update.

section2/section2.tex

@@ -24,7 +24,12 @@ Let $\mathcal{S}_{\mathrm{pre}}$ denote the pre-training corpus, where each samp
 \begin{eqnarray}
 \begin{eqnarray}
 \hat{\theta} & = & \argmax_{\theta} \sum_{\mathbf{z} \in \mathcal{S}_{\mathrm{pre}}} \sum_{i=1}^{N} \log \mathrm{Pr}_{\theta}(z_i|\mathbf{z}_{<i})
 \hat{\theta} & = & \argmax_{\theta} \sum_{\mathbf{z} \in \mathcal{S}_{\mathrm{pre}}} \sum_{i=1}^{N} \log \mathrm{Pr}_{\theta}(z_i|\mathbf{z}_{<i})
 \end{eqnarray}
 \end{eqnarray}
-where $\hat{\theta}$ denotes the optimized pre-trained parameters. Equivalently, this objective can be viewed as minimizing the cross-entropy loss between the observed next token and the model-predicted distribution. After this stage, the LLM can generate fluent text and encode rich linguistic and factual knowledge. However, the pre-training objective itself does not explicitly teach the model how to follow user instructions, satisfy task-specific formats, or align with human preferences. Therefore, additional adaptation is typically needed before deploying the model for real applications.
+where $\hat{\theta}$ denotes the optimized pre-trained parameters. Equivalently, this objective can be viewed as minimizing the cross-entropy loss between the observed next token and the model-predicted distribution. 
+
+% 一旦我们预训练完成，我们可以使用这个模型进行语言建模，但是其他的task很难进行完成（这里可以加一段描述一下pre-training LLM 并不擅长处理任务，仅仅只擅长进行language modeling）
+
+
+After this stage, the LLM can generate fluent text and encode rich linguistic and factual knowledge. However, the pre-training objective itself does not explicitly teach the model how to follow user instructions, satisfy task-specific formats, or align with human preferences. Therefore, additional adaptation is typically needed before deploying the model for real applications.
 
 
 \subsubsection{Prompting}
 \subsubsection{Prompting}