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add cmpl stuff and structure image

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@ -122,11 +122,17 @@ The quantity and quality of the obtained labels is crucial and they have an sign
This means improving the pseudo-label framework as much as possible is important. This means improving the pseudo-label framework as much as possible is important.
\subsection{Math of FixMatch}\label{subsec:math-of-fixmatch} \subsection{Math of FixMatch}\label{subsec:math-of-fixmatch}
$\mathcal{L}_u$ defines the loss-function that trains the model. The equation~\ref{eq:fixmatch} defines the loss-function that trains the model.
The sum over a batch size $B_u$ takes the average loss of this batch and should be straight forward. The sum over a batch size $B_u$ takes the average loss of this batch and should be straight forward.
The input data is augmented in two different ways. The input data is augmented in two different ways.
At first there is a weak augmentation $\mathcal{T}_{\text{weak}}(\cdot)$ which only applies basic transformation such as filtering and bluring. At first there is a weak augmentation $\mathcal{T}_{\text{weak}}(\cdot)$ which only applies basic transformation such as filtering and bluring.
Moreover, there is the strong augmentation $\mathcal{T}_{\text{strong}}(\cdot)$ which does cropouts and edge-detections. Moreover, there is the strong augmentation $\mathcal{T}_{\text{strong}}(\cdot)$ which does cropouts and edge-detections.
\begin{equation}
\label{eq:fixmatch}
\mathcal{L}_u = \frac{1}{B_u} \sum_{i=1}^{B_u} \mathbbm{1}(\max(p_i) \geq \tau) \mathcal{H}(\hat{y}_i,F(\mathcal{T}_{\text{strong}}(u_i)))
\end{equation}
The interesting part is the indicator function $\mathbbm{1}(\cdot)$ which applies a principle called `confidence-based masking`. The interesting part is the indicator function $\mathbbm{1}(\cdot)$ which applies a principle called `confidence-based masking`.
It retains a label only if its largest probability is above a threshold $\tau$. It retains a label only if its largest probability is above a threshold $\tau$.
Where $p_i \coloneqq F(\mathcal{T}_{\text{weak}}(u_i))$ is a model evaluation with a weakly augmented input. Where $p_i \coloneqq F(\mathcal{T}_{\text{weak}}(u_i))$ is a model evaluation with a weakly augmented input.
@ -135,15 +141,18 @@ $\hat{y}_i$, the obtained pseudo-label and $F(\mathcal{T}_{\text{strong}}(u_i))$
The indicator function evaluates in $0$ if the pseudo prediction is not confident and the current loss evaluation will be dropped. The indicator function evaluates in $0$ if the pseudo prediction is not confident and the current loss evaluation will be dropped.
Otherwise it will be kept and trains the model further. Otherwise it will be kept and trains the model further.
\begin{equation}
\label{eq:equation2}
\mathcal{L}_u = \frac{1}{B_u} \sum_{i=1}^{B_u} \mathbbm{1}(\max(p_i) \geq \tau) \mathcal{H}(\hat{y}_i,F(\mathcal{T}_{\text{strong}}(u_i)))
\end{equation}
\section{Cross-Model Pseudo-Labeling} \section{Cross-Model Pseudo-Labeling}
todo write stuff \cite{Xu_2022_CVPR} The newly invented approach of this paper is called Cross-Model Pseudo-Labeling (CMPL).\cite{Xu_2022_CVPR}
In Figure~\ref{fig:cmpl-structure} one can see its structure.
\section{Math}\label{sec:math} \begin{figure}[h]
\centering
\includegraphics[width=\linewidth]{../presentation/rsc/structure}
\caption{Model structures of Cross-Model Pseudo-Labeling}
\label{fig:cmpl-structure}
\end{figure}
\subsection{Math of CMPL}\label{subsec:math}
\begin{equation} \begin{equation}
\label{eq:equation} \label{eq:equation}
\mathcal{L}_u = \frac{1}{B_u} \sum_{i=1}^{B_u} \mathbbm{1}(\max(p_i) \geq \tau) \mathcal{H}(\hat{y}_i,F(\mathcal{T}_{\text{strong}}(u_i))) \mathcal{L}_u = \frac{1}{B_u} \sum_{i=1}^{B_u} \mathbbm{1}(\max(p_i) \geq \tau) \mathcal{H}(\hat{y}_i,F(\mathcal{T}_{\text{strong}}(u_i)))