Fix typos <noupdate>

src/year2/natural-language-processing/sections/_llm.tex

@@ -100,7 +100,7 @@
                     \item Higher temperatures (i.e., $\tau > 1$) allow for considering low-probability words.
                     \item Lower temperatures (i.e., $\tau \in (0, 1]$) focus on high-probability words.
                     \begin{remark}
-                        A temperature of $\tau = 0$ corresponds to greedy decoding.
+                        For $\tau \rightarrow 0$, generation becomes closer to greedy decoding.
                     \end{remark}
                 \end{itemize}
 
@@ -175,7 +175,7 @@
                         Add a new trainable head on top of the model.
 
                     \item[Parameter-efficient fine-tuning (PEFT)] \marginnote{Parameter-efficient fine-tuning (PEFT)}
-                        Continue training a selected subset of parameters (e.g., LoRA \Cref{sec:lora}).
+                        Continue training a selected subset of parameters (e.g., LoRA in \Cref{sec:lora}).
                 \end{description}
 
             \item[Supervised fine-tuning] \marginnote{Supervised fine-tuning}

src/year2/natural-language-processing/sections/_llm_usage.tex

@@ -12,7 +12,7 @@
 
 \begin{description}
     \item[Instruction tuning] \marginnote{Instruction tuning}
-        Fine-tune a model on a dataset containing various tasks expressed in natural language in the form $(\text{description}, \text{examples}, \text{solution})$, all possibly formatted using multiple templates.
+        Fine-tune a model on a dataset containing various tasks expressed in natural language in the form $(\text{description}, \text{examples}, \text{solution})$, all usually formatted using multiple templates.
 
         \begin{figure}[H]
             \centering
@@ -61,7 +61,7 @@
 
             \item Fine-tune the language model (i.e., train the policy) using an RL algorithm (e.g., PPO) and the learned reward model. 
 
-            Given a prompt $x$ and an answer $y$, the reward $r$ used for the RL update is computed as:
+            Given a prompt $x$ and an answer $y$, the reward $r$ used for RL update is computed as:
             \[ r = r_\theta(y \mid x) - \lambda_\text{KL} D_\text{KL}(\pi_{\text{PPO}}(y \mid x) \Vert \pi_{\text{base}}(y \mid x)) \]
             where:
             \begin{itemize}

src/year2/natural-language-processing/sections/_rag.tex

@@ -159,7 +159,7 @@
         \begin{description}
             \item[Mean average precision] \marginnote{Mean average precision}
                 Average AP over different queries $Q$:
-                \[ \texttt{MAP}_t = \frac{1}{|Q|} \sum_{q \in Q} \texttt{AP}_t(q) \]
+                \[ \texttt{mAP}_t = \frac{1}{|Q|} \sum_{q \in Q} \texttt{AP}_t(q) \]
         \end{description}
 \end{description}
 
@@ -267,10 +267,10 @@
 
     \item[Mean reciprocal rank] \marginnote{Mean reciprocal rank}
         Given a system that provides a ranked list of answers to a question $q_i$, the reciprocal rank for $q_i$ is:
-        \[ \frac{1}{\texttt{rank}_i} \]
+        \[ \texttt{RR} = \frac{1}{\texttt{rank}_i} \]
         where $\texttt{rank}_i$ is the index of the first correct answer in the provided ranked list.
         Mean reciprocal rank is computed over a set of queries $Q$:
-        \[ \texttt{MRR} = \frac{1}{|Q|} \sum_{i=1}^{|Q|} \frac{1}{\texttt{rank}_i} \]
+        \[ \texttt{mRR} = \frac{1}{|Q|} \sum_{i=1}^{|Q|} \frac{1}{\texttt{rank}_i} \]
 
 \end{description}
 
@@ -312,7 +312,7 @@
 \end{description}
 
 \begin{remark}
-    The current trend is to evaluate RAG performances with another LLM.
+    The current trend is to evaluate RAG performance with another LLM.
 \end{remark}
 
 \begin{remark}