\documentclass{article}
\usepackage{amsmath}
\title{pdfdiff Test Document}
\author{Test Author}
\date{2024}

\begin{document}
\maketitle

\section{Introduction}

This is the revised version of the test document.
It contains several sentences that will be changed in the modified version.

The quick brown fox jumps over the lazy dog.

\section{Methods}

We used a novel approach to solve the problem.
The algorithm runs in linear time with respect to the input size.
All experiments were conducted on a high-performance compute cluster.
We repeated each trial five times and report the mean.

The loss function is defined as
\begin{equation}
    \mathcal{L} = \sum_{i=1}^{N} \left( y_i - \hat{y}_i \right)^2 + \lambda \|\theta\|^2
\end{equation}
where $y_i$ is the true label and $\hat{y}_i = f(x_i; \theta)$ is the model prediction.

We update parameters using Adam with learning rate $\alpha = 0.001$.

\section{Results}

The results show a significant improvement over the baseline.
Our method achieves an accuracy of 89\% on the test set.
Table~1 summarises the full breakdown by category.

The overall score is computed as
\begin{equation}
    S = \frac{1}{n} \sum_{i=1}^{n} \mathbf{1}[\hat{y}_i = y_i]
\end{equation}

\section{Conclusion}

In conclusion, the proposed method works remarkably well.
Future work will explore applications to larger datasets.

\end{document}
