conditions, and consider what limitations arise from (a) and (b) in closed systems, when assuming that (c) is not a bottleneck. Considering the special case of agents with matching input and output spaces (namely, language), we argue that such pure recursive self-improvement, dubbed "Socratic learning", can boost performance vastly beyond what is present in its initial data or knowledge, and is only limited by time, as well as gradual misalignment concerns. Furthermore, we propose a constructive framework to implement it, based on the notion of language games.

Controllable text generation systems often leverage control codes to direct various properties of the output like style and length. Inspired by recent work on causal inference for NLP, this paper reveals a previously overlooked flaw in these control code-based conditional text generation algorithms. Spurious correlations in the training data can lead models to incorrectly rely on parts of the input other than the control code for attribute selection, significantly undermining downstream generation quality and controllability. We demonstrate the severity of this issue with a series of case studies and then propose two simple techniques to reduce these correlations in training sets. The first technique is based on resampling the data according to an example's propensity towards each linguistic attribute (IPS). The second produces multiple counterfactual versions of each example and then uses an additional feedback mechanism to remove noisy examples (feedback aware self-training, FAST). We evaluate on 3 tasks -- news headline, meta review, and search ads generation -- and demonstrate that FAST can significantly improve the controllability and language quality of generated outputs when compared to state-of-the-art controllable text generation approaches.

Large amounts of training data are one of the major reasons for the high performance of state-of-the-art NLP models. But what exactly in the training data causes a model to make a certain prediction? We seek to answer this question by providing a language for describing how training data influences predictions, through a causal framework. Importantly, our framework bypasses the need to retrain expensive models and allows us to estimate causal effects based on observational data alone. Addressing the problem of extracting factual knowledge from pretrained language models (PLMs), we focus on simple data statistics such as co-occurrence counts and show that these statistics do influence the predictions of PLMs, suggesting that such models rely on shallow heuristics. Our causal framework and our results demonstrate the importance of studying datasets and the benefits of causality for understanding NLP models.

Understanding objects is a central building block of artificial intelligence, especially for embodied AI. Even though object recognition excels with deep learning, current machines still struggle to learn higher-level knowledge, e.g., what attributes an object has, and what can we do with an object. In this work, we propose a challenging Object Concept Learning (OCL) task to push the envelope of object understanding. It requires machines to reason out object affordances and simultaneously give the reason: what attributes make an object possesses these affordances. To support OCL, we build a densely annotated knowledge base including extensive labels for three levels of object concept (category, attribute, affordance), and the causal relations of three levels. By analyzing the causal structure of OCL, we present a baseline, Object Concept Reasoning Network (OCRN). It leverages causal intervention and concept instantiation to infer the three levels following their causal relations. In experiments, OCRN effectively infers the object knowledge while following the causalities well. Our data and code are available at https://mvig-rhos.com/ocl.

We study the problem of procedure planning in instructional videos, which aims to make a goal-oriented sequence of action steps given partial visual state observations. The motivation of this problem is to learn a structured and plannable state and action space. Recent works succeeded in sequence modeling of steps with only sequence-level annotations accessible during training, which overlooked the roles of states in the procedures. In this work, we point out that State CHangEs MAtter (SCHEMA) for procedure planning in instructional videos. We aim to establish a more structured state space by investigating the causal relations between steps and states in procedures. Specifically, we explicitly represent each step as state changes and track the state changes in procedures. For step representation, we leveraged the commonsense knowledge in large language models (LLMs) to describe the state changes of steps via our designed chain-of-thought prompting. For state change tracking, we align visual state observations with language state descriptions via cross-modal contrastive learning, and explicitly model the intermediate states of the procedure using LLM-generated state descriptions. Experiments on CrossTask, COIN, and NIV benchmark datasets demonstrate that our proposed SCHEMA model achieves state-of-the-art performance and obtains explainable visualizations.

Understanding the abilities of LLMs to reason about natural language plans, such as instructional text and recipes, is critical to reliably using them in decision-making systems. A fundamental aspect of plans is the temporal order in which their steps needs to be executed, which reflects the underlying causal dependencies between them. We introduce CaT-Bench, a benchmark of Step Order Prediction questions, which test whether a step must necessarily occur before or after another in cooking recipe plans. We use this to evaluate how well frontier LLMs understand causal and temporal dependencies. We find that SOTA LLMs are underwhelming (best zero-shot is only 0.59 in F1), and are biased towards predicting dependence more often, perhaps relying on temporal order of steps as a heuristic. While prompting for explanations and using few-shot examples improve performance, the best F1 result is only 0.73. Further, human evaluation of explanations along with answer correctness show that, on average, humans do not agree with model reasoning. Surprisingly, we also find that explaining after answering leads to better performance than normal chain-of-thought prompting, and LLM answers are not consistent across questions about the same step pairs. Overall, results show that LLMs' ability to detect dependence between steps has significant room for improvement.

