correct eq numbering, add impl of resent50

implementation.typ

@@ -1,4 +1,89 @@
+#import "@preview/fletcher:0.5.3" as fletcher: diagram, node, edge
+#import fletcher.shapes: rect, diamond
+#import "utils.typ": todo
+
 = Implementation
+The three methods described (ResNet50, CAML, P>M>F) were implemented in a Jupyter notebook and compared to each other.
+
+== Experiments
+For all of the three methods we test the following use-cases:#todo[maybe write more to each test]
+- Detection of anomaly class (1,3,5 shots)
+- Inbalanced target class prediction (5,10,15,30 good shots, 5 bad shots)
+- 2 Way classification (1,3,5 shots)
+- Inbalanced 2 Way classification (5,10,15,30 good shots, 5 bad shots)
+- Detect only anomaly classes (1,3,5 shots)
+
+Those experiments were conducted on the MVTEC AD dataset on the bottle and cable classes.
+
+== ResNet50
+=== Approach
+The simplest approach is to use a pre-trained ResNet50 model as a feature extractor.
+From both the support and query set the features are extracted to get a downprojected representation of the images.
+The support set embeddings are compared to the query set embeddings.
+To predict the class of a query the class with the smallest distance to the support embedding is chosen.
+If there are more than one support embedding within the same class the mean of those embeddings is used (class center).
+This approach is similar to a prototypical network @snell2017prototypicalnetworksfewshotlearning.
+
+In this bachelor thesis a pre-trained ResNet50 (IMAGENET1K_V2) pytorch model was used.
+It is pretrained on the imagenet dataset and has 50 residual layers.
+
+To get the embeddings the last layer of the model was removed and the output of the second last layer was used as embedding output.
+In the following diagram the ResNet50 architecture is visualized and the cut-point is marked.
+
+#diagram(
+  spacing: (5mm, 5mm),
+  node-stroke: 1pt,
+  node-fill: eastern,
+  edge-stroke: 1pt,
+
+  // Input
+  node((1, 1), "Input", shape: rect, width: 30mm, height: 10mm, name: <input>),
+
+  // Conv1
+  node((1, 0), "Conv1\n7x7, 64", shape: rect, width: 30mm, height: 15mm, name: <conv1>),
+  edge(<input>, <conv1>, "->"),
+
+  // MaxPool
+  node((1, -1), "MaxPool\n3x3", shape: rect, width: 30mm, height: 15mm, name: <maxpool>),
+  edge(<conv1>, <maxpool>, "->"),
+
+  // Residual Blocks
+  node((3, -1), "Residual Block 1\n3x [64, 64, 256]", shape: rect, width: 40mm, height: 15mm, name: <res1>),
+  edge(<maxpool>, <res1>, "->"),
+
+  node((3, 0), "Residual Block 2\n4x [128, 128, 512]", shape: rect, width: 40mm, height: 15mm, name: <res2>),
+  edge(<res1>, <res2>, "->"),
+
+  node((3, 1), "Residual Block 3\n6x [256, 256, 1024]", shape: rect, width: 40mm, height: 15mm, name: <res3>),
+  edge(<res2>, <res3>, "->"),
+
+  node((3, 2), "Residual Block 4\n3x [512, 512, 2048]", shape: rect, width: 40mm, height: 15mm, name: <res4>),
+  edge(<res3>, <res4>, "->"),
+
+  // Cutting Line
+  edge(<res4>, <avgpool>, marks: "..|..>", stroke: 1pt, label: "Cut here", label-pos: 0.5, label-side: left),
+
+  // AvgPool + FC
+  node((7, 2), "AvgPool\n1x1", shape: rect, width: 30mm, height: 10mm, name: <avgpool>),
+  //edge(<res4>, <avgpool>, "->"),
+
+  node((7, 1), "Fully Connected\n1000 classes", shape: rect, width: 40mm, height: 10mm, name: <fc>),
+  edge(<avgpool>, <fc>, "->"),
+
+  // Output
+  node((7, 0), "Output", shape: rect, width: 30mm, height: 10mm, name: <output>),
+  edge(<fc>, <output>, "->")
+)
+
+After creating the embeddings for the support and query set the euclidean distance is calculated.
+The class with the smallest distance is chosen as the predicted class.
+
+=== Results
+
+
+== CAML
+
+== P>M>F
 
