Fix typos <noupdate>

src/year2/machine-learning-for-computer-vision/sections/_generative_models.tex

@@ -291,7 +291,7 @@
         Given:
         \begin{itemize}
             \item A generator $G(z; \theta)$ that takes as input a latent vector $z_i \sim p_\text{lat}(z)$ and produces an image $\hat{x}_j \sim p_\text{gen}(x)$,
-            \item A discriminator $D(x; \phi)$ that determines whether $x_i$ is a real image from $p_\text{real}(x)$.
+            \item A discriminator $D(x_i; \phi)$ that determines whether $x_i$ is a real image from $p_\text{real}(x)$.
         \end{itemize}
         A generative adversarial network trains both $D$ and $G$ with the aim of making $p_\text{gen}$ converge to $p_\text{real}$.
 
@@ -488,7 +488,7 @@
                     \item[Layer fade-in] 
                         When moving from an $n \times n$ to $2n \times 2n$ resolution, the following happens:
                         \begin{itemize}
-                            \item The generator outputs a linear combination between the $n \times n$ image up-sampled (with weight $1-\alpha$) and the $n \times n$ image passed through a transpose convolution (with weight $\alpha$).
+                            \item The generator outputs a linear combination between the $n \times n$ image up-sampled (with weight $1-\alpha$) and the $n \times n$ image passed through a transposed convolution (with weight $\alpha$).
                             \item The discriminator uses a linear combination between the $2n \times 2n$ image down-sampled (with weight $1-\alpha$) and the $2n \times 2n$ image passed through a convolution.
                         \end{itemize}
                         Where $\alpha$ grows linearly from 0 to 1 during training. This allows the network to use old information when the resolution changes and gradually adapt.

src/year2/machine-learning-for-computer-vision/sections/_metric_learning.tex

@@ -245,7 +245,7 @@
 \end{remark}
 
 \begin{remark}
-    With normalized embeddings, classification with softmax as pre-training objective becomes more reasonable. The advantage with softmax is that it does not require sampling informative negative examples. However, as is, it is unable to identify well separated cluster.
+    With normalized embeddings, classification with softmax as pre-training objective becomes more reasonable. The advantage with softmax is that it does not require sampling informative negative examples. However, as is, it is unable to identify well separated clusters.
 \end{remark}
 
 \begin{remark}[Recall: linear classifiers]