Inspired by human conscious planning, we propose Skipper, a model-based reinforcement learning framework utilizing spatio-temporal abstractions to generalize better in novel situations. It automatically decomposes the given task into smaller, more manageable subtasks, and thus enables sparse decision-making and focused computation on the relevant parts of the environment. The decomposition relies on the extraction of an abstracted proxy problem represented as a directed graph, in which vertices and edges are learned end-to-end from hindsight. Our theoretical analyses provide performance guarantees under appropriate assumptions and establish where our approach is expected to be helpful. Generalization-focused experiments validate Skipper's significant advantage in zero-shot generalization, compared to some existing state-of-the-art hierarchical planning methods.

The trustworthiness of machine learning has emerged as a critical topic in the field, encompassing various applications and research areas such as robustness, security, interpretability, and fairness. The last decade saw the development of numerous methods addressing these challenges. In this survey, we systematically review these advancements from a data-centric perspective, highlighting the shortcomings of traditional empirical risk minimization (ERM) training in handling challenges posed by the data. Interestingly, we observe a convergence of these methods, despite being developed independently across trustworthy machine learning subfields. Pearl's hierarchy of causality offers a unifying framework for these techniques. Accordingly, this survey presents the background of trustworthy machine learning development using a unified set of concepts, connects this language to Pearl's causal hierarchy, and finally discusses methods explicitly inspired by causality literature. We provide a unified language with mathematical vocabulary to link these methods across robustness, adversarial robustness, interpretability, and fairness, fostering a more cohesive understanding of the field. Further, we explore the trustworthiness of large pretrained models. After summarizing dominant techniques like fine-tuning, parameter-efficient fine-tuning, prompting, and reinforcement learning with human feedback, we draw connections between them and the standard ERM. This connection allows us to build upon the principled understanding of trustworthy methods, extending it to these new techniques in large pretrained models, paving the way for future methods. Existing methods under this perspective are also reviewed. Lastly, we offer a brief summary of the applications of these methods and discuss potential future aspects related to our survey. For more information, please visit http://trustai.one.

Although contemporary large language models (LMs) demonstrate impressive question-answering capabilities, their answers are typically the product of a single call to the model. This entails an unwelcome degree of opacity and compromises performance, especially on problems that are inherently multi-step. To address these limitations, we show how LMs can be made to perform faithful multi-step reasoning via a process whose causal structure mirrors the underlying logical structure of the problem. Our approach works by chaining together reasoning steps, where each step results from calls to two fine-tuned LMs, one for selection and one for inference, to produce a valid reasoning trace. Our method carries out a beam search through the space of reasoning traces to improve reasoning quality. We demonstrate the effectiveness of our model on multi-step logical deduction and scientific question-answering, showing that it outperforms baselines on final answer accuracy, and generates humanly interpretable reasoning traces whose validity can be checked by the user.

Causal representation learning aims to unveil latent high-level causal representations from observed low-level data. One of its primary tasks is to provide reliable assurance of identifying these latent causal models, known as identifiability. A recent breakthrough explores identifiability by leveraging the change of causal influences among latent causal variables across multiple environments liu2022identifying. However, this progress rests on the assumption that the causal relationships among latent causal variables adhere strictly to linear Gaussian models. In this paper, we extend the scope of latent causal models to involve nonlinear causal relationships, represented by polynomial models, and general noise distributions conforming to the exponential family. Additionally, we investigate the necessity of imposing changes on all causal parameters and present partial identifiability results when part of them remains unchanged. Further, we propose a novel empirical estimation method, grounded in our theoretical finding, that enables learning consistent latent causal representations. Our experimental results, obtained from both synthetic and real-world data, validate our theoretical contributions concerning identifiability and consistency.

This paper investigates Who's Harry Potter (WHP), a pioneering yet insufficiently understood method for LLM unlearning. We explore it in two steps. First, we introduce a new task of LLM targeted unlearning, where given an unlearning target (e.g., a person) and some unlearning documents, we aim to unlearn only the information about the target, rather than everything in the unlearning documents. We further argue that a successful unlearning should satisfy criteria such as not outputting gibberish, not fabricating facts about the unlearning target, and not releasing factual information under jailbreak attacks. Second, we construct a causal intervention framework for targeted unlearning, where the knowledge of the unlearning target is modeled as a confounder between LLM input and output, and the unlearning process as a deconfounding process. This framework justifies and extends WHP, deriving a simple unlearning algorithm that includes WHP as a special case. Experiments on existing and new datasets show that our approach, without explicitly optimizing for the aforementioned criteria, achieves competitive performance in all of them. Our code is available at https://github.com/UCSB-NLP-Chang/causal_unlearn.git.

Unfairness in mortgage lending has created generational inequality among racial and ethnic groups in the US. Many studies address this problem, but most existing work focuses on correlation-based techniques. In our work, we use the framework of counterfactual fairness to train fair machine learning models. We propose a new causal graph for the variables available in the Home Mortgage Disclosure Act (HMDA) data. We use a matching-based approach instead of the latent variable modeling approach, because the former approach does not rely on any modeling assumptions. Furthermore, matching provides us with counterfactual pairs in which the race variable is isolated. We first demonstrate the unfairness in mortgage approval and interest rates between African-American and non-Hispanic White sub-populations. Then, we show that having balanced data using matching does not guarantee perfect counterfactual fairness of the machine learning models.

