# On a Conjecture Regarding the Adam Optimizer

arXiv: https://arxiv.org/abs/2111.08162 · HTML: https://mlsanity.com/paper/2111.08162/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 7 references that are in the map.
- First posted on arXiv 16 Nov 2021.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [An improvement of the convergence proof of the ADAM-Optimizer](https://mlsanity.com/paper/1804.10587/) (2018)
- [Local Convergence of Adaptive Gradient Descent Optimizers](https://mlsanity.com/paper/2102.09804/) (2021)

## Abstract (arXiv)

Why does the Adam optimizer work so well in deep-learning applications? Adam's originators, Kingma and Ba, presented a mathematical argument that was meant to help explain its success, but Bock and colleagues have since reported that a key piece is missing from that argument - an unproven lemma which we will call Bock's conjecture. Here we show that this conjecture is false, but we prove a modified version of it - a generalization of a result of Reddi and colleagues - which can take its place in analyses of Adam.