Fix typos <noupdate>

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

@@ -290,7 +290,7 @@
     \item[Generative adversarial network (GAN)] \marginnote{Generative adversarial network (GAN)}
         Given:
         \begin{itemize}
-            \item A generator $G(z; \theta)$ that takes an input latent vector $z_i \sim p_\text{lat}(z)$ and produces an image $\hat{x}_j \sim p_\text{gen}(x)$,
+            \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 $p_\text{real}(x)$.
         \end{itemize}
         A generative adversarial network trains both $D$ and $G$ with the aim of making $p_\text{gen}$ converge to $p_\text{real}$.

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

@@ -109,16 +109,16 @@
                         \Vert f(x^{(i)}) - f(x^{(j)}) \Vert_2^2 & \text{if $y^{(i, j)} = +1$} \\
                         \max\left\{0, m - \Vert f(x^{(i)}) - f(x^{(j)}) \Vert_2\right\}^2 & \text{if $y^{(i, j)} = 0$} \\
                     \end{cases} \\
-                    &= y^{(i, j)} \Vert f(x^{(i)}) - f(x^{(j)}) \Vert_2^2 + (1-y^{(i, j)}) \max\left\{0, m - \Vert f(x^{(i)}) - f(x^{(j)}) \Vert_2\right\}
+                    &= y^{(i, j)} \Vert f(x^{(i)}) - f(x^{(j)}) \Vert_2^2 + (1-y^{(i, j)}) \max\left\{0, m - \Vert f(x^{(i)}) - f(x^{(j)}) \Vert_2\right\}^2
                 \end{split}
             \]
 
             \begin{remark}
-                A margin $m^+$ can also be added to the positive branch to prevent collapsing all embeddings of the same class to the same point.
+                A margin $m^+$ can also be included to the positive branch to prevent collapsing all embeddings of the same class to the same point.
             \end{remark}
 
             \begin{remark}
-                The negative branch $\max\left\{0, m - \Vert f(x^{(i)}) - f(x^{(j)}) \Vert_2\right\}$ is the hinge loss, which is used in SVM.
+                The negative branch $\max\left\{0, m - \Vert f(x^{(i)}) - f(x^{(j)}) \Vert_2\right\}^2$ is the hinge loss, which is used in SVM.
             \end{remark}
 
             \begin{remark}

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

@@ -202,7 +202,7 @@
     \item[Haar-like features] \marginnote{Haar-like features}
         For face detection, a $24 \times 24$ patch of the image is considered (for now) and the weak classifiers define rectangular filters composed of 2 to 4 subsections applied at fixed positions of the patch.
 
-        Given a patch $x$, a weak learned $\texttt{WL}_j$ classifies it as:
+        Given a patch $x$, a weak learner $\texttt{WL}_j$ classifies it as:
         \[
             \texttt{WL}_j(x) = \begin{cases}
                 1 & \text{if $s_j f_j \geq s_j \rho_j$} \\
@@ -594,7 +594,7 @@
                         Consider $k$ different anchors so that the RPN outputs $k$ objectness scores (overall shape of $2k \times H_L \times W_L$) and $k$ corrections (overall shape of $4k \times H_L \times W_L$) at each pixel.
 
                         \begin{remark}
-                            Virtually, this can be seen as putting together the outputs of $k$ different $1$-anchor RPN (with different anchors).
+                            Virtually, this can be seen as putting together the outputs of $k$ different $1$-anchor RPNs (with different anchors).
                         \end{remark}
                 \end{description}
 

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

@@ -134,7 +134,7 @@
         \begin{description}
             \item[Multi-head self-attention (\texttt{MHSA})] \marginnote{Multi-head self-attention}
                 Given an input $\matr{Y} \in \mathbb{R}^{M \times d_Y}$, a \texttt{MHSA} block parallelly passes it through $h$ different self-attention blocks to obtain the activations $\matr{A}^{(1)}, \dots, \matr{A}^{(h)}$. The output $\matr{A}$ of the block is obtained as a linear projection of the column-wise concatenation of the activations $\matr{A}^{(i)}$:
-                \[ \mathbb{R}^{M \times d_Y} \ni \matr{A} = \left[ A^{(1)} \vert \dots \vert A^{(h)} \right] \matr{W}_O \]
+                \[ \mathbb{R}^{M \times d_Y} \ni \matr{A} = \left[ \matr{A}^{(1)} \vert \dots \vert \matr{A}^{(h)} \right] \matr{W}_O \]
                 where $\matr{W}_O \in \mathbb{R}^{hd_V \times d_Y}$ is the projection matrix.
 
                 \begin{figure}[H]