FlowCF: Sparse Counterfactual Explanations for Mixed-Type Tabular Data using Flow Matching

In the field of Explainable AI (XAI), counterfactual (CF) explanations interpret a model's decision by suggesting the changes to the input that would lead to a more favourable outcome. To be useful in practice, such an explanation should change few features and change them as little as possible, properties known as sparsity and proximity. However, for numerical features, existing methods typically encourage small changes rather than leaving them exactly unchanged, whether they are model-agnostic and amortised, or gradient-based with full access to the model. In this paper, we propose FlowCF, a model-agnostic generative method that frames CF generation as sparse transport from the factual to the target class. We solve this transport with flow matching, which we extend to mixed feature types with a novel mixed flow operator, and exploit the resulting geometry to optimise for exact numerical sparsity through a gating network that leaves selected features exactly unchanged. Extensive experiments on six benchmark datasets demonstrate that FlowCF produces the best numerical sparsity and proximity, changing 16% of the numerical features where the best baseline changes 90%, while reducing numerical displacement by 70% relative to the best baseline and remaining comparable on the other desiderata.