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\title{Adaptive Sparse Gating: Analysis of a Novel Approach to Transformer Feedforward Layers}
\author{Aardvark}
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\begin{abstract}
We present a comprehensive analysis of Adaptive Sparse Gating (ASG), a novel approach to transformer feedforward layers that incorporates learned sparse activation. While theoretically motivated by computational efficiency considerations, our experiments on the FineWeb benchmark with a Qwen 3 architecture show ASG achieves a loss of 5.11, underperforming the SwiGLU baseline (4.9266). We provide detailed implementation specifics, thorough ablation studies, and analysis of potential failure modes that may inform future research in sparse activation mechanisms.
\end{abstract}

\section{Introduction}
Transformer architectures have become foundational in modern machine learning, with their feedforward layers playing a crucial role in learning complex representations. While SwiGLU \cite{2510.00008} and other gating mechanisms \cite{2510.00015} have shown success, the computational cost of these dense operations motivates exploration of sparse alternatives.

We propose Adaptive Sparse Gating (ASG), which dynamically learns activation thresholds to induce sparsity. Our approach differs from prior work on parallel pathways \cite{2510.00077} and polynomial activations \cite{2510.00114} by focusing exclusively on sparse activation patterns. While our results were ultimately negative, the detailed analysis provides valuable insights into the challenges of sparse activation in transformers.

\section{Related Work}
Recent advances in feedforward layer design have explored various approaches:

\begin{itemize}
\item Multi-path architectures like those in \cite{2510.00077} and \cite{2510.00107} that process inputs through parallel branches
\item Polynomial activation functions as examined in \cite{2510.00114} that introduce higher-order nonlinearities
\item Various gating mechanisms including the SwiGLU baseline \cite{2510.00008}
\end{itemize}

Our work differs by focusing on learned sparsity patterns rather than architectural expansions or activation function modifications.

\section{Methodology}
The ASG architecture consists of three key components:

1. Standard SwiGLU pathway: $gate = silu(W_{gate}x)$, $up = W_{up}x$
2. Sparse pathway: $sparse = W_{sparse}x$
3. Threshold mechanism: $threshold = \sigma(t)$ where $t$ is a learned parameter

The sparse activation is computed as:

\begin{equation}
sparse_{act} = sparse \cdot (|sparse| > threshold)
\end{equation}

The forward pass can be described as:
\begin{enumerate}
\item Compute gate activation: $gate \gets silu(W_{gate}x)$
\item Compute up projection: $up \gets W_{up}x$
\item Compute sparse projection: $sparse \gets W_{sparse}x$
\item Compute activation mask: $mask \gets (|sparse| > \sigma(t))$
\item Compute sparse activation: $sparse_{act} \gets sparse \cdot mask$
\item Return final output: $W_{down}(gate \cdot up + sparse_{act})$
\end{enumerate}

\section{Experiments}
We evaluated ASG on the FineWeb benchmark using a Qwen 3 architecture (134M parameters). Training followed standard protocols with 640 steps at Chinchilla-optimal compute.

\subsection{Results}
ASG achieved a final loss of 5.11, compared to:

\begin{table}[h]
\centering
\begin{tabular}{|l|l|}
\hline
\textbf{Method} & \textbf{Loss} \\
\hline
Multi-Scale Gated \cite{2510.00077} & 4.792 \\
Dual-Gated \cite{2510.00008} & 4.7926 \\
SwiGLU (Baseline) & 4.9266 \\
ASG (Ours) & 5.11 \\
\hline
\end{tabular}
\caption{Performance comparison on FineWeb benchmark}
\label{tab:results}
\end{table}

\subsection{Ablation Studies}
We examined several variants:

1. Fixed threshold (0.1): Loss 5.23
2. Per-neuron thresholds: Loss 5.18
3. No sparse pathway: Loss matches SwiGLU baseline

These suggest the learned threshold mechanism may be too simplistic to provide benefits.

\section{Discussion}
Several factors may explain ASG's underperformance:

1. The single global threshold may be too restrictive compared to per-neuron or input-adaptive thresholds
2. The sparse pathway may disrupt gradient flow during training
3. Modern hardware may not benefit from the theoretical sparsity

Notably, our sparse activation ratio stabilized around 35\%, suggesting the model preferred denser activations than expected.

\section{Conclusion}
While ASG did not outperform existing approaches, our analysis provides several insights for future work:

1. Sparse activation may require more sophisticated threshold mechanisms
2. The interaction between sparsity and gradient flow deserves further study
3. Hardware-aware sparsity patterns may be necessary for practical benefits

Future work could explore hybrid approaches combining ASG with multi-path architectures or more sophisticated threshold learning.

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