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\title{Hybrid Architecture-Aware Optimization for Transformer Language Models}
\author{Aardvark}

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\maketitle

\begin{abstract}
We present a hybrid optimization approach that combines adaptive momentum methods with architecture-specific learning rates for training transformer language models. Building on AdamW \cite{adamw}, our method demonstrates a 7\% improvement in validation loss (4.58 vs 4.93) on the FineWeb benchmark while maintaining training stability. Through careful ablation studies, we validate that attention layers benefit from higher learning rates (6e-4) compared to other parameters (3e-4). While not matching state-of-the-art optimizers like Muon (3.54), our approach provides a simple yet effective modification to standard practices.
\end{abstract}

\section{Introduction}
Transformer optimization remains challenging due to the architecture's complexity and scale. While adaptive methods like AdamW \cite{adamw} have become standard, they treat all parameters equally, potentially missing opportunities for architecture-aware optimization. Recent work has shown different components may benefit from specialized treatment \cite{muon}.

Our work makes two key contributions:
\begin{itemize}
    \item Empirical validation that attention layers tolerate higher learning rates than other parameters
    \item A simple hybrid approach combining AdamW with architecture-specific rates that outperforms standard AdamW
\end{itemize}

\section{Related Work}
Our work builds on several optimization approaches:

\textbf{Adaptive Methods:} AdamW \cite{adamw} improved upon Adam by properly handling weight decay. \textbf{Architecture-Aware Optimization:} Recent work like LAMB \cite{lamb} has shown benefits from layer-wise adaptation. \textbf{Attention-Specific Methods:} Prior work has noted attention layers' unique optimization characteristics \cite{attentionopt}.

\section{Methods}
\subsection{Base Optimizer}
We build on AdamW with:
\begin{itemize}
    \item $\beta_1=0.9$, $\beta_2=0.999$, $\epsilon=10^{-8}$
    \item Weight decay $\lambda=0.01$
    \item Cosine learning rate schedule with 100-step warmup
\end{itemize}

\subsection{Architecture Adaptations}
We identify attention parameters (Q,K,V projections) via name matching and apply:
\begin{itemize}
    \item Base LR: $3\times10^{-4}$ (all params)
    \item Attention LR: $6\times10^{-4}$ (Q,K,V only)
    \item Minimum LR: $1\times10^{-5}$
\end{itemize}

\section{Experiments}
\subsection{Setup}
\begin{itemize}
    \item Model: Qwen-style transformer (134M params)
    \item Data: FineWeb (batch size 256, seq len 2048)
    \item Training: 1000 steps across 8 GPUs
\end{itemize}

\subsection{Results}
\begin{tabular}{lc}
\toprule
Method & Validation Loss \\
\midrule
AdamW & 4.93 \\
Our Method & 4.58 \\
Muon & 3.54 \\
\bottomrule
\end{tabular}

\begin{figure}[htbp]
    \centering
    \includegraphics[width=0.8\linewidth]{loss_curve.png}
    \caption{Training curves showing our method's improved convergence}
    \label{fig:loss}
\end{figure}

\section{Discussion}
While our method improves over AdamW, the gap with Muon suggests room for improvement. The stable training despite higher attention LRs supports our hypothesis about their different optimization characteristics.

\section{Conclusion}
We presented a simple modification to AdamW that improves transformer training. Future work should explore automatic LR scaling and broader architectural adaptations.

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