To illustrate the left-to-right generation process, consider generating the three tokens $b$, $c$, and $d$ given an initial prefix $\langle s \rangle a$. In each step, the language model picks a token $x_i$ from the vocabulary $V$ to maximize the conditional probability $\Pr(x_i|x_0,...,x_{i-1})$, appending it to the end of the context sequence.

• Step 1: Given the context $\langle s \rangle a$, the model predicts $b$ using the decision rule $\arg\max_{x_2 \in V} \Pr(x_2|\langle s \rangle a)$. The overall sequence probability becomes $\Pr(\langle s \rangle) \cdot \Pr(a|\langle s \rangle) \cdot \Pr(b|\langle s \rangle a)$.
• Step 2: With the new context $\langle s \rangle a b$, the model predicts $c$ using $\arg\max_{x_3 \in V} \Pr(x_3|\langle s \rangle a b)$, updating the sequence probability by multiplying it by $\Pr(c|\langle s \rangle a b)$.
• Step 3: Based on the expanded context $\langle s \rangle a b c$, the model predicts $d$ using $\arg\max_{x_4 \in V} \Pr(x_4|\langle s \rangle a b c)$, again updating the total sequence probability by multiplying it by $\Pr(d|\langle s \rangle a b c)$.

This demonstrates how each predicted token is iteratively added to the context to inform the next prediction.