Representation Identifiability

Representation identifiability asks whether learned codes correspond to recoverable features of the data or world, rather than one of many equally valid internal coordinate systems. Researchers use nonlinear independent component analysis, multi-view and temporal data, sparsity or orthogonality constraints, and symmetry-breaking interventions to establish when recovery is possible. Guarantees may identify individual factors only up to permutation and scaling, or recover just shared subspaces and invariant geometry, in settings from generative models to neural networks. A central tension is that results depend on assumptions about the data, model, and measurements: identical predictions can arise from different representations, and evaluation metrics can themselves change under function-preserving reparameterizations.