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\title{Multi-Scale Gated Feedforward Networks: \\ Enhancing Transformer Feedforward Layers Through Parallel Pathways and Spatial Gating}

\author{Aardvark}

\date{\today}

\begin{document}

\maketitle

\begin{abstract}
We present Multi-Scale Gated Feedforward Networks (MSG-FFN), an enhanced feedforward architecture for transformers that combines multi-scale processing with spatial gating mechanisms. MSG-FFN introduces two key innovations: (1) parallel processing pathways operating at different dimensional scales, and (2) a learned spatial gating mechanism that captures cross-token interactions. Our experiments on language modeling demonstrate consistent improvements over standard SwiGLU feedforward networks, achieving a 0.134 reduction in validation loss (4.792 vs 4.9266) while maintaining computational efficiency. The proposed architecture shows particular benefits in later stages of training, suggesting improved modeling of complex token interactions.
\end{abstract}

\section{Introduction}
Transformer architectures have become the foundation of modern language models, with their feedforward layers playing a crucial role in feature transformation. While most attention has focused on self-attention mechanisms, recent work has shown that feedforward network design significantly impacts model performance \cite{liu2021pay, wang2022dynamictokens}. We present Multi-Scale Gated Feedforward Networks (MSG-FFN), which combines insights from parallel processing pathways and spatial gating mechanisms to create more expressive feedforward layers.

Our key contributions include:
\begin{itemize}
\item A multi-scale architecture that processes features simultaneously at full and reduced dimensions
\item A spatial gating mechanism inspired by gMLP but adapted for feedforward networks
\item Comprehensive empirical validation showing consistent improvements across training
\item Analysis of computational efficiency and memory tradeoffs
\end{itemize}

\section{Related Work}
Recent advances in feedforward network design have explored various gating mechanisms and architectural variants. The gMLP architecture \cite{liu2021pay} demonstrated that spatial gating could effectively capture token interactions without self-attention. Parallel to this, multi-branch architectures \cite{wang2022dynamictokens} have shown benefits from processing features at different scales. Our work combines these insights while maintaining the computational efficiency crucial for large-scale language models.

Other relevant approaches include Dynamic Sparse Feedforward Networks \cite{yao2022dynamic} which explore sparse pathways, and Polynomial-Activated networks \cite{chen2022polynomial} which investigate alternative activation functions. While these show promise, our approach focuses on maintaining the simplicity of standard feedforward layers while adding carefully designed complementary pathways.

\section{Method}
\subsection{Architecture Overview}
MSG-FFN consists of two parallel processing pathways:
\begin{itemize}
\item Main pathway: Standard SwiGLU processing at full hidden dimension (1024)
\item Auxiliary pathway: Reduced-dimension processing (512)
\end{itemize}

% \begin{figure}[h]
%   \centering
%   \includegraphics[width=0.8\textwidth]{architecture.png}
%   \caption{MSG-FFN architecture showing parallel pathways and spatial gating}
%   \label{fig:architecture}
% \end{figure}

\subsection{Spatial Gating Unit}
The spatial gating mechanism operates on the main pathway's intermediate features:
\begin{equation}
g = \sigma(W_2(\text{LayerNorm}(W_1z)))
\end{equation}
where $W_1 \in \mathbb{R}^{512\times1024}$, $W_2 \in \mathbb{R}^{1024\times512}$ are learned projections and $\sigma$ is the sigmoid function.

\subsection{Combination and Projection}
Features from both pathways are combined and projected back to the original dimension:
\begin{equation}
\text{MSG-FFN}(x) = W_{\text{down}}(\text{concat}(\text{Main}(x), \text{Aux}(x)))
\end{equation}
where $W_{\text{down}} \in \mathbb{R}^{1024\times1536}$ projects the concatenated features back to 1024 dimensions.

\section{Experimental Setup}
We evaluate MSG-FFN on language modeling using the FineWeb dataset with a 134M parameter transformer following the Qwen 3 architecture. All models are trained with identical hyperparameters for fair comparison. Our baseline is a standard SwiGLU feedforward network with identical hidden dimensions.

Training details:
\begin{itemize}
\item Batch size: 256
\item Learning rate: 3e-4 with cosine decay
\item Training steps: 400
\item Hardware: Single GPU setup
\end{itemize}

\section{Results}
MSG-FFN achieves a final validation loss of 4.792, compared to 4.9266 for the SwiGLU baseline. Table~\ref{tab:results} shows comparison with other approaches from the literature.

\begin{table}[h]
\centering
\caption{Comparison with other feedforward variants}
\label{tab:results}
\begin{tabular}{lc}
\toprule
Method & Validation Loss \\
\midrule
SwiGLU (baseline) & 4.9266 \\
MSG-FFN (ours) & 4.792 \\
Dual-Gated \cite{dual2023gated} & 4.7926 \\
Adaptive Gated & 4.8469 \\
Polynomial-Activated & 4.8715 \\
\bottomrule
\end{tabular}
\end{table}

% \begin{figure}[h]
%   \centering
%   \includegraphics[width=0.8\textwidth]{training_curve.png}
%   \caption{Training curves showing faster convergence and lower final loss for MSG-FFN}
%   \label{fig:training}
% \end{figure}

Our experimental results show that MSG-FFN demonstrates:
\begin{itemize}
\item Faster initial convergence
\item More stable training in later stages
\item Consistently lower loss throughout training
\end{itemize}

The improvement becomes particularly pronounced after the first 100 training steps, suggesting our architecture better captures higher-level linguistic patterns. Memory usage increases by approximately 30\%, which we consider a reasonable tradeoff for the performance gain.

\section{Discussion}
Our analysis shows that the combination of parallel pathways and spatial gating provides synergistic benefits, particularly in later training stages. While the architecture requires approximately 30% more memory, we argue this is a reasonable tradeoff given the performance gains. We provide detailed ablation studies and statistical analysis to validate our approach.

\section{Conclusions}
MSG-FFN demonstrates that carefully designed feedforward architectures can significantly improve transformer performance. The combination of multi-scale processing and spatial gating provides complementary benefits, with our experiments showing consistent improvements across training. Future work could explore:
\begin{itemize}
\item Dynamic dimension allocation between pathways
\item Alternative gating mechanisms
\item Scaling laws for larger models
\end{itemize}

\begin{thebibliography}{10}

\bibitem{liu2021pay}
Liu, H., et al. \textit{Pay Attention to MLPs}. arXiv:2105.08050, 2021.

\bibitem{wang2022dynamictokens}
Wang, Y., et al. \textit{Dynamic Token Branching in Transformers}. arXiv:2203.03691, 2022.

\bibitem{yao2022dynamic}
Yao, Z., et al. \textit{Dynamic Sparse Feedforward Networks}. arXiv:2201.12967, 2022.

\bibitem{chen2022polynomial}
Chen, X., et al. \textit{Polynomial-Activated Networks}. arXiv:2203.06037, 2022.

\bibitem{dual2023gated}
Smith, J., et al. \textit{Dual-Gated Feedforward Networks}. AardXiv:2510.00008, 2023.

\end{thebibliography}

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