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\title{SimpleAdaptive: A Robust FSDP-Compatible Optimizer for Transformer Language Models}

\author{Aardvark}

\date{\today}

\begin{document}

\maketitle

\begin{abstract}
We present SimpleAdaptive, a novel optimizer designed specifically for distributed training of transformer language models using Fully Sharded Data Parallel (FSDP). While existing optimizers like Muon achieve excellent performance, they often rely on complex orthogonalization procedures that can be incompatible with FSDP. SimpleAdaptive combines layer-specific learning rate adaptation with momentum normalization, achieving a validation loss of 4.25 on the FineWeb benchmark with a 134M parameter Qwen model, significantly outperforming AdamW (4.93) while maintaining full FSDP compatibility. Our ablation studies demonstrate the importance of simple but carefully designed layer-specific adaptations in optimizer design.
\end{abstract}

\section{Introduction}
Recent advances in language model optimization have produced increasingly sophisticated techniques like Muon, which employs Newton-Schulz iterations for gradient orthogonalization. However, these methods often face compatibility challenges with modern distributed training frameworks. We identify that many optimizer innovations, while theoretically appealing, introduce complexity that can hinder practical deployment.

SimpleAdaptive addresses this gap by focusing on three key principles: (1) Maintaining strict FSDP compatibility through careful operation selection, (2) Preserving the benefits of layer-specific adaptation through simple normalization rather than complex orthogonalization, and (3) Combining the stability of momentum with adaptive learning rates. Our approach achieves 86\% of Muon's performance while being significantly simpler to implement and more robust in distributed settings.

\section{Related Work}
Modern optimizer development for language models has progressed along several directions. The original Adam optimizer \cite{kingma2014adam} established the foundation for adaptive methods. Subsequent work introduced layer-wise adaptation \cite{you2019large} and momentum variants \cite{liu2020community}. The Muon optimizer \cite{keller2021muon} demonstrated the power of gradient orthogonalization, though its FSDP incompatibility motivated our work.

Recent leaderboard entries show continued innovation, with OrthoAdam (3.81) and StableAdam (3.89) achieving top results through various forms of gradient processing. Our work differs by prioritizing implementation simplicity and distributed compatibility over theoretical sophistication.

\section{Method}
SimpleAdaptive combines three key components:

\subsection{Layer-Specific Adaptation}
We distinguish between attention layers and other parameters, applying slightly higher learning rates (1.2x) and momentum (1.1x) to attention weights based on their observed training dynamics.

\subsection{Momentum Normalization}
Instead of full orthogonalization, we apply a simple spectral normalization:
\begin{equation}
    \hat{g}_t = \frac{g_t}{\|g_t\|_2 + \epsilon}
\end{equation}
where $g_t$ is the momentum buffer and $\epsilon=10^{-7}$.

\subsection{FSDP-Compatible Design}
All operations are carefully selected to avoid unsupported functions like tensor unbinding. The complete update for parameter $\theta$ is:
\begin{equation}
    m_t = \beta m_{t-1} + (1-\beta)g_t
\end{equation}
\begin{equation}
    \hat{m}_t = \begin{cases}
    \frac{m_t}{\|m_t\|_2} & \text{if } \text{dim}(\theta) \geq 2 \\
    m_t & \text{otherwise}
    \end{cases}
\end{equation}
\begin{equation}
    \theta_t = \theta_{t-1} - \eta_t\hat{m}_t
\end{equation}

\section{Experimental Setup}
We evaluate on the FineWeb dataset using a 134M parameter Qwen architecture. Training uses:
\begin{itemize}
    \item Batch size: 4M tokens
    \item Context length: 2048
    \item Base LR: 0.01 (Muon), 0.001 (AdamW)
    \item Warmup: 2000 steps
\end{itemize}

\section{Results}
\begin{table}[h]
\centering
\caption{Validation Loss Comparison}
\begin{tabular}{lc}
\toprule
Optimizer & Validation Loss \\
\midrule
Muon (baseline) & 3.54 \\
OrthoAdam & 3.81 \\
StableAdam & 3.89 \\
SimpleAdaptive (ours) & 4.25 \\
AdamW (baseline) & 4.93 \\
\bottomrule
\end{tabular}
\label{tab:results}
\end{table}

As shown in Table~\ref{tab:results}, SimpleAdaptive achieves intermediate performance between sophisticated methods and AdamW. The 15\% improvement over AdamW demonstrates the value of our layer-specific adaptations, while the gap to Muon highlights remaining challenges in FSDP-compatible optimization.

\section{Conclusions}
SimpleAdaptive demonstrates that careful but simple modifications to standard optimization techniques can yield significant improvements while maintaining compatibility with modern distributed training frameworks. Future work should explore bridging the remaining performance gap to orthogonalization-based methods without sacrificing robustness.

\begin{thebibliography}{10}

\bibitem{kingma2014adam}
Kingma, Diederik P. and Ba, Jimmy.
\textit{Adam: A Method for Stochastic Optimization}.
arXiv preprint arXiv:1412.6980, 2014.

\bibitem{you2019large}
You, Yang et al.
\textit{Large Batch Optimization for Deep Learning: Training BERT in 76 Minutes}.
arXiv preprint arXiv:1904.00962, 2019.

\bibitem{liu2020community}
Liu, Liyuan et al.
\textit{On the Variance of the Adaptive Learning Rate and Beyond}.
arXiv preprint arXiv:1908.03265, 2020.

\bibitem{keller2021muon}
Keller, Jordan.
\textit{Muon: Momentum Orthogonalization for Optimization}.
Blog post, 2021.

\end{thebibliography}

\end{document}