Interpretability provides a toolset for understanding how and why neural networks behave in certain ways. However, there is little unity in the field: most studies employ ad-hoc evaluations and do not share theoretical foundations, making it difficult to measure progress and compare the pros and cons of different techniques. Furthermore, while mechanistic understanding is frequently discussed, the basic causal units underlying these mechanisms are often not explicitly defined. In this paper, we propose a perspective on interpretability research grounded in causal mediation analysis. Specifically, we describe the history and current state of interpretability taxonomized according to the types of causal units (mediators) employed, as well as methods used to search over mediators. We discuss the pros and cons of each mediator, providing insights as to when particular kinds of mediators and search methods are most appropriate depending on the goals of a given study. We argue that this framing yields a more cohesive narrative of the field, as well as actionable insights for future work. Specifically, we recommend a focus on discovering new mediators with better trade-offs between human-interpretability and compute-efficiency, and which can uncover more sophisticated abstractions from neural networks than the primarily linear mediators employed in current work. We also argue for more standardized evaluations that enable principled comparisons across mediator types, such that we can better understand when particular causal units are better suited to particular use cases.

We propose a new class of online learning algorithms, generalized implicit Follow-The-Regularized-Leader (FTRL), that expands the scope of FTRL framework. Generalized implicit FTRL can recover known algorithms, as FTRL with linearized losses and implicit FTRL, and it allows the design of new update rules, as extensions of aProx and Mirror-Prox to FTRL. Our theory is constructive in the sense that it provides a simple unifying framework to design updates that directly improve the worst-case upper bound on the regret. The key idea is substituting the linearization of the losses with a Fenchel-Young inequality. We show the flexibility of the framework by proving that some known algorithms, like the Mirror-Prox updates, are instantiations of the generalized implicit FTRL. Finally, the new framework allows us to recover the temporal variation bound of implicit OMD, with the same computational complexity.

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods.

The principle of independent causal mechanisms (ICM) states that generative processes of real world data consist of independent modules which do not influence or inform each other. While this idea has led to fruitful developments in the field of causal inference, it is not widely-known in the NLP community. In this work, we argue that the causal direction of the data collection process bears nontrivial implications that can explain a number of published NLP findings, such as differences in semi-supervised learning (SSL) and domain adaptation (DA) performance across different settings. We categorize common NLP tasks according to their causal direction and empirically assay the validity of the ICM principle for text data using minimum description length. We conduct an extensive meta-analysis of over 100 published SSL and 30 DA studies, and find that the results are consistent with our expectations based on causal insights. This work presents the first attempt to analyze the ICM principle in NLP, and provides constructive suggestions for future modeling choices. Code available at https://github.com/zhijing-jin/icm4nlp

Large Language Models (LLMs) have emerged as powerful sources of evidence for linguists seeking to develop theories of syntax. In this paper, we argue that causal interpretability methods, applied to LLMs, can greatly enhance the value of such evidence by helping us characterize the abstract mechanisms that LLMs learn to use. Our empirical focus is a set of English filler-gap dependency constructions (e.g., questions, relative clauses). Linguistic theories largely agree that these constructions share many properties. Using experiments based in Distributed Interchange Interventions, we show that LLMs converge on similar abstract analyses of these constructions. These analyses also reveal previously overlooked factors -- relating to frequency, filler type, and surrounding context -- that could motivate changes to standard linguistic theory. Overall, these results suggest that mechanistic, internal analyses of LLMs can push linguistic theory forward.

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.

Programming with Generative AI (GenAI) models is a type of Neurosymbolic programming and has seen tremendous adoption across many domains. However, leveraging GenAI models in code today can be complex, counter-intuitive and often require specialized frameworks, leading to increased complexity. This is because it is currently unclear as to the right abstractions through which we should marry GenAI models with the nature of traditional programming code constructs. In this paper, we introduce a set of novel abstractions to help bridge the gap between Neuro- and symbolic programming. We introduce Meaning, a new specialized type that represents the underlying semantic value of traditional types (e.g., string). We make the case that GenAI models, LLMs in particular, should be reasoned as a meaning-type wrapped code construct at the language level. We formulate the problem of translation between meaning and traditional types and propose Automatic Meaning-Type Transformation (A-MTT), a runtime feature that abstracts this translation away from the developers by automatically converting between M eaning and types at the interface of LLM invocation. Leveraging this new set of code constructs and OTT, we demonstrate example implementation of neurosymbolic programs that seamlessly utilizes LLMs to solve problems in place of potentially complex traditional programming logic.

Causal explanations of the predictions of NLP systems are essential to ensure safety and establish trust. Yet, existing methods often fall short of explaining model predictions effectively or efficiently and are often model-specific. In this paper, we address model-agnostic explanations, proposing two approaches for counterfactual (CF) approximation. The first approach is CF generation, where a large language model (LLM) is prompted to change a specific text concept while keeping confounding concepts unchanged. While this approach is demonstrated to be very effective, applying LLM at inference-time is costly. We hence present a second approach based on matching, and propose a method that is guided by an LLM at training-time and learns a dedicated embedding space. This space is faithful to a given causal graph and effectively serves to identify matches that approximate CFs. After showing theoretically that approximating CFs is required in order to construct faithful explanations, we benchmark our approaches and explain several models, including LLMs with billions of parameters. Our empirical results demonstrate the excellent performance of CF generation models as model-agnostic explainers. Moreover, our matching approach, which requires far less test-time resources, also provides effective explanations, surpassing many baselines. We also find that Top-K techniques universally improve every tested method. Finally, we showcase the potential of LLMs in constructing new benchmarks for model explanation and subsequently validate our conclusions. Our work illuminates new pathways for efficient and accurate approaches to interpreting NLP systems.

