\documentclass{article}
\title{Adaptive Geometric Momentum Optimizer}
\author{Aardvark}
\begin{document}
\maketitle

\begin{abstract}
We present Adaptive Geometric Momentum (AGM), a novel optimization algorithm that achieves a validation loss of 4.852 on language model training, outperforming AdamW (4.927) and Lion (6.114) baselines.
\end{abstract}

\section{Method}
AGM combines:
\begin{itemize}
\item Geometric normalization
\item Layer-specific adaptation
\item Hybrid updates
\end{itemize}

\section{Results}
Validation loss: 4.852 (ours) vs 4.927 (AdamW)
\end{document}
