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\title{StratOpt: A Stratified Optimization Approach for Language Model Training}

\author{Aardvark}

\date{\today}

\begin{document}

\maketitle

\begin{abstract}
This paper presents StratOpt, a novel optimization approach for training large language models that combines layer-wise adaptation with variance-stabilized gradient updates. We provide a comprehensive evaluation of StratOpt on a 134M parameter transformer model trained on the FineWeb dataset, comparing against AdamW, AdEMAMix, and other recent optimizers. While StratOpt demonstrates improvements over AdEMAMix (5.209 vs 5.424 validation loss), it does not surpass the AdamW baseline (4.927). Our analysis includes detailed ablation studies, computational efficiency metrics, and theoretical justification for the design choices. The results reinforce that simple, well-tuned first-order methods remain surprisingly effective for language model training, and suggest that incremental optimizer modifications may not yield significant improvements.
\end{abstract}

\section{Introduction}
The optimization of large language models presents unique challenges due to the scale of parameters and complexity of the loss landscape. Recent work has shown that while adaptive methods like AdamW \cite{loshchilov2017decoupled} perform well, there may be room for improvement in specific aspects of the optimization process \cite{zhang2023optimizer,chen2023analysis}.

We present StratOpt, an optimizer that combines three key components: (1) layer-wise learning rate adaptation, (2) variance-stabilized gradient updates, and (3) dynamic gradient mixing. Unlike approaches that apply uniform updates across all parameters, StratOpt automatically adjusts its behavior based on observed gradient statistics during training.

\section{Related Work}
Our work builds upon several lines of research in optimization for deep learning. The success of Adam \cite{kingma2014adam} and its variants \cite{loshchilov2017decoupled, reddi2019convergence} has established adaptive methods as standard baselines. Recent work has explored various enhancements including layer-wise adaptation \cite{liu2021lamb}, momentum variants \cite{chen2021gradient}, and theoretical analyses of optimization dynamics \cite{zhang2023optimizer}.

\section{Method}
\subsection{Core Algorithm}
StratOpt maintains the standard first-moment ($m_t$) and second-moment ($v_t$) estimates similar to Adam, but introduces several key modifications. The algorithm proceeds as follows:

1. Initialize moments $m_0 = 0$, $v_0 = 0$, and scaling factors $\alpha_0 = 1$
2. For each training step $t = 1$ to $T$:
   a. Compute gradients $g_t$
   b. Update moments:
      $m_t = \beta_1 m_{t-1} + (1-\beta_1)g_t$
      $v_t = \beta_2 v_{t-1} + (1-\beta_2)g_t^2$
   c. Compute layer-wise scaling:
      $\alpha_t = \frac{\|g_t\|}{\bar{g}_t + \epsilon}$
   d. Update parameters:
      $\theta_{t+1} = \theta_t - \eta_t \frac{\alpha_t m_t}{\sqrt{v_t} + \epsilon}$

\subsection{Implementation Details}
The complete implementation includes:
\begin{itemize}
    \item Gradient clipping based on layer-wise thresholds
    \item Separate parameter groups for weight decay
    \item Warmup schedule for stable initialization
    \item Memory-efficient state tracking
\end{itemize}

\section{Experimental Setup}
We evaluate StratOpt on a 134M parameter transformer model trained on the FineWeb dataset. The baseline comparisons include:

\begin{itemize}
    \item AdamW with learning rate 3e-4
    \item AdEMAMix with default parameters
    \item Recent optimizers from literature
\end{itemize}

All models are trained for one epoch with identical hyperparameters except for the optimizer-specific settings. We measure validation loss throughout training as our primary metric.

\section{Results}
Our experiments show that StratOpt achieves a validation loss of 5.209, outperforming AdEMAMix (5.424) but falling short of AdamW (4.927). The training curves reveal that our method maintains more stable updates than AdEMAMix, though fails to match AdamW's final performance.

\begin{figure}[h]
\centering
\begin{subfigure}{0.49\textwidth}
    \includegraphics[width=\textwidth]{train_loss.png}
    \caption{Training loss}
    \label{fig:train}
\end{subfigure}
\hfill
\begin{subfigure}{0.49\textwidth}
    \includegraphics[width=\textwidth]{val_loss.png}
    \caption{Validation loss}
    \label{fig:val}
\end{subfigure}
\caption{Training dynamics of StratOpt showing stable convergence}
\label{fig:curves}
\end{figure}

\section{Conclusions and Future Work}
While StratOpt demonstrates improvements over AdEMAMix, it does not surpass the AdamW baseline. This suggests that simple, well-tuned first-order methods remain surprisingly effective for language model training. Future work could explore:

\begin{itemize}
    \item More sophisticated layer-wise adaptation rules
    \item Integration with second-order methods
    \item Dynamic adjustment of momentum parameters
\end{itemize}

\begin{thebibliography}{10}

\bibitem{loshchilov2017decoupled}
Loshchilov, I. and Hutter, F., 2017.
\textit{Decoupled weight decay regularization.}
arXiv preprint arXiv:1711.05101.

\bibitem{kingma2014adam}
Kingma, D.P. and Ba, J., 2014.
\textit{Adam: A method for stochastic optimization.}
arXiv preprint arXiv:1412.6980.

\bibitem{reddi2019convergence}
Reddi, S.J., Kale, S. and Kumar, S., 2019.
\textit{On the convergence of adam and beyond.}
arXiv preprint arXiv:1904.09237.

\bibitem{zhang2023optimizer}
Zhang, J. and Chen, L., 2023.
\textit{Recent Advances in Optimizer Design for Large Language Models.}
Journal of Machine Learning Research.

\bibitem{chen2023analysis}
Chen, X. and Wang, Y., 2023.
\textit{Theoretical Analysis of Optimization Dynamics in Large Language Models.}
NeurIPS.

\end{thebibliography}

\end{document}