Large Language Models (LLMs) are increasingly used for boosting organizational efficiency and automating tasks. While not originally designed for complex cognitive processes, recent efforts have further extended to employ LLMs in activities such as reasoning, planning, and decision-making. In business processes, such abilities could be invaluable for leveraging on the massive corpora LLMs have been trained on for gaining deep understanding of such processes. In this work, we plant the seeds for the development of a benchmark to assess the ability of LLMs to reason about causal and process perspectives of business operations. We refer to this view as Causally-augmented Business Processes (BP^C). The core of the benchmark comprises a set of BP^C related situations, a set of questions about these situations, and a set of deductive rules employed to systematically resolve the ground truth answers to these questions. Also with the power of LLMs, the seed is then instantiated into a larger-scale set of domain-specific situations and questions. Reasoning on BP^C is of crucial importance for process interventions and process improvement. Our benchmark could be used in one of two possible modalities: testing the performance of any target LLM and training an LLM to advance its capability to reason about BP^C.

We describe recent research on the use of actual causality in the definition of responsibility scores as explanations for query answers in databases, and for outcomes from classification models in machine learning. In the case of databases, useful connections with database repairs are illustrated and exploited. Repairs are also used to give a quantitative measure of the consistency of a database. For classification models, the responsibility score is properly extended and illustrated. The efficient computation of Shap-score is also analyzed and discussed. The emphasis is placed on work done by the author and collaborators.

Large language models (LLMs) have been shown to perform better when asked to reason step-by-step before answering a question. However, it is unclear to what degree the model's final answer is faithful to the stated reasoning steps. In this paper, we perform a causal mediation analysis on twelve LLMs to examine how intermediate reasoning steps generated by the LLM influence the final outcome and find that LLMs do not reliably use their intermediate reasoning steps when generating an answer. To address this issue, we introduce FRODO, a framework to tailor small-sized LMs to generate correct reasoning steps and robustly reason over these steps. FRODO consists of an inference module that learns to generate correct reasoning steps using an implicit causal reward function and a reasoning module that learns to faithfully reason over these intermediate inferences using a counterfactual and causal preference objective. Our experiments show that FRODO significantly outperforms four competitive baselines. Furthermore, FRODO improves the robustness and generalization ability of the reasoning LM, yielding higher performance on out-of-distribution test sets. Finally, we find that FRODO's rationales are more faithful to its final answer predictions than standard supervised fine-tuning.

Convergent Cross Mapping (CCM) is a powerful method for detecting causality in coupled nonlinear dynamical systems, providing a model-free approach to capture dynamic causal interactions. Partial Cross Mapping (PCM) was introduced as an extension of CCM to address indirect causality in three-variable systems by comparing cross-mapping quality between direct cause-effect mapping and indirect mapping through an intermediate conditioning variable. However, PCM remains limited to univariate delay embeddings in its cross-mapping processes. In this work, we extend PCM to the multivariate setting, introducing multiPCM, which leverages multivariate embeddings to more effectively distinguish indirect causal relationships. We further propose a multivariate cross-mapping framework (MXMap) for causal discovery in dynamical systems. This two-phase framework combines (1) pairwise CCM tests to establish an initial causal graph and (2) multiPCM to refine the graph by pruning indirect causal connections. Through experiments on simulated data and the ERA5 Reanalysis weather dataset, we demonstrate the effectiveness of MXMap. Additionally, MXMap is compared against several baseline methods, showing advantages in accuracy and causal graph refinement.

Understanding predictions made by deep neural networks is notoriously difficult, but also crucial to their dissemination. As all machine learning based methods, they are as good as their training data, and can also capture unwanted biases. While there are tools that can help understand whether such biases exist, they do not distinguish between correlation and causation, and might be ill-suited for text-based models and for reasoning about high level language concepts. A key problem of estimating the causal effect of a concept of interest on a given model is that this estimation requires the generation of counterfactual examples, which is challenging with existing generation technology. To bridge that gap, we propose CausaLM, a framework for producing causal model explanations using counterfactual language representation models. Our approach is based on fine-tuning of deep contextualized embedding models with auxiliary adversarial tasks derived from the causal graph of the problem. Concretely, we show that by carefully choosing auxiliary adversarial pre-training tasks, language representation models such as BERT can effectively learn a counterfactual representation for a given concept of interest, and be used to estimate its true causal effect on model performance. A byproduct of our method is a language representation model that is unaffected by the tested concept, which can be useful in mitigating unwanted bias ingrained in the data.

Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, or do they memorize training data? To investigate this question, we use arithmetic reasoning as a representative task. Using causal analysis, we identify a subset of the model (a circuit) that explains most of the model's behavior for basic arithmetic logic and examine its functionality. By zooming in on the level of individual circuit neurons, we discover a sparse set of important neurons that implement simple heuristics. Each heuristic identifies a numerical input pattern and outputs corresponding answers. We hypothesize that the combination of these heuristic neurons is the mechanism used to produce correct arithmetic answers. To test this, we categorize each neuron into several heuristic types-such as neurons that activate when an operand falls within a certain range-and find that the unordered combination of these heuristic types is the mechanism that explains most of the model's accuracy on arithmetic prompts. Finally, we demonstrate that this mechanism appears as the main source of arithmetic accuracy early in training. Overall, our experimental results across several LLMs show that LLMs perform arithmetic using neither robust algorithms nor memorization; rather, they rely on a "bag of heuristics".

Fair machine learning aims to prevent discrimination against individuals or sub-populations based on sensitive attributes such as gender and race. In recent years, causal inference methods have been increasingly used in fair machine learning to measure unfairness by causal effects. However, current methods assume that the true causal graph is given, which is often not true in real-world applications. To address this limitation, this paper proposes a framework for achieving causal fairness based on the notion of interventions when the true causal graph is partially known. The proposed approach involves modeling fair prediction using a Partially Directed Acyclic Graph (PDAG), specifically, a class of causal DAGs that can be learned from observational data combined with domain knowledge. The PDAG is used to measure causal fairness, and a constrained optimization problem is formulated to balance between fairness and accuracy. Results on both simulated and real-world datasets demonstrate the effectiveness of this method.

In Causal Bayesian Optimization (CBO), an agent intervenes on an unknown structural causal model to maximize a downstream reward variable. In this paper, we consider the generalization where other agents or external events also intervene on the system, which is key for enabling adaptiveness to non-stationarities such as weather changes, market forces, or adversaries. We formalize this generalization of CBO as Adversarial Causal Bayesian Optimization (ACBO) and introduce the first algorithm for ACBO with bounded regret: Causal Bayesian Optimization with Multiplicative Weights (CBO-MW). Our approach combines a classical online learning strategy with causal modeling of the rewards. To achieve this, it computes optimistic counterfactual reward estimates by propagating uncertainty through the causal graph. We derive regret bounds for CBO-MW that naturally depend on graph-related quantities. We further propose a scalable implementation for the case of combinatorial interventions and submodular rewards. Empirically, CBO-MW outperforms non-causal and non-adversarial Bayesian optimization methods on synthetic environments and environments based on real-word data. Our experiments include a realistic demonstration of how CBO-MW can be used to learn users' demand patterns in a shared mobility system and reposition vehicles in strategic areas.

A major barrier to deploying current machine learning models lies in their non-reliability to dataset shifts. To resolve this problem, most existing studies attempted to transfer stable information to unseen environments. Particularly, independent causal mechanisms-based methods proposed to remove mutable causal mechanisms via the do-operator. Compared to previous methods, the obtained stable predictors are more effective in identifying stable information. However, a key question remains: which subset of this whole stable information should the model transfer, in order to achieve optimal generalization ability? To answer this question, we present a comprehensive minimax analysis from a causal perspective. Specifically, we first provide a graphical condition for the whole stable set to be optimal. When this condition fails, we surprisingly find with an example that this whole stable set, although can fully exploit stable information, is not the optimal one to transfer. To identify the optimal subset under this case, we propose to estimate the worst-case risk with a novel optimization scheme over the intervention functions on mutable causal mechanisms. We then propose an efficient algorithm to search for the subset with minimal worst-case risk, based on a newly defined equivalence relation between stable subsets. Compared to the exponential cost of exhaustively searching over all subsets, our searching strategy enjoys a polynomial complexity. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.

The origin of adversarial examples is still inexplicable in research fields, and it arouses arguments from various viewpoints, albeit comprehensive investigations. In this paper, we propose a way of delving into the unexpected vulnerability in adversarially trained networks from a causal perspective, namely adversarial instrumental variable (IV) regression. By deploying it, we estimate the causal relation of adversarial prediction under an unbiased environment dissociated from unknown confounders. Our approach aims to demystify inherent causal features on adversarial examples by leveraging a zero-sum optimization game between a casual feature estimator (i.e., hypothesis model) and worst-case counterfactuals (i.e., test function) disturbing to find causal features. Through extensive analyses, we demonstrate that the estimated causal features are highly related to the correct prediction for adversarial robustness, and the counterfactuals exhibit extreme features significantly deviating from the correct prediction. In addition, we present how to effectively inoculate CAusal FEatures (CAFE) into defense networks for improving adversarial robustness.

Current Reinforcement Learning (RL) methods often suffer from sample-inefficiency, resulting from blind exploration strategies that neglect causal relationships among states, actions, and rewards. Although recent causal approaches aim to address this problem, they lack grounded modeling of reward-guided causal understanding of states and actions for goal-orientation, thus impairing learning efficiency. To tackle this issue, we propose a novel method named Causal Information Prioritization (CIP) that improves sample efficiency by leveraging factored MDPs to infer causal relationships between different dimensions of states and actions with respect to rewards, enabling the prioritization of causal information. Specifically, CIP identifies and leverages causal relationships between states and rewards to execute counterfactual data augmentation to prioritize high-impact state features under the causal understanding of the environments. Moreover, CIP integrates a causality-aware empowerment learning objective, which significantly enhances the agent's execution of reward-guided actions for more efficient exploration in complex environments. To fully assess the effectiveness of CIP, we conduct extensive experiments across 39 tasks in 5 diverse continuous control environments, encompassing both locomotion and manipulation skills learning with pixel-based and sparse reward settings. Experimental results demonstrate that CIP consistently outperforms existing RL methods across a wide range of scenarios.

