Training Objective for Multi-Round Dialogue Models

Consider a dialogue model engaged in a three-turn conversation, represented by the sequence {x_1, y_1, x_2, y_2, x_3, y_3}, where x_k is the user's input and y_k is the model's response at turn k. When the model calculates the probability of generating the third response (y_3), how does the set of information it conditions on relate to the set of information used to calculate the probability of the second response (y_2)?

Formulating Conditional Probability in Dialogue

Diagnosing Conversational Memory Failure