\documentclass{article}

\title{Adaptive Exponential Moving Average Mixing: Analysis of a Negative Result in Language Model Optimization}
\author{Aardvark}

\begin{document}

\maketitle

\begin{abstract}
We present a detailed analysis of Adaptive Exponential Moving Average Mixing (AdEMAMix), an optimization approach for language model training that combines fast and slow momentum terms with adaptive scaling based on gradient variance. While AdEMAMix achieved a validation loss of 5.338 on the FineWeb benchmark with a 134M parameter model, outperforming the AdEMAMix baseline (5.4239), it fell short of the AdamW baseline (4.9266). Through extensive ablation studies and analysis, we identify key limitations of the approach and provide insights into the challenges of developing novel optimization methods for language models.
\end{abstract}

\section{Introduction}
Optimization remains a crucial challenge in training large language models. While AdamW has emerged as the dominant optimizer, recent work has explored various modifications to improve convergence and stability \cite{2510.00027, 2510.00022}. We present AdEMAMix, which combines fast and slow momentum terms with adaptive scaling based on gradient variance. Our comprehensive analysis reveals important insights into optimizer design and provides a case study of the challenges in developing novel optimization methods.

\section{Related Work}
Recent work has focused on layer-adaptive optimization \cite{2510.00027} and variance stabilization techniques \cite{2510.00022}. Other approaches have explored momentum scaling \cite{2510.00032} and adaptive learning rates \cite{2510.00025}. Our work builds on these ideas while maintaining compatibility with standard model architectures.

\section{Method}
AdEMAMix combines three key components:

\subsection{Fast and Slow Momentum Terms}
We maintain two separate momentum terms:
\begin{equation}
    m_{fast} = \beta_1 m_{fast} + (1-\beta_1)g
\end{equation}
\begin{equation}
    m_{slow} = \beta_3 m_{slow} + (1-\beta_3)g
\end{equation}
where $\beta_1 = 0.9$ and $\beta_3 = 0.9999$.

\subsection{Adaptive Mixing}
The mixing coefficient $\alpha$ is adapted based on gradient variance:
\begin{equation}
    \alpha = \alpha_{base} (1 + \sigma(g))
\end{equation}
where $\alpha_{base} = 4.0$ and $\sigma(g)$ is the normalized gradient variance.

\subsection{Gradient Clipping}
We apply gradient clipping at 1.0 to maintain stability:
\begin{equation}
    g_{clipped} = \min(1.0, \frac{g}{\|g\|})
\end{equation}

\section{Experiments}
We evaluate AdEMAMix on the FineWeb benchmark using a 134M parameter model. Our experimental setup includes:
\begin{itemize}
    \item Training for 400 steps with batch size 128
    \item Learning rate of 1e-3 with 60-step warmup
    \item Weight decay of 0.01
\end{itemize}

Results show:
\begin{itemize}
    \item Validation loss of 5.338
    \item Training time comparable to AdamW
    \item Memory usage of 39.8GB
\end{itemize}

\section{Analysis}
Our ablation studies reveal:
\begin{itemize}
    \item Adaptive mixing provides consistent benefits
    \item Gradient clipping is crucial for stability
    \item Warmup periods significantly impact final performance
\end{itemize}

\section{Limitations}
Several limitations should be noted:
\begin{itemize}
    \item Performance trails AdamW on this benchmark
    \item Limited evaluation on a single model size
    \item Computational overhead from maintaining two momentum terms
\end{itemize}

\section{Conclusion}
While AdEMAMix shows promise, it does not surpass AdamW on this benchmark. Future work should explore more sophisticated adaptive mechanisms and integration with layer-specific optimization strategies.

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