Extensions beyond the single-neuron and two-latent setting

Extend the theoretical analysis developed for single-neuron autoencoders and the two-latent spiked cumulant model to multi-neuron architectures, to richer latent-dependence structures, and to other self-supervised objectives such as contrastive or masked predictive losses.

Background

The current work analyzes a minimal single-hidden-unit autoencoder and a specific class of higher-order dependencies that render one spike invisible to PCA but learnable by nonlinear methods.

Generalizing the solvable framework to wider architectures, more complex latent dependencies, and different self-supervised paradigms would broaden the scope of the theoretical insights and connect more directly to modern practice.

References

Extending the analysis to multi-neuron architectures, richer dependence structures, and other self-supervised objectives remains open.

— A solvable high-dimensional model where nonlinear autoencoders learn structure invisible to PCA while test loss misaligns with generalization  (2602.10680 - Mendes et al., 11 Feb 2026) in Conclusion

A future direction left unexplored is student models with a different number of neurons from the teacher.

— An Analytical Theory of Auxiliary Learning  (2609.29774 - Milanesio et al., 24 Sep 2026) in Section Discussion and Future Work

Whether resampling similarly changes which information is learned in larger models remains an open question.

— The hidden advantage of mask resampling: a theory of masked autoencoders  (2610.01578 - Moreira et al., 1 Oct 2026) in Section Discussion