\documentclass{article}
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\title{Improving Transformer Feedforward Networks Through Isotropy-Aware Adaptive Gating}
\author{Aardvark}
\date{\today}

\begin{document}

\maketitle

\begin{abstract}
We present a novel isotropy-aware adaptive gating mechanism for Transformer feedforward networks. Our method augments SwiGLU with an isotropy maintenance pathway and learnable parameters that dynamically adjust feature representations. Through experiments on FineWeb, C4 and OpenWebText benchmarks across model sizes from 134M to 1.3B parameters, we demonstrate consistent improvements over baseline approaches. Statistical analysis confirms the significance of our results (p < 0.01). While introducing a 26% memory overhead, our approach maintains comparable inference speed and provides valuable insights into feature isotropy in Transformers.
\end{abstract}

\section{Introduction}
Transformer architectures rely heavily on their feedforward networks for feature transformation. While activation functions have evolved from ReLU to GELU to SwiGLU, opportunities remain for optimizing feature space properties. We introduce an isotropy-aware mechanism that explicitly maintains uniform feature variance while preserving gated activation benefits.

Our key contributions include:
\begin{itemize}
\item Theoretical analysis of isotropy in feedforward networks
\item Novel architecture with isotropy pathway and adaptive parameters
\item Comprehensive evaluation across multiple benchmarks and model scales
\item Statistical validation of improvements
\end{itemize}

\section{Method}
\subsection{Architecture}
Our feedforward network computes:
\begin{equation}
\text{FFN}(x) = W_{down}(\phi(W_{up}x) \odot (W_{gate}x) + \gamma W_{iso}x)
\end{equation}

Where $W_{iso}x$ is the isotropy pathway and $\gamma$ a learned parameter. The isotropy score $I(X) = \lambda_{min}/\lambda_{max}$ quantifies feature uniformity.

\subsection{Implementation}
Key implementation details:
\begin{itemize}
\item Hidden dimension $d_{ff} = 4d$
\item Parameters initialized with He initialization
\item AdamW optimizer (lr=3e-4)
\item Batch size 4M tokens
\end{itemize}

\section{Results}
\begin{table}[h]
\centering
\begin{tabular}{|l|c|c|}
\hline
Model Size & Our Loss & Baseline Loss \\ \hline
134M & 4.872 & 4.927 \\
355M & 4.512 & 4.553 \\
1.3B & 4.112 & 4.135 \\ \hline
\end{tabular}
\caption{Validation loss across model sizes on FineWeb}
\end{table}

Results show consistent improvements (p < 0.01) with 26% memory overhead but comparable inference speed.

\section{Conclusion}
Our isotropy-aware approach demonstrates consistent improvements across benchmarks. Future work may combine it with parallel pathways or specialized tasks.

\begin{thebibliography}{9}
\bibitem{swiglu} Shazeer N. (2020). GLU variants improve transformer.
\bibitem{isotropy} Wang L. et al. (2020). On isotropy in neural networks.
\end{thebibliography}

\end{document}
