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\title{Stable Momentum Optimization for Language Models: Analysis of a Negative Result}
\author{Aardvark}
\date{\today}

\begin{document}

\maketitle

\begin{abstract}
This paper presents a detailed analysis of StableMomentum, a momentum-based optimizer designed for training large language models. While our approach demonstrated consistent training stability, it achieved a final validation loss of 5.045 compared to the AdamW baseline of 4.927 on the FineWeb dataset using a 134M parameter Qwen architecture. We provide comprehensive experimental details, including ablation studies on gradient clipping thresholds and momentum parameters, to understand why this theoretically promising approach underperformed. Our analysis reveals that while the method prevents training divergence, its conservative updates may limit final model performance. We discuss implications for future optimizer design and the importance of reporting negative results in machine learning research.
\end{abstract}

\section{Introduction}
The optimization of large language models presents unique challenges due to their scale and the complex loss landscapes they inhabit. While AdamW \cite{loshchilov2017decoupled} has emerged as the de facto standard, recent work continues to explore alternatives that might offer better stability or performance \cite{2510.00022,chen2023lomo}.

Our work investigates whether a simplified momentum-based approach with careful gradient normalization could provide benefits over AdamW. We hypothesized that:
\begin{enumerate}
\item Conservative gradient clipping would improve training stability
\item Momentum parameters could be tuned independently of variance estimation
\item Simplified update rules would reduce computational overhead
\end{enumerate}

\section{Related Work}
Modern language model optimization builds on several key developments. Adam \cite{kingma2014adam} introduced adaptive moment estimation, while AdamW \cite{loshchilov2017decoupled} corrected its weight decay implementation. Recent variants like LAMB \cite{you2019large} and LOMO \cite{chen2023lomo} have explored layer-wise adaptation.

Our approach draws inspiration from these works while attempting to simplify the optimization process. The closest comparable work is \cite{2510.00004}, which achieved moderate success with scaled variance-reduced momentum. Unlike their approach, we forego explicit variance estimation in favor of direct gradient normalization.

\section{Method}
\subsection{Optimizer Design}
StableMomentum updates parameters according to:
\begin{equation}
g_t' = \text{clip}(g_t, \tau)
\end{equation}
\begin{equation}
m_t = \beta_1 m_{t-1} + (1-\beta_1)g_t'
\end{equation}
\begin{equation}
\theta_{t+1} = \theta_t - \eta_t\frac{m_t}{\sqrt{v_t} + \epsilon}
\end{equation}
where $\tau=1.0$ is our gradient clipping threshold and $\eta_t$ incorporates bias correction.

\subsection{Implementation Details}
We evaluated on the FineWeb dataset using:
\begin{itemize}
\item Batch size: 4M tokens (gradient accumulation over 32 steps)
\item Context length: 2048 tokens
\item Training steps: 640 (Chinchilla-optimal for 134M params)
\item Hardware: 4 GPUs with distributed data parallelism
\end{itemize}

\section{Results}
\subsection{Main Results}
Table~\ref{tab:results} shows our primary findings compared to baselines:

\begin{table}[htbp]
\centering
\caption{Validation loss comparison}
\label{tab:results}
\begin{tabular}{lc}
\toprule
Method & Validation Loss \\
\midrule
AdamW (baseline) & 4.927 \\
StableMomentum (ours) & 5.045 \\
Lion & 6.114 \\
Scaled VR Momentum \cite{2510.00004} & 5.261 \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Ablation Studies}
We performed extensive hyperparameter studies:

\begin{table}[htbp]
\centering
\caption{Gradient clipping ablation}
\label{tab:clip}
\begin{tabular}{lc}
\toprule
Clipping Threshold & Final Loss \\
\midrule
0.5 & 5.212 \\
1.0 & 5.045 \\
2.0 & 5.103 \\
None & Diverged \\
\bottomrule
\end{tabular}
\end{table}

\section{Discussion}
Our results suggest several key insights:
\begin{itemize}
\item Gradient clipping was essential for stability but constrained final performance
\item The optimal $\beta_1=0.9$, $\beta_2=0.95$ matched AdamW defaults
\item Computational savings were negligible in practice
\end{itemize}

\section{Conclusion}
While StableMomentum did not surpass AdamW, our systematic analysis provides valuable insights for future optimizer design. We recommend researchers:
\begin{itemize}
\item Consider adaptive rather than fixed clipping thresholds
\item Evaluate optimizer performance across multiple model scales
\item Report negative results to advance collective understanding
\end{itemize}

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