Criterion for indecisive components in NNCA/ECA expansion

Determine a quantitative criterion for identifying components of the orthonormal basis vectors v_j learned in neural network component analysis (NNCA) or emulator-based component analysis (ECA) that are indecisive for the spectral output in the vector expansion x ≈ Σ_j t_j v_j used to reconstruct standardized structural input features from latent variables t_j. The criterion should specify, in terms of the learned basis vectors and latent variables, when the expansion predicts the mean value for a feature due to z-score standardization, thereby indicating that the feature is spectrally irrelevant in the reconstruction.

Background

In the NNCA approach, the encoder performs the ECA-style projection of standardized structural inputs onto orthonormal basis vectors to obtain latent variables, which are then decoded to predict spectral targets. For structural reconstruction, the authors expand latent variables back into the structural space using x ≈ Σ_j t_j v_j. They observe that, due to z-score standardization, the expansion predicts the mean value for spectrally irrelevant parameters, implying the existence of a criterion to decide which components (and corresponding features) are indecisive for the spectral output.

Within their reconstruction study on amorphous GeO2, NNCA improves recovery of Ge–O distances but not Ge–Ge distances from spectral moments. This behavior motivates the need for a principled rule to flag basis-vector components that do not contribute decisively to the spectral features, which the authors note requires investigation across more systems than those currently available.