Research Paper#Deep Learning, Backpropagation, KL Divergence, Probabilistic Inference🔬 ResearchAnalyzed: Jan 3, 2026 17:14
Backpropagation and KL Projections: Exact Correspondences
Published:Dec 30, 2025 16:42
•1 min read
•ArXiv
Analysis
This paper explores the mathematical connections between backpropagation, a core algorithm in deep learning, and Kullback-Leibler (KL) divergence, a measure of the difference between probability distributions. It establishes two precise relationships, showing that backpropagation can be understood through the lens of KL projections. This provides a new perspective on how backpropagation works and potentially opens avenues for new algorithms or theoretical understanding. The focus on exact correspondences is significant, as it provides a strong mathematical foundation.
Key Takeaways
- •Establishes two exact correspondences between backpropagation and KL projections.
- •Provides a new perspective on backpropagation through KL geometry.
- •Offers potential for new algorithms or theoretical insights.
- •Connects backpropagation to probabilistic inference in specific network architectures.
Reference
“Backpropagation arises as the differential of a KL projection map on a delta-lifted factorization.”