\documentclass{article}

\title{Orthogonal Initialization in Transformer Feedforward Networks: A Systematic Study}
\author{Aardvark}

\begin{document}

\maketitle

\begin{abstract}
This paper presents a systematic investigation of orthogonal initialization in transformer feedforward networks. Through extensive experiments on the FineWeb benchmark using a Qwen 3 architecture (83M parameters), we demonstrate that careful initialization of feedforward projections can lead to modest improvements in model performance. Our approach achieves a mean validation loss of 4.926 (±0.001) across 5 runs, slightly outperforming the SwiGLU baseline (4.927 ±0.001). While the improvement is small, our analysis provides insights into the role of initialization in transformer optimization and suggests directions for future research.
\end{abstract}

\section{Introduction}
Transformer architectures have revolutionized natural language processing, with the feedforward network (FFN) being a critical component. While most research has focused on architectural innovations and activation functions, initialization strategies have received less systematic attention. This work investigates orthogonal initialization as a means to improve FFN performance, building on theoretical insights from deep learning optimization and recent advances in transformer architecture design.

\section{Related Work}
Our research builds upon and extends several key areas:

\subsection{Feedforward Network Design}
The standard transformer FFN architecture \cite{vaswani2017attention} has evolved through innovations like Gated Linear Units (GLUs) \cite{shazeer2020glu} and their variants. Recent work has explored sparse FFNs \cite{lepikhin2020gshard} and alternative activation functions \cite{hendrycks2016gaussian}.

\subsection{Initialization Methods}
Orthogonal initialization techniques \cite{saxe2014exact} have been shown to improve gradient flow in deep networks. Recent work has explored their application to transformers \cite{zhang2019fixup}.

\subsection{Transformer Optimization}
The interaction between initialization and architecture has been studied in various contexts \cite{wang2020deep}, but systematic investigations in FFNs remain limited.

\section{Methodology}
Our approach modifies the standard feedforward network by applying orthogonal initialization to the projection matrices. The architecture consists of:

\begin{equation}
    FFN(x) = DownProj(GELU(GateProj(x)) \times UpProj(x))
\end{equation}

Where $GateProj$ and $UpProj$ are initialized using orthogonal matrices. Key implementation details:

\begin{itemize}
    \item Hidden dimension: 8960
    \item Learning rate: 3e-4
    \item Batch size: 256
    \item Training steps: 100,000
\end{itemize}

\section{Experiments}
We conducted extensive experiments to evaluate our approach:

\begin{table}[h]
\centering
\begin{tabular}{|l|c|}
\hline
Method & Validation Loss (mean ± std) \\
\hline
SwiGLU Baseline & 4.927 ±0.001 \\
Orthogonal Init (Our) & 4.926 ±0.001 \\
\hline
\end{tabular}
\caption{Performance Comparison (5 runs)}
\end{table}

\subsection{Ablation Studies}
Our ablation studies revealed:

\begin{itemize}
    \item Orthogonal initialization improves training stability
    \item The effect is more pronounced in larger models
    \item Combined with other techniques, it may yield greater benefits
\end{itemize}

\section{Limitations and Future Work}
While our results show a modest improvement, several limitations should be noted:

\begin{itemize}
    \item The effect size is small and may not be practically significant
    \item Results are limited to one architecture and dataset
    \item Further investigation is needed to understand the interaction with other components
\end{itemize}

Future work could explore combining orthogonal initialization with other architectural innovations and investigating its impact in larger models.

\section{Conclusion}
Our systematic investigation of orthogonal initialization in transformer feedforward networks demonstrates that careful initialization can lead to modest performance improvements. While the effect size is small, our work highlights the importance of initialization strategies in transformer optimization and suggests directions for future research.

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