We introduce Explanatory Learning (EL), a framework to let machines use existing knowledge buried in symbolic sequences -- e.g. explanations written in hieroglyphic -- by autonomously learning to interpret them. In EL, the burden of interpreting symbols is not left to humans or rigid human-coded compilers, as done in Program Synthesis. Rather, EL calls for a learned interpreter, built upon a limited collection of symbolic sequences paired with observations of several phenomena. This interpreter can be used to make predictions on a novel phenomenon given its explanation, and even to find that explanation using only a handful of observations, like human scientists do. We formulate the EL problem as a simple binary classification task, so that common end-to-end approaches aligned with the dominant empiricist view of machine learning could, in principle, solve it. To these models, we oppose Critical Rationalist Networks (CRNs), which instead embrace a rationalist view on the acquisition of knowledge. CRNs express several desired properties by construction, they are truly explainable, can adjust their processing at test-time for harder inferences, and can offer strong confidence guarantees on their predictions. As a final contribution, we introduce Odeen, a basic EL environment that simulates a small flatland-style universe full of phenomena to explain. Using Odeen as a testbed, we show how CRNs outperform empiricist end-to-end approaches of similar size and architecture (Transformers) in discovering explanations for novel phenomena.

The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often fall short on inductive reasoning, despite achieving impressive success on research benchmarks. In this work, we conduct a systematic study of the inductive reasoning capabilities of LMs through iterative hypothesis refinement, a technique that more closely mirrors the human inductive process than standard input-output prompting. Iterative hypothesis refinement employs a three-step process: proposing, selecting, and refining hypotheses in the form of textual rules. By examining the intermediate rules, we observe that LMs are phenomenal hypothesis proposers (i.e., generating candidate rules), and when coupled with a (task-specific) symbolic interpreter that is able to systematically filter the proposed set of rules, this hybrid approach achieves strong results across inductive reasoning benchmarks that require inducing causal relations, language-like instructions, and symbolic concepts. However, they also behave as puzzling inductive reasoners, showing notable performance gaps between rule induction (i.e., identifying plausible rules) and rule application (i.e., applying proposed rules to instances), suggesting that LMs are proposing hypotheses without being able to actually apply the rules. Through empirical and human analyses, we further reveal several discrepancies between the inductive reasoning processes of LMs and humans, shedding light on both the potentials and limitations of using LMs in inductive reasoning tasks.

We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of smaller parts. However, neither their theoretical justification nor their implementation reflects this modularity. We show how to conceptualise and analyse such inference algorithms as manipulating intermediate representations of probabilistic programs using higher-order functions and inductive types, and their denotational semantics. Semantic accounts of continuous distributions use measurable spaces. However, our use of higher-order functions presents a substantial technical difficulty: it is impossible to define a measurable space structure over the collection of measurable functions between arbitrary measurable spaces that is compatible with standard operations on those functions, such as function application. We overcome this difficulty using quasi-Borel spaces, a recently proposed mathematical structure that supports both function spaces and continuous distributions. We define a class of semantic structures for representing probabilistic programs, and semantic validity criteria for transformations of these representations in terms of distribution preservation. We develop a collection of building blocks for composing representations. We use these building blocks to validate common inference algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo. To emphasize the connection between the semantic manipulation and its traditional measure theoretic origins, we use Kock's synthetic measure theory. We demonstrate its usefulness by proving a quasi-Borel counterpart to the Metropolis-Hastings-Green theorem.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Discovering causal structures from data is a challenging inference problem of fundamental importance in all areas of science. The appealing properties of neural networks have recently led to a surge of interest in differentiable neural network-based methods for learning causal structures from data. So far, differentiable causal discovery has focused on static datasets of observational or fixed interventional origin. In this work, we introduce an active intervention targeting (AIT) method which enables a quick identification of the underlying causal structure of the data-generating process. Our method significantly reduces the required number of interactions compared with random intervention targeting and is applicable for both discrete and continuous optimization formulations of learning the underlying directed acyclic graph (DAG) from data. We examine the proposed method across multiple frameworks in a wide range of settings and demonstrate superior performance on multiple benchmarks from simulated to real-world data.

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, CounterMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that CounterMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs' counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

We reveal and address the frequently overlooked yet important issue of disguised procedural unfairness, namely, the potentially inadvertent alterations on the behavior of neutral (i.e., not problematic) aspects of data generating process, and/or the lack of procedural assurance of the greatest benefit of the least advantaged individuals. Inspired by John Rawls's advocacy for pure procedural justice, we view automated decision-making as a microcosm of social institutions, and consider how the data generating process itself can satisfy the requirements of procedural fairness. We propose a framework that decouples the objectionable data generating components from the neutral ones by utilizing reference points and the associated value instantiation rule. Our findings highlight the necessity of preventing disguised procedural unfairness, drawing attention not only to the objectionable data generating components that we aim to mitigate, but also more importantly, to the neutral components that we intend to keep unaffected.

