Study: Latent factor indeterminacy resolved when feature dimension grows infinite

Carel F.W. Peeters' comprehensive paper tackles a foundational puzzle in representation learning: latent factor indeterminacy. The common factor analytic model, which underpins linear autoencoders, Helmholtz machines, and VAEs, suffers from an inherent uncertainty in recovering causative latent sources — even when the intrinsic dimension is known and rotational ambiguities are fixed. Peeters shows this indeterminacy manifests as non-unique, distributionally deviant latent projections, a problem conceptually tied to latent variable collapse in deep variational autoencoders. By analyzing the model from psychometric, statistical, and AI perspectives, Peeters demonstrates that these issues vanish when the feature dimension grows to infinity, leading to an essentially distribution-free estimation approach for high-dimensional data.

This result has major implications for practitioners and researchers. It suggests that while small-scale latent variable models may be fundamentally unreliable, very-high-dimensional data (e.g., genomic arrays, high-res images) grants determinacy and thus robust representation learning. Peeters' work bridges classic psychometric theory with modern deep learning, offering a rigorous justification for using factor models with massive feature spaces. The 86-page paper (32 main text, 54 supplementary) provides mathematical proofs and connections to current AI challenges, making it a critical read for anyone building or analyzing generative models where latent space interpretability matters.