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