 == Experiment Setup
 % todo

main.typ

@@ -3,6 +3,7 @@
 #import "utils.typ": inwriting, draft, todo, flex-caption, flex-caption-styles
 #import "glossary.typ": glossary
 #import "@preview/glossarium:0.2.6": make-glossary, print-glossary, gls, glspl
+#import "@preview/equate:0.2.1": equate
 
 #show: make-glossary
 #show: flex-caption-styles
@@ -72,9 +73,12 @@ To everyone who contributed to this thesis, directly or indirectly, I offer my h
 )
 
 // set equation and heading numbering
-#set math.equation(numbering: "(1)")
+#show: equate.with(breakable: true, sub-numbering: true)
+#set math.equation(numbering: "(1.1)")
 #set heading(numbering: "1.1")
 
+// Allow references to a line of the equation.
+//#show ref: equate
 
 // Set font size
 #show heading.where(level: 3): set text(size: 1.05em)

materialandmethods.typ

@@ -1,5 +1,6 @@
 #import "@preview/subpar:0.1.1"
 #import "utils.typ": todo
+#import "@preview/equate:0.2.1": equate
 
 = Material and Methods
 
@@ -283,17 +284,16 @@ The softmax function has high similarities with the Boltzmann distribution and w
 === Cross Entropy Loss
 #todo[Maybe remove this section]
 Cross Entropy Loss is a well established loss function in machine learning.
-@crel #cite(<crossentropy>) shows the formal general definition of the Cross Entropy Loss.
-And @crel is the special case of the general Cross Entropy Loss for binary classification tasks.
+@crelformal #cite(<crossentropy>) shows the formal general definition of the Cross Entropy Loss.
+And @crelbinary is the special case of the general Cross Entropy Loss for binary classification tasks.
 
 $
-H(p,q) &= -sum_(x in cal(X)) p(x) log q(x)\
-H(p,q) &= -(p log(q) + (1-p) log(1-q))\
-cal(L)(p,q) &= -1/N sum_(i=1)^(cal(B)) (p_i log(q_i) + (1-p_i) log(1-q_i))
+H(p,q) &= -sum_(x in cal(X)) p(x) log q(x) #<crelformal>\
+H(p,q) &= -(p log(q) + (1-p) log(1-q)) #<crelbinary>\
+cal(L)(p,q) &= -1/N sum_(i=1)^(cal(B)) (p_i log(q_i) + (1-p_i) log(1-q_i)) #<crelbatched>
 $ <crel>
-#todo[Check how multiline equation refs work]
 
-Equation~$cal(L)(p,q)$ @crel #cite(<handsonaiI>) is the Binary Cross Entropy Loss for a batch of size $cal(B)$ and used for model training in this Practical Work.
+Equation~$cal(L)(p,q)$ @crelbatched #cite(<handsonaiI>) is the Binary Cross Entropy Loss for a batch of size $cal(B)$ and used for model training in this Practical Work.
 
 === Cosine Similarity
 To measure the distance between two vectors some common distance measures are used.

sources.bib

@@ -118,3 +118,12 @@
       primaryClass={cs.LG},
       url={https://arxiv.org/abs/2310.10971},
 }
+
+
+@misc{handsonaiI,
+    author        = {Andreas Schörgenhumer, Bernhard Schäfl, Michael Widrich},
+    title         = {Lecture notes in Hands On AI I, Unit 4 \& 5},
+    month         = {October},
+    year          = {2021},
+    publisher={Johannes Kepler Universität Linz}
+}