Theoretical guarantees for identifiability

Establish theoretical guarantees for identifiability of the learned representations within the self-supervised learning framework proposed in the paper, specifying conditions under which the latent factors of the data-generating process are provably recoverable.

Background

The authors empirically demonstrate recovery of data-generating factors in controlled settings, but emphasize that they do not provide formal identifiability guarantees.

They explicitly defer the development of such guarantees to future work, marking a concrete theoretical gap concerning provable recovery of latent factors.

References

Finally, we do not provide theoretical guarantees for identifiability and leave it as future work.

— Self-Supervised Learning from Structural Invariance  (2602.02381 - Zhang et al., 2 Feb 2026) in Section 6 (Limitations and future work)

For higher-dimensional observations, the same arguments would apply if the learned representation admitted such an H and allowed the transition noise to be identified; however, we do not establish conditions under which such a representation can be learned.

— Causal Representation Learning with Instantaneous and Lagged Relations via Nonstationarity  (2610.03452 - Yamada et al., 2 Oct 2026) in Section 3.2, “Identification of the Causal Graph”