It isolates the stochastic direction (the sign of the gradient) from the adaptive step size (the relative variance).
It shows that Adam minimizes a specific form of sharpness —specifically the trace of the square root of the Hessian—which is fundamentally different from how SGD behaves. 4. Better Embeddings with Coupled Adam Splitting Adam
Published in 2025, this paper "splits" the problem of in LLM embeddings. It isolates the stochastic direction (the sign of
Based on your interest in "Splitting Adam," you are likely referring to research surrounding the widely used in machine learning. There isn't one single paper with that exact title, but several "interesting" papers analyze splitting the algorithm's components or its behavior in complex ways: 1. The Sign, Magnitude and Variance of Stochastic Gradients Better Embeddings with Coupled Adam Published in 2025,
It proposes Coupled Adam to fix this specific side effect.
If you are coming from a statistics or rare-event simulation background, "ADAM" refers to .
It argues that Adam's second moment actually causes word representations to become narrow and directional (anisotropic).