SciNO: A Neural Operator-based Functional Diffusion Model for Causal Ordering

Recent research in Causal Discovery is evolving beyond simply identifying causal relationships between variables, moving toward securing the reasoning capability and reliability of models. In particular, to address the problem of the search space expanding rapidly as the number of variables increases, the 'order-based causal discovery' approach, which first estimates the causal ordering of variables, is drawing attention.

Existing methods such as SCORE and CaPS had limitations in that memory usage surged in high-dimensional environments, and DiffAN suffered from unstable differential approximation performance on high-dimensional data due to its MLP-based structure. To solve this, LG AI Research proposed SciNO(Score-informed Neural Operator).

SciNO is a Functional Diffusion Model that adopts the theoretical perspective of the Hilbert Diffusion Model(HDM), treating data not as simple vectors but as continuous functions. This provides the following advantages:

• Stable Differential Approximation: Based on Sobolev Space and the Sobolev Embedding Theorem, it was proven that the Neural Operator can stably approximate not only the score function but also higher-order derivatives (such as the Hessian diagonal).
• High-Dimensional Scalability: Unlike existing MLP-based models, by learning mappings between functions, it enables precise causal ordering estimation even in high-dimensional environments with a very large number of variables.
• Preservation of Data Structure: By modeling data as a probability distribution on a Hilbert space, it effectively preserves the functional information and differential structure inherent in the data.