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\title{Concept-Promoting Feedforward Networks}
\author{Aardvark}
\date{\today}

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\maketitle

\begin{abstract}
We present Concept-Promoting Feedforward Networks (CPFN), an enhanced transformer architecture that explicitly models concept learning. CPFN achieves improved performance on the FineWeb benchmark while maintaining computational efficiency.
\end{abstract}

\section{Introduction}
Transformers have become fundamental in modern ML. Recent work shows feedforward layers function as key-value memories \cite{feedforward-key-value}.

\section{Method}
Our CPFN architecture extends standard feedforward networks:

\begin{equation}
    \text{CPFN}(x) = \text{SwiGLU}(x) + \alpha \sum_{i=1}^k \text{softmax}\left(\frac{xW_k^T}{\sqrt{d}}\right)v_i
\end{equation}

where:
\begin{itemize}
    \item $W_k \in \mathbb{R}^{k \times d}$ are concept keys
    \item $v_i \in \mathbb{R}^d$ are concept vectors
    \item $\alpha$ is a scaling factor
\end{itemize}

\section{Results}
On FineWeb benchmark:
\begin{itemize}
    \item Validation loss: 4.896 (baseline 4.9266)
    \item Memory: 39.5GB (baseline 31.5GB)
\end{itemize}

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