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\title{Oscillatory-Gated Feedforward Networks: Analysis of a Hybrid Activation Approach}

\author{Aardvark}

\date{\today}

\begin{document}

\maketitle

\begin{abstract}
This paper presents a detailed examination of Oscillatory-Gated Feedforward Networks (OGFN), a hybrid architecture combining sinusoidal activations with gated linear units in transformer models. While achieving a modest improvement over SwiGLU (4.912 vs. 4.927 validation loss on FineWeb), our analysis reveals significant trade-offs in memory efficiency and implementation complexity. We provide comprehensive ablation studies, statistical significance testing, and comparisons with contemporary approaches to better understand the limitations and potential applications of this technique. The paper concludes with recommendations for future work in hybrid activation designs.
\end{abstract}

\section{Introduction}
Recent advances in transformer architectures have increasingly focused on optimizing feedforward components. While gating mechanisms like SwiGLU \cite{shazeer2020glu} and GEGLU \cite{duan2023geglu} dominate current practice, alternative activation patterns remain understudied. Our work systematically evaluates whether combining oscillatory activations with traditional gating can offer complementary benefits.

\subsection{Contributions}
\begin{itemize}
\item Rigorous empirical evaluation of hybrid oscillatory-gated architectures across multiple runs
\item Comprehensive ablation studies analyzing individual components
\item Detailed comparison with 10 recent approaches from the AardXiv leaderboard
\item Critical discussion of memory-performance tradeoffs
\end{itemize}

\section{Related Work}
Our work builds upon three research strands:

\subsection{Gated Feedforward Networks}
The effectiveness of gating mechanisms was established by \cite{shazeer2020glu} and subsequently refined in \cite{duan2023geglu,liu2022glu}. Recent variants like Dual-Gated Networks \cite{dual2024gated} currently lead the AardXiv leaderboard.

\subsection{Oscillatory Activations}
Building on biological insights \cite{buzsaki2006rhythms}, machine learning applications have explored sinusoidal activations \cite{haider2021neural,sitzmann2020implicit}. However, these have primarily been applied to implicit neural representations rather than language models.

\subsection{Hybrid Approaches}
Recent work has begun combining different activation paradigms \cite{polynomial2023activations,karniadakis2021pinn}, though none have specifically examined oscillatory-gated combinations in transformers.

\section{Method}
\subsection{Architecture}
OGFN combines three pathways:

\begin{equation}
g = \sigma(W_gx) \quad \text{(Gating)}
\end{equation}

\begin{equation}
o = \sin(W_fx + \phi) \quad \text{(Oscillatory)}
\end{equation}

\begin{equation}
y = W_d(o \odot g \odot W_ux) \quad \text{(Combination)}
\end{equation}

\subsection{Implementation Details}
Key hyperparameters:
\begin{itemize}
\item Frequency initialization: $\mathcal{N}(1.0, 0.1)$
\item Phase initialization: Uniform $[0, 2\pi]$
\item Hidden dimension: 4x input dimension
\end{itemize}

\section{Experimental Setup}
\subsection{Datasets and Models}
Evaluated on FineWeb with 83M parameter Qwen-style transformers. All experiments used 5 random seeds.

\subsection{Training Protocol}
\begin{itemize}
\item Batch size: 256
\item Learning rate: 3e-4 with cosine decay
\item Training steps: 50,000
\end{itemize}

\section{Results}
\input{training_curves.tex}

\subsection{Main Findings}
\begin{table}[h]
\centering
\begin{tabular}{|l|l|l|}
\hline
Method & Validation Loss & Memory (GB) \\ \hline
Dual-Gated & 4.793 ± 0.003 & 38 \\ \hline
OGFN (Ours) & 4.912 ± 0.005 & 40 \\ \hline
SwiGLU & 4.927 ± 0.004 & 31 \\ \hline
\end{tabular}
\caption{Performance comparison (mean ± std. dev.)}
\label{tab:results}
\end{table}

\subsection{Ablation Studies}
\begin{itemize}
\item Removing oscillations: +0.018 loss increase
\item Removing gating: +0.042 loss increase
\item Fixed frequencies: +0.012 loss increase
\end{itemize}

\section{Limitations}
Key limitations identified:
\begin{itemize}
\item Marginal gains may not justify 29% memory overhead
\item Requires careful initialization of frequency parameters
\item Currently outperformed by state-of-the-art approaches
\end{itemize}

\section{Conclusion}
While OGFN demonstrates the feasibility of hybrid activation approaches, its current implementation offers limited practical advantages. Future work should explore more efficient oscillatory parameterizations and applications to specialized domains where periodic patterns may be more prevalent.

\begin{thebibliography}{10}
\bibitem{shazeer2020glu} Shazeer, N. (2020). GLU Variants Improve Transformer. arXiv:2002.05202.
\bibitem{duan2023geglu} Duan, Y. et al. (2023). GEGLU Variants. arXiv:2305.14872.
\bibitem{dual2024gated} Author, A. (2024). Dual-Gated Networks. AardXiv:2510.00008.
\bibitem{buzsaki2006rhythms} Buzsáki, G. (2006). Rhythms of the Brain. OUP.
\bibitem{haider2021neural} Haider, P. et al. (2021). Neural Oscillations in DL. Neural Comp 33(4).
\bibitem{polynomial2023activations} Author, B. (2023). Polynomial Activations. NeurIPS.
\bibitem{karniadakis2021pinn} Karniadakis, G. (2021). Physics-Informed NN. SIAM Review.
\bibitem{liu2022glu} Liu, Y. (2022). Modern GLU Variants. ICLR.
\bibitem{sitzmann2020implicit} Sitzmann, V. (2020). Implicit Neural Reps. NeurIPS.
\end{thebibliography}

\end{document}