add cmpl stuff and structure image

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lukas-heiligenbrunner 2023-05-19 18:18:57 +02:00
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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.
\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 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.
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`.
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.
@ -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.
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}
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}
\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)))