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Manifold-Matching Autoencoders

arXiv cs.LG / 3/18/2026

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Key Points

  • The paper introduces Manifold-Matching Autoencoders (MMAE), a regularization technique that aligns latent-space pairwise distances to input-space distances using mean squared error.
  • Because MMAE operates on pairwise distances rather than coordinates, it enables flexible, lower-dimensional representations of data.
  • Experiments show MMAE outperforms similar regularization methods in preserving nearest-neighbor structures and topological features measured by persistent homology.
  • MMAE provides a scalable approximation to Multi-Dimensional Scaling, offering a practical tool for manifold learning in unsupervised learning contexts.

Abstract

We study a simple unsupervised regularization scheme for autoencoders called Manifold-Matching (MMAE): we align the pairwise distances in the latent space to those of the input data space by minimizing mean squared error. Because alignment occurs on pairwise distances rather than coordinates, it can also be extended to a lower-dimensional representation of the data, adding flexibility to the method. We find that this regularization outperforms similar methods on metrics based on preservation of nearest-neighbor distances and persistent homology-based measures. We also observe that MMAE provides a scalable approximation of Multi-Dimensional Scaling (MDS).

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