diff --git a/summary/main.tex b/summary/main.tex index d978f4c..6dffcd2 100644 --- a/summary/main.tex +++ b/summary/main.tex @@ -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)))