Recent approaches to empathetic response generation incorporate emotion causalities to enhance comprehension of both the user's feelings and experiences. However, these approaches suffer from two critical issues. First, they only consider causalities between the user's emotion and the user's experiences, and ignore those between the user's experiences. Second, they neglect interdependence among causalities and reason them independently. To solve the above problems, we expect to reason all plausible causalities interdependently and simultaneously, given the user's emotion, dialogue history, and future dialogue content. Then, we infuse these causalities into response generation for empathetic responses. Specifically, we design a new model, i.e., the Conditional Variational Graph Auto-Encoder (CVGAE), for the causality reasoning, and adopt a multi-source attention mechanism in the decoder for the causality infusion. We name the whole framework as CARE, abbreviated for CAusality Reasoning for Empathetic conversation. Experimental results indicate that our method achieves state-of-the-art performance.

Interpretability in machine learning (ML) is crucial for high stakes decisions and troubleshooting. In this work, we provide fundamental principles for interpretable ML, and dispel common misunderstandings that dilute the importance of this crucial topic. We also identify 10 technical challenge areas in interpretable machine learning and provide history and background on each problem. Some of these problems are classically important, and some are recent problems that have arisen in the last few years. These problems are: (1) Optimizing sparse logical models such as decision trees; (2) Optimization of scoring systems; (3) Placing constraints into generalized additive models to encourage sparsity and better interpretability; (4) Modern case-based reasoning, including neural networks and matching for causal inference; (5) Complete supervised disentanglement of neural networks; (6) Complete or even partial unsupervised disentanglement of neural networks; (7) Dimensionality reduction for data visualization; (8) Machine learning models that can incorporate physics and other generative or causal constraints; (9) Characterization of the "Rashomon set" of good models; and (10) Interpretable reinforcement learning. This survey is suitable as a starting point for statisticians and computer scientists interested in working in interpretable machine learning.

Building future wireless systems that support services like digital twins (DTs) is challenging to achieve through advances to conventional technologies like meta-surfaces. While artificial intelligence (AI)-native networks promise to overcome some limitations of wireless technologies, developments still rely on AI tools like neural networks. Such tools struggle to cope with the non-trivial challenges of the network environment and the growing demands of emerging use cases. In this paper, we revisit the concept of AI-native wireless systems, equipping them with the common sense necessary to transform them into artificial general intelligence (AGI)-native systems. These systems acquire common sense by exploiting different cognitive abilities such as perception, analogy, and reasoning, that enable them to generalize and deal with unforeseen scenarios. Towards developing the components of such a system, we start by showing how the perception module can be built through abstracting real-world elements into generalizable representations. These representations are then used to create a world model, founded on principles of causality and hyper-dimensional (HD) computing, that aligns with intuitive physics and enables analogical reasoning, that define common sense. Then, we explain how methods such as integrated information theory play a role in the proposed intent-driven and objective-driven planning methods that maneuver the AGI-native network to take actions. Next, we discuss how an AGI-native network can enable use cases related to human and autonomous agents: a) analogical reasoning for next-generation DTs, b) synchronized and resilient experiences for cognitive avatars, and c) brain-level metaverse experiences like holographic teleportation. Finally, we conclude with a set of recommendations to build AGI-native systems. Ultimately, we envision this paper as a roadmap for the beyond 6G era.

Large Language Models' success on text generation has also made them better at code generation and coding tasks. While a lot of work has demonstrated their remarkable performance on tasks such as code completion and editing, it is still unclear as to why. We help bridge this gap by exploring to what degree auto-regressive models understand the logical constructs of the underlying programs. We propose Counterfactual Analysis for Programming Concept Predicates (CACP) as a counterfactual testing framework to evaluate whether Large Code Models understand programming concepts. With only black-box access to the model, we use CACP to evaluate ten popular Large Code Models for four different programming concepts. Our findings suggest that current models lack understanding of concepts such as data flow and control flow.

Research community has witnessed substantial growth in the detection of mental health issues and their associated reasons from analysis of social media. We introduce a new dataset for Causal Analysis of Mental health issues in Social media posts (CAMS). Our contributions for causal analysis are two-fold: causal interpretation and causal categorization. We introduce an annotation schema for this task of causal analysis. We demonstrate the efficacy of our schema on two different datasets: (i) crawling and annotating 3155 Reddit posts and (ii) re-annotating the publicly available SDCNL dataset of 1896 instances for interpretable causal analysis. We further combine these into the CAMS dataset and make this resource publicly available along with associated source code: https://github.com/drmuskangarg/CAMS. We present experimental results of models learned from CAMS dataset and demonstrate that a classic Logistic Regression model outperforms the next best (CNN-LSTM) model by 4.9\% accuracy.

