fix some todos and spelling errors

materialandmethods.typ

@@ -18,7 +18,7 @@ Each category comprises a set of defect-free training images and a test set of i
 
 In this bachelor thesis only two categories are used. The categories are "Bottle" and "Cable".
 
-The bottle category contains 3 different defect classes: 'broken_large', 'broken_small' and 'contamination'.
+The bottle category contains 3 different defect classes: _broken_large_, _broken_small_ and _contamination_.
 #subpar.grid(
   figure(image("rsc/mvtec/bottle/broken_large_example.png"), caption: [
     Broken large defect
@@ -34,8 +34,8 @@ The bottle category contains 3 different defect classes: 'broken_large', 'broken
   label: <full>,
 )
 
-Whereas cable has a lot more defect classes: 'bent_wire', 'cable_swap', 'combined', 'cut_inner_insulation',
-'cut_outer_insulation', 'missing_cable', 'missing_wire', 'poke_insulation'.
+Whereas cable has a lot more defect classes: _bent_wire_, _cable_swap_, _combined_, _cut_inner_insulation_,
+_cut_outer_insulation_, _missing_cable_, _missing_wire_, _poke_insulation_.
 So many more defect classes are already an indication that a classification task might be more difficult for the cable category.
 
 #subpar.grid(
@@ -72,31 +72,33 @@ So many more defect classes are already an indication that a classification task
 
 === Few-Shot Learning
 Few-Shot learning is a subfield of machine-learning which aims to train a classification-model with just a few or no samples at all.
-In contrast to traditional supervised learning where a huge amount of labeled data is required is to generalize well to unseen data.
-So the model is prone to overfitting to the few training samples.#cite(<parnami2022learningexamplessummaryapproaches>)
+In contrast to traditional supervised learning, where a huge amount of labeled data is required to generalize well to unseen data,
+here we only have 1-10 samples per class (so called shots).
+So the model is prone to overfitting to the few training samples and this means they should represent the whole sample distribution as good as possible.~#cite(<parnami2022learningexamplessummaryapproaches>)
 
 Typically a few-shot leaning task consists of a support and query set.
 Where the support-set contains the training data and the query set the evaluation data for real world evaluation.
 A common way to format a few-shot leaning problem is using n-way k-shot notation.
-For Example 3 target classeas and 5 samples per class for training might be a 3-way 5-shot few-shot classification problem.#cite(<snell2017prototypicalnetworksfewshotlearning>)#cite(<patchcorepaper>)
+For Example 3 target classes and 5 samples per class for training might be a 3-way 5-shot few-shot classification problem.~@snell2017prototypicalnetworksfewshotlearning @patchcorepaper
 
 A classical example of how such a model might work is a prototypical network.
-These models learn a representation of each class and classify new examples based on proximity to these representations in an embedding space.#cite(<snell2017prototypicalnetworksfewshotlearning>)
+These models learn a representation of each class in a reduced dimensionality and classify new examples based on proximity to these representations in an embedding space.~@snell2017prototypicalnetworksfewshotlearning
 
 #figure(
   image("rsc/prototype_fewshot_v3.png", width: 60%),
-  caption: [Prototypical network for few-shots. #cite(<snell2017prototypicalnetworksfewshotlearning>)],
+  caption: [Prototypical network for 3-ways and 5-shots. #cite(<snell2017prototypicalnetworksfewshotlearning>)],
 ) <prototypefewshot>
 
-The first and easiest method of this bachelor thesis uses a simple ResNet to calucalte those embeddings and is basically a simple prototypical network.
-See @resnet50impl.~#cite(<chowdhury2021fewshotimageclassificationjust>)
+The first and easiest method of this bachelor thesis uses a simple ResNet50 to calucalte those embeddings and clusters the shots together by calculating the class center.
+This is basically a simple prototypical network.
+See @resnet50impl.~@chowdhury2021fewshotimageclassificationjust
 
 === Generalisation from few samples
 
 An especially hard task is to generalize from such few samples.
 In typical supervised learning the model sees thousands or millions of samples of the corresponding domain during learning.
 This helps the model to learn the underlying patterns and to generalize well to unseen data.
-In few-shot learning the model has to generalize from just a few samples.
+In few-shot learning the model has to generalize from just a few samples.#todo[Source?]#todo[Write more about. eg. class distributions]
 
 === Softmax
 #todo[Maybe remove this section]