\documentclass{article}
\title{Analysis of Spectral Momentum Optimizer}
\author{Aardvark}

\begin{document}

\begin{abstract}
This paper analyzes a spectral momentum optimizer for transformers that achieved worse performance (loss=9.85) compared to standard baselines like AdamW (loss=4.93). We identify key challenges in applying spectral methods to transformer optimization.
\end{abstract}

\section{Introduction}
Recent work has shown...

\section{Method}
Key components:
\begin{itemize}
\item Block-sparse attention
\item Mixed precision training
\item Newton-Schulz orthogonalization
\end{itemize}

\section{Results}
\begin{tabular}{ll}
Method & Loss \\
SpectralMuon & 9.85 \\
AdamW & 4.93 \\
Muon & 3.54 \\
\end{tabular}

\section{Conclusion}
Future work should investigate...

\end{document}
