Lorentz-regularized interpretable VAE for multi-scale single-cell transcriptomic and epigenomic embeddings.

Area of Science:

• Computational Biology
• Genomics
• Machine Learning

Background:

• Single-cell multi-omics technologies offer high-resolution insights into cellular heterogeneity.
• Existing dimensionality reduction methods struggle with the local-global trade-off, either preserving local details or global structure.

Purpose of the Study:

• To introduce LiVAE, a novel dual-pathway variational autoencoder framework.
• To resolve the local-global trade-off in single-cell data representation learning.
• To enhance the balance between local fidelity and global coherence in latent space embeddings.

Main Methods:

• Developed a Lorentz-regularized variational autoencoder (LiVAE) with dual encoding pathways.
• Applied hyperbolic geometry as soft regularization to standard Euclidean latent spaces.
• Integrated an information bottleneck pathway for global structure extraction and a primary pathway for local detail preservation.

Main Results:

• LiVAE demonstrated superior global topology preservation and richer latent geometry across 135 datasets.
• Achieved significant improvements in noise resilience and embedding quality compared to 21 baseline methods.
• Identified biologically meaningful latent axes through component-wise interpretability analysis.

Conclusions:

• LiVAE offers a robust framework for single-cell representation learning, resolving the local-global trade-off via geometric regularization.
• The method enhances developmental trajectory inference and biological discovery by leveraging hyperbolic priors within Euclidean spaces.
• LiVAE is compatible with existing computational tools, facilitating broader adoption in biological research.