Sample complexity of RAD and nonlinear independent component analysis

Determine the sample complexity of Real Analytic Decoders (RAD) and other nonlinear Independent Component Analysis methods.

Background

The paper establishes identifiability for nonlinear Independent Component Analysis under real-analytic generating transformations and source distributions whose probability densities have discontinuities in their first derivatives, with the Laplace distribution as a principal example. Although the theoretical result addresses identifiability, it does not characterize how many observations are required for RAD or related nICA methods to reliably recover the latent sources. The authors explicitly identify this sample-complexity characterization as an open problem.

References

However, there are still many open problems to be investigated, including the sample complexity of RAD and other nICA methods, and the trade-off between universal approximation and source recovery ability in nICA.

— Kinks vs. Smoothness: Identifiability of Real Analytic nICA for Laplace-like Sources  (2609.21926 - Manring et al., 18 Sep 2026) in Section 7, Conclusion and Future Work

However, there are still many open problems to be investigated, including the sample complexity of RAD and other nICA methods, and the trade-off between universal approximation and source recovery ability in nICA.

— Kinks vs. Smoothness: Identifiability of Real Analytic nICA for Laplace-like Sources  (2609.21926 - Manring et al., 18 Sep 2026) in Section 7, Conclusion and Future Work