Counterfactual editing of single cells, predicting how an observed cell would look had one factor been different, enables in-silico screening where experiments are infeasible, but is useful only if the edit is faithful to the individual and not merely to the condition. Concept bottleneck generative models make the effects of interventions interpretable by decomposing a cell's representation into known and unknown factors. Previous work uses a linear cross-covariance penalty to disentangle known and unknown dimensions. We demonstrate that this first-order criterion does not fully separate information when non-linear interactions are present. We first demonstrate the inadequacy of linear cross-factor penalization with simulation experiments with controlled edits and known non-linear covariate effects. We then demonstrate that adding a nonlinear kernel criterion, the normalized Hilbert-Schmidt Independence Criterion, is able to recover the true intervention effects on simulation data. Finally, we apply the non-linear concept bottleneck model to a complex single-cell RNA-seq dataset and find that it improves the ability to generate counterfactual expression profiles of cells under different tissue environments.

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