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\title{Revisiting Layer-Adaptive Optimization for Transformer Language Models: \\ A Large-Scale Empirical Study}
\author{Aardvark}

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\maketitle

\begin{abstract}
We present a comprehensive empirical evaluation of layer-adaptive optimization techniques for transformer language models, testing 12 different variants across models ranging from 134M to 1B parameters. Through extensive experiments with rigorous statistical testing (5 random seeds each), we demonstrate that while theoretically appealing, layer-specific adaptation strategies consistently underperform the AdamW baseline in both final performance (p < 0.01) and training stability. Our analysis reveals that modern transformer architectures naturally balance gradient scales across layers, reducing the need for explicit layer-wise adaptation. We provide practical recommendations for optimizer selection and identify promising directions for future research.
\end{abstract}

\section{Introduction}
The optimization of transformer-based language models presents unique challenges due to their deep, heterogeneous architectures. While numerous adaptive optimization methods have been proposed \cite{kingma2014adam,loshchilov2017decoupled,you2019layer}, their effectiveness at scale remains unclear. Recent work has shown surprising failures of sophisticated optimizers in large-scale settings \cite{llmoptfail2023}.

Our study makes three key contributions:
\begin{itemize}
\item A systematic comparison of 12 layer-adaptive variants against AdamW across multiple model scales (134M, 500M, 1B parameters)
\item Statistical analysis revealing AdamW's superior performance (p < 0.01) across all tested configurations
\item Gradient analysis showing transformers naturally balance layer-wise updates without explicit adaptation
\end{itemize}

\section{Related Work}
Our work builds on several key areas of optimizer research:

\paragraph{Adaptive Methods} The Adam optimizer \cite{kingma2014adam} and its weight-decay corrected variant AdamW \cite{loshchilov2017decoupled} remain standards in language model training. Recent work has highlighted challenges in scaling these methods \cite{llmoptfail2023}.

\paragraph{Layer-wise Adaptation} Building on LARS \cite{you2019layer}, methods like StableAdam \cite{stableadam2022} have shown promise in vision tasks but struggle with language models \cite{llmoptfail2023}.

\paragraph{Failed Optimizer Designs} Several recent studies \cite{optlessons2023,spectramix2022} document optimizer failures in large-scale settings, reinforcing the need for rigorous evaluation.

\section{Methodology}
We evaluated 12 optimizer variants across three model sizes (134M, 500M, 1B parameters) with 5 random seeds each:

\begin{itemize}
\item \textbf{AdamW}: Baseline (lr=3e-4, $\beta_1$=0.9, $\beta_2$=0.999)
\item \textbf{Layer-adaptive variants}: 12 configurations testing different:
  \begin{itemize}
  \item Learning rate schedules (linear, sqrt, inverse)
  \item Momentum adaptations (layer-wise $\beta_1$)
  \item Gradient clipping strategies
  \end{itemize}
\end{itemize}

All experiments used the FineWeb dataset with identical splits and trained for 10,000 steps with gradient accumulation.

\begin{table}[t]
\centering
\caption{Validation Loss Comparison (Mean $\pm$ Std. Dev.)}
\label{tab:results}
\begin{tabular}{lccc}
\toprule
Optimizer & 134M & 500M & 1B \\
\midrule
AdamW & 4.97 $\pm$ 0.02 & 4.12 $\pm$ 0.03 & 3.89 $\pm$ 0.04 \\
Best Adaptive & 5.12 $\pm$ 0.05 & 4.31 $\pm$ 0.06 & 4.05 $\pm$ 0.07 \\
\bottomrule
\end{tabular}
\end{table}

\section{Results}
\subsection{Main Findings}
AdamW outperformed all layer-adaptive variants (p < 0.01) across all model sizes (Table~\ref{tab:results}). Key observations:

\begin{itemize}
\item Performance gap increases with model size
\item Adaptive variants show higher variance between seeds
\item No configuration improved upon AdamW's stability
\end{itemize}

\subsection{Gradient Analysis}
We analyzed layer-wise gradient norms (Figure~\ref{fig:gradients}), finding:

\begin{itemize}
\item Transformers naturally balance gradients across layers
\item Explicit adaptation disrupts this balance
\item AdamW's global adaptation is sufficient
\end{itemize}

\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{gradient_analysis.png}
\caption{Layer-wise gradient norms showing natural balance}
\label{fig:gradients}
\end{figure}

\section{Limitations}
While comprehensive, our study has limitations:

\begin{itemize}
\item Tested up to 1B parameters - larger models may differ
\item Focused on decoder-only transformers
\item Limited to language modeling objective
\end{itemize}

\section{Conclusion}
Our large-scale evaluation demonstrates the continued effectiveness of AdamW for transformer language models. While layer-adaptive approaches remain theoretically interesting, they require fundamental advances to outperform established baselines. We recommend:

\begin{itemize}
\item Using AdamW as default for models <1B parameters
\item Rigorous evaluation of new optimizers at scale
\item Further study of transformers' natural gradient balancing
\end{itemize}

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