Kolmogorov-Arnold causal generative models
| Authors | Alejandro Almodóvar et al. |
| Year | 2026 |
| Field | Machine Learning |
| arXiv | 2603.20184 |
| Download | |
| Categories | cs.LG, stat.ML |
Abstract
Causal generative models provide a principled framework for answering observational, interventional, and counterfactual queries from observational data. However, many deep causal models rely on highly expressive architectures with opaque mechanisms, limiting auditability in high-stakes domains. We propose KaCGM, a causal generative model for mixed-type tabular data where each structural equation is parameterized by a Kolmogorov--Arnold Network (KAN). This decomposition enables direct inspection of learned causal mechanisms, including symbolic approximations and visualization of parent--child relationships, while preserving query-agnostic generative semantics. We introduce a validation pipeline based on distributional matching and independence diagnostics of inferred exogenous variables, allowing assessment using observational data alone. Experiments on synthetic and semi-synthetic benchmarks show competitive performance against state-of-the-art methods. A real-world cardiovascular case study further demonstrates the extraction of simplified structural equations and interpretable causal effects. These results suggest that expressive causal generative modeling and functional transparency can be achieved jointly, supporting trustworthy deployment in tabular decision-making settings. Code: https://github.com/aalmodovares/kacgm
Engineering Breakdown
Plain English
This paper introduces KaCGM, a causal generative model that uses Kolmogorov-Arnold Networks (KANs) to parameterize structural equations for mixed-type tabular data. The key innovation is replacing opaque deep architectures with interpretable KAN-based mechanisms that allow direct inspection of learned causal relationships, symbolic approximations, and parent-child visualizations. The authors validate their approach using distributional matching and independence diagnostics on exogenous variables, enabling both high-stakes interpretability and generative query capabilities (observational, interventional, and counterfactual). This addresses a critical gap: existing causal models sacrifice auditability for expressiveness, but KaCGM preserves both.
Core Technical Contribution
The core novelty is parameterizing causal structural equations with Kolmogorov-Arnold Networks instead of standard neural networks, enabling transparent inspection of causal mechanisms without sacrificing generative modeling capability. KANs decompose functions into sums of univariate functions, making individual causal pathways human-readable and providing natural hooks for symbolic approximation and mechanistic visualization. This is fundamentally different from prior causal models (e.g., neural causal models, variational approaches) which treat learned relationships as black boxes and require post-hoc explanation techniques. The decomposition is query-agnostic, meaning the learned structure answers observational, interventional, and counterfactual questions from a single model without retraining.
How It Works
The system starts with observational tabular data containing mixed types (continuous, categorical, ordinal). It learns a Directed Acyclic Graph (DAG) structure representing causal relationships, then for each node, fits a KAN that maps parent variables to the child variable. Each KAN internally decomposes as a sum of univariate functions, which the system can directly visualize and approximate symbolically (e.g., extracting equations like 'y ≈ sin(x₁) + 0.5x₂'). The exogenous variables (noise terms) are inferred and validated using distributional matching (checking if inferred noise matches expected noise properties) and independence diagnostics (confirming exogenous variables are truly independent of each other). At inference time, the model answers causal queries by manipulating the learned DAG and KAN parameters: observational queries read observations directly, interventional queries clamp variables to specific values, and counterfactual queries condition on observed data then intervene.
Production Impact
For regulated industries (healthcare, finance, lending), this directly addresses compliance and auditability requirements: regulators can inspect the symbolic equations parameterizing each causal decision, not just request prediction explanations post-hoc. Engineers can validate that learned causal structures make domain sense before deployment—visualizing that a model learned 'credit score depends on income and payment history' rather than discovering spurious correlations. The trade-off is computational: KANs add overhead during both training (fitting univariate functions) and inference (evaluating compositions) compared to standard neural networks, though the paper doesn't specify latency impacts. Integration into existing ML pipelines is moderate friction: you need DAG structure learning (handled by causal discovery algorithms like GES or PC) and KAN implementations (now available in libraries), plus domain expertise to validate learned graphs before deployment.
Limitations and When Not to Use This
The paper assumes the causal DAG is acyclic and identifiable from observational data alone, assumptions that frequently fail in real systems with feedback loops or unobserved confounders. Scalability to high-dimensional data (thousands of features) is unclear—KANs are most effective for low-to-moderate dimensions, and the validation pipeline (distributional matching + independence diagnostics) requires substantial computational resources. The abstract doesn't detail how well the symbolic approximations preserve model accuracy, creating risk of interpretability theater where humans understand simplified equations that don't actually reflect model behavior. Performance on datasets with missing data, measurement error, or non-linear causal relationships beyond KAN expressiveness remains unvalidated.
Research Context
This work builds on two decades of causal graphical models (Pearl's do-calculus, SCMs) and recent neural parameterizations of causal models (e.g., neural causal models, differentiable causal discovery). It's motivated by frustration with black-box neural causal models and post-hoc explanation techniques (SHAP, attention visualizations) that often mislead. KANs themselves are recent (Kolmogorov-Arnold representation theorem applied to neural networks) and are gaining traction as interpretable alternatives to standard MLPs across domains. This paper essentially asks: can we use KANs' interpretability properties to make causal models auditable without losing generative power? The research direction opens up interpretable causal inference at scale, connecting causal discovery, mechanistic interpretability, and production ML governance.
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