From 8d76a7fef4468cf4d1b73236f42bec1fabc54903 Mon Sep 17 00:00:00 2001
From: lukas-heiligenbrunner <lukas.heiligenbrunner@gmail.com>
Date: Fri, 19 May 2023 18:18:57 +0200
Subject: [PATCH] add cmpl stuff and structure image

---
 summary/main.tex | 25 +++++++++++++++++--------
 1 file changed, 17 insertions(+), 8 deletions(-)

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)))