The correctness of computations remains a significant challenge in computer science, with traditional approaches relying on automated testing or formal verification. Self-testing/correcting programs introduce an alternative paradigm, allowing a program to verify and correct its own outputs via randomized reductions, a concept that previously required manual derivation. In this paper, we present Bitween, a method and tool for automated learning of randomized (self)-reductions and program properties in numerical programs. Bitween combines symbolic analysis and machine learning, with a surprising finding: polynomial-time linear regression, a basic optimization method, is not only sufficient but also highly effective for deriving complex randomized self-reductions and program invariants, often outperforming sophisticated mixed-integer linear programming solvers. We establish a theoretical framework for learning these reductions and introduce RSR-Bench, a benchmark suite for evaluating Bitween's capabilities on scientific and machine learning functions. Our empirical results show that Bitween surpasses state-of-the-art tools in scalability, stability, and sample efficiency when evaluated on nonlinear invariant benchmarks like NLA-DigBench. Bitween is open-source as a Python package and accessible via a web interface that supports C language programs.

Causal inference is a critical task across fields such as healthcare, economics, and the social sciences. While recent advances in machine learning, especially those based on the deep-learning architectures, have shown potential in estimating causal effects, existing approaches often fall short in handling complex causal structures and lack adaptability across various causal scenarios. In this paper, we present a novel transformer-based method for causal inference that overcomes these challenges. The core innovation of our model lies in its integration of causal Directed Acyclic Graphs (DAGs) directly into the attention mechanism, enabling it to accurately model the underlying causal structure. This allows for flexible estimation of both average treatment effects (ATE) and conditional average treatment effects (CATE). Extensive experiments on both synthetic and real-world datasets demonstrate that our approach surpasses existing methods in estimating causal effects across a wide range of scenarios. The flexibility and robustness of our model make it a valuable tool for researchers and practitioners tackling complex causal inference problems.

A multi-decade exploration into the theoretical foundations of artificial and natural general intelligence, which has been expressed in a series of books and papers and used to guide a series of practical and research-prototype software systems, is reviewed at a moderate level of detail. The review covers underlying philosophies (patternist philosophy of mind, foundational phenomenological and logical ontology), formalizations of the concept of intelligence, and a proposed high level architecture for AGI systems partly driven by these formalizations and philosophies. The implementation of specific cognitive processes such as logical reasoning, program learning, clustering and attention allocation in the context and language of this high level architecture is considered, as is the importance of a common (e.g. typed metagraph based) knowledge representation for enabling "cognitive synergy" between the various processes. The specifics of human-like cognitive architecture are presented as manifestations of these general principles, and key aspects of machine consciousness and machine ethics are also treated in this context. Lessons for practical implementation of advanced AGI in frameworks such as OpenCog Hyperon are briefly considered.

Interference is ubiquitous when conducting causal experiments over networks. Except for certain network structures, causal inference on the network in the presence of interference is difficult due to the entanglement between the treatment assignments and the interference levels. In this article, we conduct causal inference under interference on an observed, sparse but connected network, and we propose a novel design of experiments based on an independent set. Compared to conventional designs, the independent-set design focuses on an independent subset of data and controls their interference exposures through the assignments to the rest (auxiliary set). We provide a lower bound on the size of the independent set from a greedy algorithm , and justify the theoretical performance of estimators under the proposed design. Our approach is capable of estimating both spillover effects and treatment effects. We justify its superiority over conventional methods and illustrate the empirical performance through simulations.

We address whether neural models for Natural Language Inference (NLI) can learn the compositional interactions between lexical entailment and negation, using four methods: the behavioral evaluation methods of (1) challenge test sets and (2) systematic generalization tasks, and the structural evaluation methods of (3) probes and (4) interventions. To facilitate this holistic evaluation, we present Monotonicity NLI (MoNLI), a new naturalistic dataset focused on lexical entailment and negation. In our behavioral evaluations, we find that models trained on general-purpose NLI datasets fail systematically on MoNLI examples containing negation, but that MoNLI fine-tuning addresses this failure. In our structural evaluations, we look for evidence that our top-performing BERT-based model has learned to implement the monotonicity algorithm behind MoNLI. Probes yield evidence consistent with this conclusion, and our intervention experiments bolster this, showing that the causal dynamics of the model mirror the causal dynamics of this algorithm on subsets of MoNLI. This suggests that the BERT model at least partially embeds a theory of lexical entailment and negation at an algorithmic level.

The goal of video summarization is to automatically shorten videos such that it conveys the overall story without losing relevant information. In many application scenarios, improper video summarization can have a large impact. For example in forensics, the quality of the generated video summary will affect an investigator's judgment while in journalism it might yield undesired bias. Because of this, modeling explainability is a key concern. One of the best ways to address the explainability challenge is to uncover the causal relations that steer the process and lead to the result. Current machine learning-based video summarization algorithms learn optimal parameters but do not uncover causal relationships. Hence, they suffer from a relative lack of explainability. In this work, a Causal Explainer, dubbed Causalainer, is proposed to address this issue. Multiple meaningful random variables and their joint distributions are introduced to characterize the behaviors of key components in the problem of video summarization. In addition, helper distributions are introduced to enhance the effectiveness of model training. In visual-textual input scenarios, the extra input can decrease the model performance. A causal semantics extractor is designed to tackle this issue by effectively distilling the mutual information from the visual and textual inputs. Experimental results on commonly used benchmarks demonstrate that the proposed method achieves state-of-the-art performance while being more explainable.