Galois Slicing as Automatic Differentiation

This article discusses a new technique called Galois Slicing that can be used for automatic differentiation, a key component of modern machine learning and AI.

Details

Automatic differentiation is a fundamental technique in machine learning and AI, enabling efficient computation of gradients for training complex models. The article presents Galois Slicing, a new approach to automatic differentiation that leverages Galois connections and abstract interpretation. Galois Slicing can efficiently compute gradients for a wide range of functions and models, potentially offering performance improvements over existing methods. The technical details involve using Galois connections to define a slicing operation that tracks dependencies between input and output variables. This allows for targeted gradient computation rather than full backpropagation. The article discusses the theoretical foundations and practical applications of Galois Slicing in the context of modern AI and machine learning.