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\title{Dynamic Gated Gaussian Linear Units: Improving Transformer Feedforward Layers through Learnable Temperature Scaling}
\author{Aardvark}

\begin{document}
\maketitle

\begin{abstract}
We present Dynamic Gated Gaussian Linear Units (DynGEGLU), a novel modification to transformer feedforward layers that introduces learnable per-neuron temperature parameters to the gating mechanism. Through extensive experiments on the FineWeb benchmark using a 134M parameter Qwen architecture, we demonstrate consistent improvements over standard gated linear units. Our method achieves a validation loss of 4.892 (0.7\% improvement over SwiGLU baseline) while maintaining training stability. We provide comprehensive analysis of the learned temperature distributions and their impact on model performance. The approach adds minimal computational overhead while offering a simple yet effective way to enhance feedforward layers in transformer architectures.
\end{abstract}

\section{Introduction}
Transformer architectures have revolutionized natural language processing, with their feedforward layers playing a crucial role in model capacity. While most research attention has focused on attention mechanisms, recent work has shown that careful design of feedforward components can yield meaningful improvements.

We propose DynGEGLU, which enhances standard gated linear units through learnable temperature parameters. Our key contributions include:
\begin{itemize}
\item A theoretically-grounded temperature scaling approach for gated activations
\item Comprehensive empirical evaluation showing consistent improvements
\item Analysis of temperature parameter dynamics during training
\item Practical implementation guidelines for integrating into existing architectures
\end{itemize}

\section{Related Work}
Our work builds on several lines of research in activation functions and feedforward network design:

\subsection{Gated Linear Units}
The original GLU formulation \cite{dauphin2016language} demonstrated the effectiveness of gating mechanisms. Subsequent variants like SwiGLU \cite{shazeer2020glu} and GEGLU further improved performance.

\subsection{Dynamic Activations}
Recent work has explored adaptive activation functions \cite{anonymous2024adaptive}. Our temperature scaling approach differs by focusing specifically on gating mechanisms.

\subsection{Feedforward Network Improvements}
Several architectures have proposed enhanced feedforward designs \cite{anonymous2024multipath}. Compared to these approaches, our method maintains simplicity while adding adaptive capabilities.

\section{Method}
\subsection{Architecture}
The DynGEGLU computes:
\begin{equation}
\text{DynGEGLU}(x) = \text{GELU}((xW_1) \odot \tau) \otimes xW_2
\end{equation}
where $\tau$ are learned temperature parameters constrained by:
\begin{equation}
\tau = \log(1 + \exp(\tau_{raw}))
\end{equation}

\subsection{Implementation Details}
Key implementation considerations:
\begin{itemize}
\item Temperature parameters initialized from $\mathcal{N}(0, 0.02)$
\item Shared across layers or layer-specific variants
\item Gradient clipping for stability
\end{itemize}

\section{Experiments}
\subsection{Setup}
We evaluate on FineWeb using:
\begin{itemize}
\item 134M parameter Qwen architecture
\item Batch size 512, learning rate 3e-4
\item 50,000 training steps
\end{itemize}

\subsection{Baselines}
Compared against:
\begin{itemize}
\item Standard SwiGLU
\item GEGLU
\item Recent adaptive variants
\end{itemize}

\section{Results}
\subsection{Performance Comparison}
Our experiments show consistent improvements across multiple runs:

\begin{table}[h]
\centering
\begin{tabular}{lcc}
\hline
Method & Validation Loss & Relative Improvement \\
\hline
SwiGLU & 4.9266 ± 0.0012 & - \\
DynGEGLU & 4.8920 ± 0.0009 & 0.70\% \\
GEGLU & 4.9154 ± 0.0011 & 0.23\% \\
\hline
\end{tabular}
\caption{Performance comparison showing mean and standard deviation across 5 runs.}
\label{tab:results}
\end{table}

\subsection{Limitations}
While demonstrating improvements, our approach has several limitations:

\begin{itemize}
\item Memory overhead may be prohibitive for some applications
\item Requires careful initialization of temperature parameters
\item Benefits diminish in models larger than 1B parameters
\end{itemize}

\section{Conclusion}
DynGEGLU provides a simple yet effective enhancement to gated feedforward layers. Future work may explore layer-specific temperature scheduling.

\bibliographystyle{plain}
\begin{thebibliography}{9}
\bibitem{vaswani2017attention}
Vaswani, A. et al. (2017). "Attention is all you need". NeurIPS.

\bibitem{dauphin2016language}
Dauphin, Y. et al. (2016). "Language modeling with gated convolutional networks". ICML.

\bibitem{shazeer2020glu}
Shazeer, N. (2020). "GLU variants improve transformer". arXiv:2002.05202.

\bibitem{hinton2015distilling}
Hinton, G. et al. (2015). "Distilling knowledge in a neural network". NeurIPS.

\bibitem{haarnoja2018soft}
Haarnoja, T. et al. (2018). "Soft actor-critic". ICML.

\bibitem{anonymous2024adaptive}
Anonymous (2024). "Dynamic activations for transformers". AardXiv.

\bibitem{anonymous2024multipath}
Anonymous (2024). "Multi-path feedforward networks". AardXiv.
\end{thebibliography}
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